54 THERMIONIC VACUUM TUBE current to the anode be observed as a function of the temperature of the cathode, the current will at first increase until it reaches a value indicated by Ci (Fig. 18). Any further increase in cathode temperature causes no further increase in the current, and the part CiDi of the curve is obtained. The current given by CiDi is frequently referred to as the " temperature saturation current," and the condition characterized by this lack of increase of current with increase of cathode temperature as temperature saturation. The reason why under these conditions the current does not in- crease along CiCzCz as would be expected from Richardson's equation is because at cathode temperatures greater than that cor- responding to Ci, so many electrons are emitted that the resulting volume density of their charge causes all other emitted electrons to be repelled, and these return to the cathode. The applied voltage EI is then not high enough to draw all the emitted electrons away to the anode. If now the voltage be increased to E 2 the current increases, since more electrons are now drawn away from the supply at the cathode, the full space charge effect being maintained by fewer electrons being compelled to return to the cathode. From Fig. 18 it is seen that with the voltage 2 the cathode must be raised to a minimum temperature corresponding to 2 before the full space charge effect can manifest itself. It is seen, then, that the higher the applied voltage, the higher must be the cathode temperature to obtain the full space charge effect. It is also seen that the part OC of Fig. 18 corresponds to the part AB of Fig. 17, and CD of Fig. 18 to OA of Fig. 17. The saturation current is obtained w^hen the applied voltage is so high that a variation of voltage does not cause any appreciable variation in current, while the condition under which the thermionic tube operates, as a voltage operating device, is characterized by the condition that the cathode temperature is so high that the current does not vary appreciably with variation in cathode temperature. 25. Current-voltage Relation for Infinite Parallel Plates. To get an understanding of the quantitative effect on the current by the space charge of the electrons, it may be well first to consider the ideal and simple case that results when we neglect the com- plicating factors encountered in practice and then consider the modifications introduced by these factors. In deriving the equa- tions for this simple oase, we shall therefore assume that the elec- trodes are infinitely large parallel plates, capable of being main- PHYSICS OF THE THERMIONIC VALVE 55 tained at any desired temperature. Both electrodes will be assumed to be equipotential surfaces. The cathode will be main- tained at a high temperature, the anode remaining cold. It follows from Richardson's theory that the hot plate will emit electrons, the emission being the result of the kinetic energy of the electrons becoming sufficiently high to overcome the surface force that tends to hold the electrons within the cathode. It will be recognized that the energy and distribution of energy of the electrons play an important part in the mechanism of electron emission. A derivation of the relation between current and voltage, which takes into consideration the energy distribution between the electrons, is quite complicated. J. J. Thomson 1 has given the equations resulting from the assumption that the electrons all emerge with one initial velocity. In 1911, C. D. Child 2 gave the full solution, based on the assumption that the initial velocity of emission is zero. Langmuir 3 of the General Electric Company and Schottky 4 also published derivations of the space charge equation and made a careful investigation of some of the phenomena observed in thermionic tubes. We shall now derive Child's equation, making the same assump- tions, and then consider the modifications introduced by a con- sideration of the factors neglected in the simple derivation, and more particularly how these factors contribute to produce the type of current-voltage characteristic generally obtained in prac- tical thermionic tubes. We shall therefore assume that both cathode and anode are equipotential parallel surfaces of infinite extent, and that the electrons emerge from the hot cathode with zero velocity. The cathode C and anode P (Fig. 19) will be sup- posed to be in an enclosure in which a perfect vacuum is main- tained. The degree of vacuum necessary to approximate this per- fection will be discussed in the next chapter. The cathode C can be raised to any desired temperature. Let the anode P be raised to a potential Vi, while the cathode remains grounded. As long as the temperature of C is so low that practi- cally no electrons are emitted, the potential gradient between the 1 J. J. THOMSON, Conduction of Electricity through Gases, 2d Ed., p. 223. 2 C. D. CHILD, Phys. Rev. Vol. 32, p. 498, 1911. 3 1. LANGMUIR, Phys. Rev., (2), Vol. 2, p. 450, 1913. 4 SCHOTTKY, Jahrb. d. Radioaktivitat u. Elektronik, Vol. 12, p. 147, 1915. : LIBRARY THE THERMIONIC VACUUM TUBE AND ITS APPLICATIONS "Ms Qraw-MlBock & 7m PUBLISHERS OF BOOKS Coal Age v Electric Railway Journal Electrical ^rld ^ Engineering News-Record American Machinist v Ingenieria Internacional Engineering S Mining Journal * Po we r Chemical 6 Metallurgical Engineering Electncal Merchandising aiiimiiililiniiiililiiii iiiin|iiiiiiiliiiiiiliniiii 'iinifdiiiiiiiriiiiiiHliiiHiirmHihliiiiiilAniiii THE THERMIONIC VACUUM TUBE AND ITS APPLICATIONS BY H. J. VAN DER BIJL, M.A., Ph.D. M.AmJ.E.E., M.I.R.E., Mem. Am. Phys. Soc., Scientific & Technical Adviser, Dept. of Mines & Industries, Union of South Africa, Late Research Physicist, American Tel. & Tel. Co. and Western Electric Co., New York FIRST EDITION THIRD IMPRESSION McGRAW-HILL BOOK COMPANY, INC, NEW YORK: 370 SEVENTH AVENUE LONDON: 6 & 8 BOUVERIE ST., E. C. 4 1920 Library COPYRIGHT, 1920 BY THE McGRAW-HILL BOOK COMPANY, INC. PREFACE Ix a comparatively short time the applications of Ther- mionics have grown to a considerable extent, and are now not only of great value in engineering fields, but are also penetrating more and more into university and college laboratories. It is difficult for those who are interested in the subject, but who have not had the opportunity or the time to follow its development closely, to abstract from the literature, which has become quite voluminous, the principles of operation of thermionic vacuum tubes. This and the popularity which the remarkable abiHty of these tubes to perform a great variety of functions has gained for them, have created a need for a book describing in a connected manner the more important phenomena exhibited by the passage of electrons through high vacua. In this work I have endeavored to set forth the principles of operation of thermionic vacuum tubes, and to coordinate the phenomena encountered in a study of this field. Such a proced- ure is sure to result in a more valuable book than a detailed descrip- tion without proper coordination of the many investigations that have been published on this subject. I have tried to make the treatment sufficiently elementary to meet the demands that will necessarily be made on a book of this kind. This is especially the case with the first few chapters, which must be regarded as very elementary and are mainly intended for those who are interested in the applications of thermionic tubes but are not sufficiently acquainted with the properties and behavior of electrons to understand the operation of these tubes. I wish to express my indebtedness to several of my colleagues who have read parts or all of the manuscript. In this connection I wish to mention especially Mr. C. A. Richmond and Dr. P. I. Wold. H. J. v. d. B. CONTENTS INTRODUCTION xi CHAPTER I PROPERTIES OF ELECTRONS SECTION PAQB 1. Electron and Corpuscle 1 2. Lines of Force and Tubes of Force 2 3. Field of "Stationary Electron." 4 4. Field of the "Moving Electron" 5 5. Mass of the Electron 6 6. Effect of Electric Field on the Motion of an Electron 9 7. Effect of Magnetic Field on the Motion of an Electron 10 8. The Accelerated Electron. Radiation 13 9. Relation between Space Charge and Potential Distribution 15 CHAPTER II DlSLODGMENT OF ELECTRONS FROM ATOMS OF VAPORS AND GASES. lONIZATION 10. Occurrence of Electrons 16 11. lonization 16 12. Constitution of the Atom 17 13. Radiation from Atoms Caused by Bombardment of Electrons 19 14. lonization Voltage and Convergence Frequency 21 CHAPTER III DlSLODGMENT OF ELECTRONS FROM SOLID SUBSTANCES 15. Free Electrons 23 16. Force that Holds Electrons in Substances 23 17. Contact Electromotive Force 26 18. Measurement of Contact, E.M.F .' 28 19. Elements of Thermionics. 30 20. Influence of Surface Conditions on Electron Affinity 34 21. Photo-electric Effect 38 vii viii CONTENTS SECTION"! PAOE 22. Control of Space Current by Means of an Auxiliary or Third Elec- trode 42 23. Secondary Electron Emission. Delta Rays 47 CHAPTER IV PHYSICS OF THE THERMIONIC VALVE 24. Current-voltage Characteristic of Thermionic Valve 50 25. Current-voltage Relation of Infinite Parallel Plates 54 26. Quantitative Relation for Concentric Cylinders 59 27. Influence of Initial Velocities 61 28. Effect of Voltage Drop in the Filament 64 29. Influence of Limitation of Current by Thermionic Emission 70 30. Effect of Curvature of the Characteristic 73 31. Energy Dissipation at the Anode 75 32. Efficiency of the Cathode 76 33. Life of a Vacuum Tube 84 CHAPTER V INFLUENCE OF GAS ON THE DISCHARGE 34. Volume Effect of Gas. lonization by Collision 86 35. Mean Free Path of Electrons in Gases 88 36. lonization at Low Pressures 90 37. Effects of lonization by Collision 91 38. Influence of lonization. on the Infra-saturation Part of the Charac- teristic 93 39. Effect of Gas on the Electron Emission. Surface Effect 98 40. Influence of Occluded Gases 102 41 . lonization at High Pressures 106 42. Difference between Gas-free Discharge and Arc Discharge 107 CHAPTER VI RECTIFICATION OF CURRENTS BY THE THERMIONIC VALVE 43. Conditions for Rectification 109 44. The Fleming Valve Ill 45. Valve Detector with Auxiliary Anode Battery 112 46. Thermionic Valve as High Power Rectifier 115 47. Optimum Voltage for Rectification 117 48. Types of Thermionic Valves 120 49. Rectification Efficiency 123 50. Production of Constant Source of High Voltage with the Thermionic Valve 132 51. The Thermionic Valve as a Voltage Regulator . 142 CONTENTS ix CHAPTER VII THE THERMIONIC AMPLIFIER SECTION PAGE 52. Action of the Auxiliary Electrode 146 53. Current-voltage Characteristics of the Thermionic Amplifier 150 54. Amplification Constant 160 55. Plate Resistance and Impedance 160 56. Mutual Conductance 165 57. Shape of Output Wave in Circuit of Low External Impedance 166 58. Characteristic of Circuit Containing Tube and Resistance in Series. . 169 59. Static and Dynamic Characteristics 170 60. Conditions for Distortionless Amplification 178 61. Amplification Equations of the Thermionic Amplifier 180 62. Voltage Amplification 181 63. Power Amplification 185 64. Experimental Verification of Amplification Equations. 189 65. Methods of Measuring the Amplification Constant 193 66. Measurement of the Plate Resistance 195 67. Direct Measurement of the Mutual Conductance 199 68. Circuit for Measuring Amplification Constant, Plate Resistance and Mutual Conductance 203 69. Influence of the Electrode Capacities 205 70. Low Frequencies an d therefore the magnetic force produced at the point P by the moving electron is ev sin 6 H It is known from elementary physics that the energy in unit volume of a magnetic field at a point where the magnetic intensity is H is -g-. Hence the energy of the field at the point P is eV sin 2 6 Srrr 4 ' PROPERTIES OF ELECTRONS 7 Integrating this over the whole space from infinity up to a small o o distance a from 0, the total energy of the field is found to be '. 3a Now, the kinetic energy of mass m moving with a velocity v is %mv 2 . If the body has a charge e we have to add to this energy -5, so that the total energy of the system is 6o> (2) and it therefore appears that the mass of the moving charged body 2 e 2 is m' + ^r- instead of only m', the mass of the uncharged body. tjd The second term represents the electromagnetic mass. The quantity a is what we may term the radius of the electron. This, however, does not necessarily mean that the electron is a well- defined sphere of radius a; all it means is that where an electron manifests itself the modification of the ether is such as would exist if a charge e were uniformly distributed over the surface of a sphere of radius equal to a. The quantity a merely represents one of the limits of integration arbitrarily assumed in summing the total magnetic energy in the whole space through which the electron moves. In deriving the above expression for the energy of the moving electron, it was assumed that the field of the moving electron is the same as that of the stationary electron. This is, however, only the case if the electron moves slowly, because when a Faraday tube is moved it tends to set itself at right angles to the direction of motion. The tubes constituting the electron therefore tend to crowd together in a plane perpendicular to the direction of motion of the electron. The result is an increase in the inertia or mass of the electron, because more work must be done to move a Faraday tube parallel to itself than along its own direction, just- as it is harder to move a log of wood in the water parallel to itself than to move it endwise. This increase in the mass of the electron only becomes appreciable when it moves with a speed greater than about one- tenth that of light; for speeds less than this the expression (2) -can be taken to give the mass of the elec- tron to a first approximation, but for higher speeds the deter- mination of the mass becomes more complicated. The mass of 8 THERMIONIC VACUUM TUBE the electron is measured by the ratio of the force to the accelera- tion to which it gives rise. According to the theory of Abraham and Lorentz the electron has two masses: the longitudinal mass, when it is accelerated in the direction of motion, and the trans- verse mass, when it is accelerated perpendicular to the direction of motion of the electron. If m represents the mass of the slow- moving electron, then the longitudinal and transverse masses mi and m,2 are given by m\ _ 1 7^2 _ 1 w where c is the speed of light. It is seen that as the speed of the electron approaches that of light, its electromagnetic mass tends to become infinitely large. The transverse mass of the high- speed electron for various speeds has been determined by Kauf- mann and Bucherer. 1 Their experiments verify the above ex- pression for the transverse mass. From this it would seem that the mass of the electron is entirely electromagnetic. Later developments of the Theory of Relativity have rendered this con- clusion somewhat questionable, so that there does not seem to be definite experimental evidence to indicate that the electronic mass is entirely electromagnetic. 2 On the assumption that the mass is entirely electromagnetic equation (2) would give the following expression for the simple mass of the slow-moving electron. (3) If the known values of e and m are inserted in this expression we find a value for a which is 2X 10~ 13 cm. This effective radius of the slow-moving electron is therefore only about one fifty- thousandth of the radius of the hydrogen atom. 1 W. KAUFMANN, Goott. Nachr. Math.-Phys. Kl., p. 143, 1901; p. 291, 1902, p. 90, 1903. For later experiments of KAUFMANN, Ann. d. Phys., Vol. 19, p. 487, 1906. A. H. BUCHERER, Phys. Zeitschr., Vol. 9, p. 755, 1908. 2 For a discussion of this and allied questions, the reader might refer to H. A. LORENTZ, " The Theory of Electrons " and L. SILBERSTEIN, " The Theory of Relativity." PROPERTIES OF ELECTRONS 9 6. Effect of Electric Field on the Motion of an Electron. To find the effect of an electric field on an electron is a compara- tively simple matter as long as the field is uniform. Suppose we have two infinitely large parallel plates OY and QR (Fig. 3) with a potential difference V between them, and let the electron be projected with a velocity VQ from the point in the direction OQ. On account of the electric field between the plates the velocity of the electron will be con- tinually increased on its way to Q. The kinetic energy of the electron at the moment of its leaving is \mv ...... (7) 2m vo 2 sin 2 This equation gives the point R at which the electron will strike the plate QR when the distance x between the plates and the intensity of the field are known. If the electron starts from in the ctirection OY, < is 90 and equation (7) becomes This equation enables us to calculate the deviation x of an electron from its path by an electric field perpendicular to the original direction of motion of the electron. So far we have assumed that the lines of force between the plates are straight. If this is not the case the motion of the electron is not easily determined. The case in which the electron moves from a straight wire to a plate is one in which the field is not uniform. Such cases are frequently met with in the study of discharge through vacuum tubes, and the problems involved become so difficult that the desired result is often more easily determined empirically. Such is, for example the case with the three-electrode thermionic amplifier. The classification of cases dealing with electric fields that can be represented by straight lines of force and which can be handled mathematically is a purely geometrical matter. Such fields are obtained with the following structures: (a) Both electrodes are infinitely large parallel plates; (b) one electrode is an infinitely long cylinder and the other an infinitely long wire in the axis of the cylinder; (c) both electrodes are infinitely long co-axial cylinders; (d) one electrode is a sphere and the other a Doint in the center of the sphere; (e) both electrodes are concentric spheres. It will be recognized that in all these cases the lines of electric force are straight. 7. Effect of Magnetic Field on the Motion of an Electron. Now, instead of an electric field let us apply a magnetic field to the moving electron. As was shown above an electron moving with a velocity v is equivalent to an electric current i ve. We can therefore directly apply the well-known law connecting the mechanical force F exerted by a magnetic field of intensity H on a current i\ namely, F = nHi, where p is the permeability of the PROPERTIES OF ELECTRONS 11 medium. Since we are considering the motion of an electron through space we can put' /* = 1, so that the force on the electron is F = Hev ......... (9) This force is at every instant at right angles to both the direction of motion of the electron and that of the magnetic field. Thus, referring to Fig. 3, if the electron starts in the direction OX and the magnetic field be perpendicular to the plane of the paper and directed downwards, the electron will be deviated from OX in the direction OY r . Now, when the force acting on a body is always at right angles to its direction of motion the body must describe a circular path, the force being given by do) where r is the radius of curvature. Hence, we get from (9) and (10): mv This equation shows how strong the magnetic field must be to make the electron travel in a circle of any desired radius. Equation (11) expresses an interesting and useful result. We shall mention a few of its applications here. We saw above that a moving electron creates a magnetic field whose lines of force are circles having their centers along the path of the electron. Now consider two electrons moving side by side in the same direc- tion. Obviously the magnetic field produced by each must exert a mechanical force on the other in the sense explained above. A consideration of the directions of these mechanical forces will show that the two moving electrons tend to attract each other. This result is not contrary to the fundamental law of electrostatics that like charges are repellent. The mutual attraction exerted by the electrons is due only to their motion and increases with their velocity. If they moved in opposite directions they would repel each other. It follows from this that an electron stream in a vacuum tube would tend to shrink together if the velocity with which, the electrons move become sufficiently high, the shrinkage increasing with the velocity with which the electrons comprising the stream move. In ordinary cases the velocity of the electrons 12 THERMIONIC VACUUM TUBE in a vacuum tube is so small (of the order of a million centimeters per second) that the shrinkage of the electron stream due to the reduction in the mutual electrostatic repulsion is inappreciable. If the electron source in a vacuum tube is a hot cathode the electrons are emitted from it in all directions : the electron stream will therefore generally spread out as the distance from the cathode increases. This spreading can be prevented by means of a magnetic field applied in a suitable way to the stream. In Fig. 4 let C be the hot cathode, P an anode and A an electrode with an aperture in its center. Let A and P be connected and a poten- tial difference applied between them and the cathode. ' Of the electrons moving away from the cathode some go to A and some shoot through the aperture in A and pass on to P, Between C v Hi V-V FIG. 4. FIG. 5. and A their velocity will be continually increased by the electric field existing between C and A, but after passing A they will continue to move with the same velocity which they had on reaching A, since A and P are at the same potential. If now a magnetic field in the direction AP be applied by means of a coil as shown in the figure, it will be seen, by applying the above laws, that the electrons will travel along a helical path, the diameter of which decreases as the strength of the magnetic field is in- creased. In Fig. 5, H represents the direction of the magnetic field, F the direction of the force on the electron, and S the path of the electron, which is at right angles to F and H. The motion due to the force F } when added to the primary motion in the direction of H, which the electron has when passing through the aperture in A of Fig. 4, results in the electron describing a helical path. If the magnetic field be made sufficiently strong the PROPERTIES OF ELECTRONS 13 diameter of the helix can be made so narrow that the electrons practically travel in a straight line along the axis of the tube. The study of the motion of an electron in a magnetic field has been successfully applied to the determination of the mass of the electron. Referring to equation (8) it is seen that if we know the velocity VQ with .which an electron moves and determine experimentally the extent y to which the electron stream is de- flected by an electric field X whose direction is at right angles to the direction of motion of the electron, we can calculate the Q value of . In order to obtain the velocity all that is necessary wi is to apply a magnetic field in such a way as to counterbalance the deflection of the electron stream caused by the electric field. Then the magnetic force given by equation (9) must be equal to the electric force eX, Hence (12) Millikan has accurately determined the value e of the electronic- p charge. 1 Hence, knowing e and we can obtain the mass m 01 the electron. This value has been found to be 9.01X 10~ 28 grm. 8. The Accelerated Electron. Radiation. We have seen that an electron possesses inertia. 'From this it follows that in order to accelerate an electron work must be done on it and if it is retarded in its motion it must give up part of its kinetic energy. If the inertia of an electron is wholly electromagnetic the work done in accelerating it is work done on lines of force. Suppose a charge with its connecting lines of force moves through space with a uniform velocity. If this charge is suddenly retarded the ends of the lines of force terminating on it will be, so to speak, jerked backwards. In accordance with the properties of lines of force this kink created at the end of the line will not be trans- mitted along the whole line instantaneously but will be propagated along it with a finite velocity the velocity of light. These kinks in the lines are the seat of that part of the energy which the electron gives up when retarded. It can be shown that the electric and magnetic forces associated with a .kinked line are more intense than those associated with a straight line. In 1 R. A. MILLIKAN, " The Electron," University of Chicago Press, 1917. 14 THERMIONIC VACUUM TUBE the latter case the electric force at a distance r from the center > P(* of the electron is -5 electrostatic units, or -^ electromagnetic units, c being the velocity of light, and the magnetic force that given by equation (la). If, however, an electron be retarded the electric and magnetic forces E and H at a point distant r from the center of the electron at the moment the kink passes through that point are : (13) where / is the acceleration and 6 the angle between the r and the direction of motion of the electron. E and H are at right angles to each other and to the direction of propagation of the kink in the line. The energy radiated by the electron is there- fore radiated as electromagnetic energy with the speed of light. 2e 2 / 2 The total amount of energy radiated by the electron is ~ ^-. o c If now such an electromagnetic disturbance passes over an electron moving with uniform velocity the electric and magnetic fields associated with it will be modified by the intense fields in the disturbances and this modification is propagated to the center of the moving electron along the lines of force constituting it. The result is a change in the motion of the electron. It is seen therefore that the energy of a moving electron can be transformed in co radiation energy and vice versa, the transformation always taking place when the electron is retarded or accelerated. This result is an important agency in the production of dislodged elec- trons, that is, electrons in such a state that they can be readily utilized for purposes of discharge in vacuum tubes. An electron which is bound to an atom of a gas or vapor, or to a substance, can be dislodged by passing an electromagnetic disturbance in the form of light or X-rays over it, in which case the energy imparted to the electron may be so great that it can overcome the forces that bind it to the atom or substance. A bound electron can also be dislodged by arresting the motion of a high-speed electron in its neighborhood. In this case the kinetic energy of the moving electron is first transformed into PROPERTIES OF ELECTRONS' 15' energy of radiation, part of which is in turn transferred to the bound electron. 9. Relation between Space Charge and Potential Distribution. In dealing with the conduction of electricity by dislodged electrons or positive ions, it is necessary to consider the effect exerted by their presence on the potential distribution between the electrodes. The difference between the number of electrons and positive ions in unit volume, multiplied by the charge per ion, is usually referred to as the space charge or volume density of electrification. If, in the space between two electrodes, there are no positive ions, and n electrons, and if the charge on the positive ion and the electron be eo and e, then the distribution of potential between the electrodes can be expressed by Mnc-^o), .... (14) where V is the potential at a point having the coordinates x, y and z. This equation is known as Poisson's equation. It has been used extensively in investigations dealing with the conduction of electricity through gases and high vacua. In applying this equation to the case in which the charges are contained between two infinitely large parallel plates, between which a potential difference is applied, the lines of force are straight and everywhere perpendicular to the plates, so that the equipotential surfaces are planes parallel to the plates. The last two terms on the left-hand side of equation (14) therefore vanish and we get d 2 V ..... (15) where p is the volume density of electrification or space charge. If there are no free charges between the plates, or if the total positive 'charge in every volume element is equal to the total dV negative charge, we have ne nQU e = Q, and -7 = constant. We then have the simple case if infinitely large parallel plates at dif- ferent potentials, but with no charges between them, in which the potential at different points is a linear function of the distance x from one plate. For the case of high vacuum tubes in which the current is carried almost exclusively by electrons, no = and = ne. CHAPTER II DISLODGMENT OF ELECTRONS FROM ATOMS OF VAPORS AND GASES. IONIZATION 10. Occurrence of Electrons. In this and the following chapter will be discussed the conditions in which electrons normally exist and the means whereby they can be brought into such a state that they are readily available for discharge in vacuum tubes. Since all charged bodies attract, or are attracted by, oppositely charged or uncharged bodies, it is to be expected that there are comparatively few electrons floating around free in nature. By far the larger number of electrons exist as the building stones of which all matter is built up, and they are held in this condition by very strong forces. These forces are due to the positive elec- trons in the nuclei of the atoms. Such atomic systems, con- sisting of electrons and positive electrons, are electrically neutral and are not affected by an electric field. The fact that the conductivity of a gas or vapor is very small is an indication that there can only be very few electrons in the gas or vapor that are not bound in electrically neutral systems. In the case of con- ducting solids the number of electrons that are free, or that can readily be made free by the application of an electric field, is com- paratively large, so that such solids are said to be good conduc- tors of electricitjr. But such electrons cannot be said to be dis- lodged. They are only available for discharge through conductors and not for discharge between conductors separated by a' gaseous or vacuous medium. For the latter purpose they must be dis- lodged not only from the atoms in the substance but also from the substance itself. 11. lonization. The process of the production of dislodged electrons is known as ionization. In ah 1 cases this process involves overcoming the forces that hold the electrons in the atoms or in the substance. In accordance with the properties of electrons 16 ELECTRONS FROM VAPORS AND GASES 17 described in the preceding chapter it will be evident that this can be done in three ways, viz. : (a) by means of the impact of electrons or positive ions on the atoms or substance; (6) by means of electro- magnetic radiation: (c) by means of heat. The first of these three processes gives rise to the phenomenon of delta rays, or secondary electron emission, the second gives rise to the so-called photoelectric effect, and the third forms the basis of the subject of thermionics. The present chapter will be devoted to a dis- cussion of the phenomena accompanying the dislodgment of electrons from the atoms of vapors and gases, the problems of the dislodgment of electrons from solid substances being reserved for the next chapter. 12. Constitution of the Atom. Although very little is known about the exact nature of the processes going on in an atom when its equilibrium is disturbed, there are nevertheless a certain num- ber of experimentally determined facts giving rise to theories that successfully account for many of the phenomena encountered in the ionization of atoms. There is very little doubt but that the atom consists of a number of electrons grouped around a number of positive electrons. The absolute value of the positive electronic charge is the same as the electron, but its mass is 1845 times as great. The positive electrons in an atom form the atomic nucleus, while the electrons are separated from the nucleus by distances that are large compared with their size. For our present purposes it does not matter how these mutually repellent positive electrons are held together in the nucleus; it is likely that they are held together by electrons so that the nucleus really consists of a group of positive and nega- tive electrons having a resultant positive charge equal to the sum of the electronic charges outside the nucleus. There is reason to believe that the electrons grouped around the positive nucelus revolve in nearly circular orbits round the nucleus. If the elec- trons did not revolve, the force of attraction between them and the nucleus would cause them to drop into the nucleus. On the other hand, it follows from ordinary mechanics that when an elec- tron revolves round a positive nucleus ic must be constantly accelerated and must therefore be constantly radiating energy. In such case a simple system like the hydrogen atom, which con- sists of a single positive and one negative electron, would radiate all of its energy in such a short time that it really could not exist 18 THERMIONIC VACUUM TUBE at all. An attempt to overcome this difficulty has been made by Bohr by making an assumption which frankly repudiates New- tonian mechanics for atomic systems. Bohr assumes that although the electrons revolve round the positive nucleus, it does not radiate any of its energy as long as it remains at the same distance from the nucleus, energy being only radiated or absorbed when this distance is decreased or increased, and this happens only when the distance is changed by definite amounts so that the energy is radiated or absorbed in definite quanta. Bohr's atom has been successful in explaining and predicting a number of phenomena, but although there is an element of truth in it, it is still far from the whole truth. We shall therefore not enter into any further discussion of it. Suffice it to say that the necessity for introducing such assumptions as Bohr's, and the assumption of energy radiation by definite quanta, which was originated by Planck, seems to indicate that in dealing with atomic systems we can apply the Newtonian system of mechanics only when the atoms are in a steady but not in a varying state. Since Newtonian mechanics was built up on an experimental basis of large-scale phenomena, one would not necessarily expect it to give an explana- tion of atomic phenomena. But apart from the question of the behavior of the electrons in the atom, recent experiments have given conclusive evidence that the atom consists of a number of electrons held together in some configuration by a heavy positive nucleus. The total charge of the nucleus is equal to the sum of the charges of the electrons, so that the atom is electrically neutral. The total positive charge, or the number of electrons, determines the chemi- cal nature of the atom. Starting with the lightest known element, hydrogen, all the elements with a few slight deviations are obtained, in the order of their atomic weights, by successively adding one electron and the equivalent positive charge. The process of ionization consists in the detachment of one or more electrons from the atom, thus leaving the atom positively charged. An atom from which one or more electrons have been removed is known as a positive ion. If the atoms of a gas be ionized and a potential difference be applied between two plates immersed in the gas, the positive ions will move, under the in- fluence of the electric field, to the negative plate and the electrons to the positive plate. If the pressure of the gas is not too low ELECTRONS FROM VAPORS AND GASES 19 and the speed of the ions or electrons not too high, the electrons that have been detached from the atoms will attract other neutral atoms and thus form negative ions, and these will move to the positive plate. A negative ion is therefore an atom which has more electrons than are necessary to balance the charge due to the positive nucleus. In order to ionize an atom the forces that hold the electrons to the nucleus must be overcome. These forces depend partly on the distance between the electron and the positive nucleus. Considering the case of an atomic system, consisting of a single positive and one negative electron, the mass of the former being very much larger than that of the latter, the electron can revolve round the positive electron, or escape from it, according as its kinetic energy is smaller or greater than its potential energy, and in the formation of the system a certain amount of work is done by the electrical forces until this equality is attained. This energy of formation therefore gives a measure of the work which must be done to remove the electron from the nucleus, and will be greater the smaller the distance between the electron and the nucleus. Secondly, the work necessary to remove the electron depends on the number of electrons grouped round the nucleus, and on the con- figuration of the system. It can be seen in a general way that if there are a number of electrons grouped, for example, in a ring round the nucleus, the repulsion exerted by the other electrons would make it easier to remove an electron than would be the case of a system consisting of only one electron and one positive electron. Now, the way in which the electrons are grouped depends upon the number of electrons in the atom. If they are grouped in rings the heaviest atom that can have all its electrons in one ring only is that which contains eight electrons, namely, the oxygen atom. Heavier atoms would then have their electrons arranged in two rings, still heavier in three rings, and so on. It can therefore be seen in a general way that it would require a smaller expenditure of energy to detach an electron from an oxygen atom than from an atom of hydrogen. 13. Radiation from Atoms caused by Bombardment of Elec- trons. Let us now look into the process of ionization in greater detail. Suppose we have a tube containing mercury vapor and two electrodes, A and B, one of which is a source of electrons. Let a potential difference be applied between the electrodes so that 20 THERMIONIC VACUUM TUBE the electrons are driven from the one to the other, say, from A to B. On their way these electrons will collide with some of the atoms of the vapor, the velocity with which they collide increasing on their way in virtue of the electric field between the electrodes. If the electrons start with zero velocity from the electrode A, their velocity v after having dropped through a potential difference V is given by Ve = %mv*, where e is the electronic charge. Now, it has been found 1 that as long as the electrons strike the atoms of the vapor with a velocity which is less than that corresponding to a drop through a certain definite voltage, which, in the case of mercury, is about 5 volts, they are reflected from the atoms with- out any loss of energy. The impact is therefore elastic. If, however, the electrons strike the atoms with a velocity greater than this value, they lose part or all of their energy, and at the same time the atom radiates energy in the form of monochromatic light. The frequency v of the light radiated is given by the following relation: Ve = hv ...... .- . (1) where V is the voltage through which the electron has dropped, and h ; s Planck's constant of action. The product hv has the dimenj.,^ o>f energy. The above equation expresses one of the most important relations of modern physics. It was not derived from the impact experiments of Franck and Hertz just men- tioned; these experiments give only one of the experimental verifications of the relation. It was originally deduced by Ein- stein on the basis of Planck's quantum theory of radiation. Ein- stein's equation will be more fully discussed when we come to con- sider the photo-electric effect. The emission of light in the form of monochromatic radiation is due to the electron in the atom not acquiring sufficient energy from the colliding electron to get out of reach of the forces of attraction of the nucleus, and it consequently drops back to its original position, thus giving up the energy, in the form of mono- chromatic radiation, which it has acquired from the colliding electron. The frequency of the light emitted is characteristic of the atom and is referred to as characteristic radiation. All known atoms have a large number of characteristic frequencies. 1 FRANCK AND HERTZ, Verb. d. D. Phys. Ges., Vol. 16, pp. 457 and 512 1914. ELECTRONS FROM VAPORS AND GASES 21 These frequencies form the line spectra observed in the discharge through gases and vapors. The blue glow observed in vacuum tubes that are not well evacuated is due to the impact of electrons on the molecules of the residual gas and is the resultant of a large number of character- istic frequencies emitted when the electrons in the atoms that are displaced by the colliding electrons drop back to their original positions of equilibrium. Whenever the blue glow appears some of the electrons in the atoms are displaced beyond the forces of attrac- tion of the atoms and take part in the current convection through the tube. This process of completely detaching electrons from the atoms by means of colliding electrons is known as ionization by collision. The blue glow in vacuum tubes is therefore always an indication that ionization by collision takes place. As was explained in the first chapter, an electron can also acquire energy from a light wave passing over it. And since the energy in a wave and the energy of an electron are related as shown by equation (1), it follows that a wave of frequency v and produce the same effects explained above that are produced by an electron that has dropped through a voltage F, where F and v are related by equation (1). 14. Ionization Voltage and Convergence Frequency. The least energy with which an electron must collide with an atom in order to completely detach an electron from the atom of any gas or vapor is known as the ionization energy of the gas or vapor. This amount of energy is usually expressed in terms of the voltage through which, the electron drops before it collides with the atom, and is then referred to as the ionization voltage. The ionization voltage is the ionization energy divided by the charge of the elec- tron. When an electron in the atom is displaced to such an extent that the force of attraction of the parent atom just manages to pull it back to its original position within the atom, a character- istic radiation is emitted whose frequency is known as the converg- ence frequency. It is the shortest wave length that can be emitted by the most loosely-bound electrons in the normal atom. Apply- ing equation (1) we can, if we know the convergence frequency, compute the ionization voltage. This relatign is important be- cause it is often easier to obtain the ionization voltage by measur- ing the convergence frequency from observation of the line spectra 22 THERMIONIC VACUUM TUBE of the gas or vapor than by measuring the ionization voltage itself. Direct determinations have been made of the ionization voltage of various gases and vapors, but there is reason to believe that most of the values obtained are not reliable. The following values of the ionization voltage, computed from the convergence frequencies, give an idea of the order of magnitude of this important quantity. Ionization Voltage Substance. Voltg Mercury vapor 10 . 4 Zinc vapor 9 . 24 Magnesium vapor 9.13 Calcium vapor . 9 . 96 Helium 29.00 Hydrogen 13.6 Since an electron can ionize a gas atom after having dropped through the ionization voltage of the gas, it follows that in a vac- uum tube which contains some residual gas, ionization always takes place if the voltage applied between cathode and anode exceeds the ionization voltage. Now, it is impossible completely to remove the last traces of gases and vapors from a vacuum tube. Hence, in thermionic tubes operating on applied voltage greater than those given in the above table some ionization by collision always takes place, although the amount of ionization in well- evacuated tubes may not be large enough to cause an appreciable effect on the operation of the lube. A discharge which is carried entirely by electrons is a pure electron discharge. When the term is applied to the discharge through vacuum tubes, as actually realized in practice, it does not necessarily mean a discharge which is carried entirely by electrons, but one in which the number of positive ions formed by collision ionization is so small as not to have any appreciable influence on the operation of the tube. CHAPTER III DISLODGMENT OF ELECTRONS FROM SOLID SUBSTANCES 15. Free Electrons. If a substance contains electrons that are not bound to atoms to form electrically neutral systems, the sub- stance must be conducting, because if it were placed in an electric field the free electrons would move in the direction of the field and thus establish a current in the substance. In order to account for the conductivity of metallic substances the assumption has been made that metals contain a large number of free electrons. This assumption has been questioned. On the other hand, the fact that a substance conducts electricity indicates that it must enable electrons to pass freely through it under the application of an electric field. It is possible that the conductivity of metals is due to the frequency of collision of the atoms of the metal with each other. When two atoms collide there is a chance that an electron originally belonging to one of the atoms comes so well within the field of force of the other atom that it is attracted with equal forces by both atoms, so that the resultant force on the electron is very small. The electron would therefore be essentially free at that moment and if the metal were placed in an electric field by applying a potential difference between its ends, the electron would move in the direction of the field. This would, of course, leave one of the atoms positively charged, but its loss would immediately be compensated for by electrons coming from the source of potential difference. On account of the frequency of collisions of the atoms in the metal a large number of electrons can thus be set free and made to move along the lines of force of an applied field. In the case of gases where the atoms are rela- tively far apart, the chance of this happening is very small, so that a gas is not a good conductor of electricity. 16. Force that Holds Electrons in Substance. The electrons and atoms of a solid substance, like the atoms of a gas, possess 23 24 THERMIONIC VACUUM TUBE kinetic energy and are in a constant state of motion. Now, if the electrons in a substance possess kinetic energy the ques- tion arises why do they not escape from the substance. The answer to this question is an assumption that there exists at the surface of the substance a force which tends to keep the electrons in the substance. Being an assumption it is necessarily a very unsatisfactory answer. But there is a good reason to believe that this assumption, which was made by O. W. Richardson in 1901, is one which did not lead us astray. In fact recent developments regarding the structure of the atom lead us to believe that such a force which tends to hold electrons in a substance must necessarily exist at the surface of the substance, and Richardson's assumption can be explained in a manner which is entirely consistent with our physical conceptions. In order to escape from the surface of the substance an electron must do work in overcoming the force which tends to hold it in the substance, and this amount of work it does at the expense of its own kinetic energy. For all known substances the work which an electron must do to escape, and the amount of kinetic energy possessed by the electrons in the substances are of such order of magnitude that only very few electrons manage to escape at ordinary temperatures. By far the larger number of them would have to expend more energy than they possess, so that they are held within the substance. The work which an electron must do to escape from the surface of a substance is sometimes referred to as the " electron evaporation constant." Generally it is expressed in terms of equivalent volts. The evaporation constant w and the equivalent voltage are con- nected by the relation w where e is the electron charge. We shall in the following refer to as the electron affinity. This quantity is the most important con- stant in thermionics. It determines the thermionic current that can be obtained from any particular type of cathode at any desired temperature, and is characteristic of the substance used as cathode. The smaller < is, the larger is the thermionic current that can be obtained. It is desirable that cathodes be used in thermionic tubes for which < is as small as possible, because the power that ELECTRONS FROM SOLID SUBSTANCES 25 must be dissipated in the heating of the cathode to obtain a definite thermionic current decreases as < is decreased. This implies economy of operation as well as increased life of the tube, be- cause of the lower temperature at which the cathode can be operated. The coated type of cathode (Wehnelt cathode) is an example of a cathode that has been so treated as to obtain a low- value of the electron affinity. To obtain a better insight into the nature of the electron affinity, let us consider an evacuated enclosure divided into two parts A and B by a surface S. Let A and B each contain a number of electrons arid suppose that the electrons in B can pass freely through the surface into A , but in passing from A to B they must do a certain amount of work w. The electrons in A and B possess kinetic energy like the molecules of a gas; they will therefore move about at random, continually passing through the surface s in either direction. The steady state will be reached when as many electrons pass per second from A to B as from B to A. When this state is attained there will be more electrons in A than in B. The relation between these numbers is given by Boltzman's equation: w A7 n = Ne~kT or w = kTlog , . . . . . (2) where N and n denote the number of electrons per unit volume in A and B respectively, T the temperature cf the system, w the work which an electron must do to move from A to B and k the gas con- stant per electron, sometimes referred to as Boltzmann's constant. This constant k is two-thirds of the average kinetic energy which an electron possesses at a temperature of 1 absolute and is equal tol.36Xl(T 16 erg. We can now replace the part A within our enclosure by a metal, so that the surface S is the surface of the metal. The replacement is entirely in accordance with our fundamental assumption that in escaping from the metal an electron must do a certain definite amount of work. The number of electrons immediately outside the surface of the metal will then be related to the number inside the metal by the above equation (2). It is seen then that the number n that escape from the metal depend upon the two factors T and w, and that this number increases as the temperature of the system is increased or as w is decreased. Moreover, it is seen 26 THERMIONIC VACUUM TUBE that, since both T and w appear in the exponent of , a small change in either of them causes a considerable change in the number of electrons that escape from the metal. If, on the other hand, both T and w be kept constant, the number which escapes increases as the number of electrons N in the metal is increased. This increase is, however, not nearly as effective as that occasioned by a decrease in w. These considerations show the importance of the constant w. Its influence on the phenomena encountered in the thermionic discharges goes even further than this, as we shall now proceed to show. 17. Contact Electromotive Force. The advent of galvanic electricity was the discovery by Volta, over a hundred years ago, that when two pieces of different metals were placed in a contact and then separated they acquire electric charges. If the two pieces of different metals were placed in an electrolyte and joined by a wire outside the electrolyte a current is established in the circuit so formed. The nature of this force which drives elec- tricity round the circuit and is known as contact electromotive force was never understood until recently. It was only in the last two decades that it was shown conclusively, mainly by O. W. Richardson and P. Debije, that the contact electromotive force is an intrinsic property of metals and is determined by the electron evaporation constant w. The connection between the contact E.M.F. and the evaporation constant w can be gathered from the following. Since an electron must do work in escaping through the surface of a metal, it follows that two points, one outside of the surface and the other inside, must be at different potentials. This difference of potential is given by equation (1). Now suppose we have two slabs of different material, such as copper and zinc. Let them be connected by a copper wire as shown in Fig. 6, and let the number of electrons per unit volume in the copper and zinc be, respectively, NI and AT 2 . Since the two pieces of metal are metallically connected all points in the metallic circuit must be at the same potential, except for a very small potential difference which occurs at the junction AB of the two metals. Let the circuit be grounded, so that it can be considered to be at zero potential. Let the work which an electron must do to escape from the copper slab be w\ , so that in moving from the metal to a point just outside the surface its potential changes from zero to a value Vi, say. Let the corresponding values for the zinc slab be W2 ELECTRONS FROM SOLID SUBSTANCES 27 and V 2 , and let us see how much work must be done in moving an electron from a point in the copper through the space to a point inside the zinc. In moving through the surface of the copper an amount of work, wi, must be done by the electron. In moving from here to a point just outside the zinc surface it does an amount of work equal to (Vi V 2 )e, where e is the charge of the electron, and in moving through the surface of the zinc slab the work done is W2. The total amount of work done is therefore Cu FIG. 6. Now, since the number of electrons per unit volume in the copper and the zinc is NI and N2, respectively, we have by equation (2) : kT N-, ' A J\ /O\ Vi V 2 = log-TT '(*) e & N 2 e kT TVi The term log -^ gives rise to the small E.M.F. set up at the junction AB of the metals and accounts for the Peltier effect. It is so small in comparison with the other terms in equation (3) that it can be neglected. Hence, referring to equation (1), it follows that The difference Vi V 2 is called the contact potential difference between the two metals, and, as is seen from equation (4), it is equal to the difference between the electron affinities of the metals. 28 THERMIONIC VACUUM TUBE 18. Measurement of Contact E.M.F. That this difference of potential actually exists between the two metals can be shown in the following way: Suppose the circuit be cut at a place C, and the two ends connected' to the quadrants of a quadrant electrom- eter. Let us connect one of the plates (say, the copper plate) and the corresponding pair of quadrants to ground, while the other side of the system remains insulated. The system constituted by the plates Cu and Zn, and the quadrants, has a definite electro- static capacity depending on the distance between the plates. If the plates first be placed close together and then jerked apart, the capacity of the system will change, and if a potential differ- ence exists between the plates the electrometer will show a deflec- tion. If the potential difference is P and the deflection di, the sensitivity of the measuring system is given by Now, instead of directly grounding the copper plate, let it be connected to ground through a battery which maintains it at a constant potential V, so that the potential difference between the two plates is P+ V. If the plates are now placed the same distance apart as they were initially in the first operation, and then again pulled apart to the same extent as before, the electrometer will show a different deflection cfe, and the sensitivity of the measuring system is now given by p+r Equating these two expressions for the sensitivity, the contact potential difference P between the two plates is : P=v * We shall see later that the contact potential difference, and hence also the electron affinity, depends very much on the nature of the surface of the substance. It can be modified very appre- ciably by gas occluded in the surface. The notable effect of gas has led some to believe that the contact potential difference is not an intrinsic property of metals but is occasioned entirely by the ELECTRONS FROM SOLID SUBSTANCES 29 presence of gas. There is, however, no doubt but that contact potential difference must exist between metals in the best obtain- able vacuum, and that it is determined by the electron affinity. A film of gas on the surface of the substance can increase or decrease the electron affinity and so change the contact potential difference between it and another substance. It will be shown later that this also produces a change in the thermionic current obtainable from the substance. Thus, when hydrogen is occluded in the surface of platinum the work which an electron must do to escape from the surface of the platinum is decreased, while oxygen occluded in the surface of calcium increases it. The following table gives the electron affinities for a number of substances, 1 expressed in volts: Tungsten 4.52 Zinc 3.4 Platinum 4.4 Thorium 3.4 Tantalum 4.3 Aluminium 3.0 Molybdenum 4.3 Magnesium 2.7 Carbon 4.1 Titanium 2.4 Silver 4.1 Lithium 2 . 35 Copper 4.0 Sodium 1 .82 Bismuth 3.7 Mercury 4.4 Tin 3.8 Calcium 3.4 Iron 3.7 The difference between any two of these values gives the con- tact potential difference between the corresponding substances. We shall see that the contact potential difference plays an important part in thermionic amplifiers and detectors of electro- magnetic waves that are so designed as to operate on small plate voltages. The values of electron affinities given in the above table are of such order of magnitude that under normal conditions only very few of the electrons in the substance possess sufficient kinetic energy to enable them to escape by overcoming the force of attrac- tion at the surface. In order to make use of electrons for the purpose of discharge through vacuum tubes they must first be dislodged from the parent substance. We shall now proceed to a discussion of the agencies whereby 1 Most of these are averaged values compiled by LANGMUIR (Trans. Am. Electro-chem. Soc., Vol. 29, p. 166, 1916) from measurements of RICHARD- SON, MILLIKAN, HENNING, LANGMUIR, and others. 30 THERMIONIC VACUUM TUBE the dislodgment of the electrons can be effected. As was stated in Section (11) these agencies are: (1) heat; (2) electromagnetic radiation, and (3) impact of electrons. These agencies form the basis of the subjects of Thermionics, Photo-electricity and Second- ary Electron Emission, respectively. 19. Elements of Thermionics. The first of these agencies which is the most important for our immediate purposes has been known for a considerable time. In fact, it has been known for over one hundred years that when a metal is brought into a state of incandescence the air in its neighborhood becomes a conductor of electricity. The phenomenon was studied in detail by Elster and Geitel during the years of 1882-1889. They found that when a metallic filament was placed near a plate the latter acquired a charge when the filament was heated to incandescence. At red heat the plate acquired a positive charge, but when the tempera- ture of the filament was raised to white heat the plate charged up negatively. If the filament and plate were placed in an enclosure which could be evacuated, the tendency for the plate to charge up negatively was increased. This effect also came to the notice of Edison in 1883. He noticed that if a metallic plate be inserted in the vacuous space of an incandescent lamp and this conductor be connected to the positive end of the filament, a current was established in the shunt circuit so formed, namely, the circuit PFG (Fig. 7). But if the plate was connected to the negative end of the filament, the galvanometer showed no deflection. A study of this effect, which is sometimes called the " Edison Effect " was made by J. A. Fleming in 1896, 1 but the true nature of the phenomenon was not understood until the work of J. J. Thomson and O. W. Richardson. In 1899, the former showed 2 that the phenomenon was the result of negative electricity given off from the hot filament in the form 1 J. A. FLEMING, Phila. Mag.; Vol. 42, p. 52, 1896. 2 J. J. THOMSON, Phil. Mag., Vol. 48, p. 547, 1899. FIG. 7. ELECTRONS FROM SOLID SUBSTANCES 31 of electrons. This explained, for example, why in the Edison effect a current was observed to flow through the galvanometer (7. When the plate was connected to the positive end of the filament, the filament had a negative potential with respect to the plate, and the electrons given off by the filament were driven to the plate. Since the time of Thomson's experiment there has been no doubt in the minds of physicists that the carriers of electricity from the filament are electrons, but the mechanism of the emission of these electrons from the hot filament was not known until O. W. Richardson l showed, in 1901, that the electrons are emitted solely in virtue of their kinetic energy and need no chemical reac- tion at the surface of the filament. This result of Richardson's work was the first definite expression of what may be termed a pure electron emission. Richardson's theory was based on an assumption that had previously been made and successfully applied, that the electrons in a metal, which are free to move under the influence of an electric field, behave like the molecules of a gas, that is, they have velocities distributed according to Maxwell's law. It was stated in Section 16 that these electrons are held in the substance by a force existing at the surface of the substance. There is still some speculation regarding the exact nature of this force which seems to be closely related to the structure of the atoms or mole- cules of the substance. At ordinary atmospheric temperatures very few electrons possess sufficient kinetic energy to overcome this force. The number escaping at such temperatures is there- fore extremely small. According to Maxwell's law of velocity distribution some electrons will at one moment have zero velocity, others again will have extremely high velocities, while the majority will possess velocities ranging between these two extreme values. Only the few electrons with the very high velocities will be able to escape through the surface. The energy w which an electron must expend to overcome the force of attraction at the surface is related to the number of electrons per cubic centimeter inside and outside the surface by equation (2). From this equation it is seen that as the temperature is raised the number n of electrons outside the surface increases. Now, in vacuum tubes we are not so much concerned with the relative number of electrons inside and outside 1 0. W. RICHARDSON, Proc. Camb. Phil. Soc., Vol. 11, p. 286, 1901. Phil. Trans. Roy. Soc., Vol. 11, p. 497, 1903. 32 THERMIONIC VACUUM TUBE of the surface in the state of equilibrium as with the rate at which they escape when they are carried away as fast as they are emitted. This can be ascertained by applying a potential difference between the body which emits the electrons and a conductor placed in its neighborhood. It will be understood in the following that this potential difference is always high enough to draw all the electrons away as fast as they are emitted. Applying the principles of the kinetic theory of gases it can be shown that, to an approximation which is sufficiently close for our purposes, the number n' of elec- trons that pass per unit time through unit area of the surface from the inside is given by: IkT n tt\/o , \27rra' kT (5) where m is the mass of the electron, and n is the number of elec- trons per cubic centimeter outside the surface. This number of electrons can be obtained in terms of the number N per cubic centimeter inside the surface by combining the relation (5) with equation (2). Thus: IrT . kT . 27rra n' is the number of electrons that would move per second to a conductor which is charged positively and placed in the neighbor- hood of the emitting substance. If e be the electronic charge, then n'e is the saturation current per square centimeter surface of the emitting substance, or or ^ 7,=A!T 1/2 T ......... - (7) The constant b in this equation is a temperature and is ex- pressed in absolute (Kelvin) degrees. It is, however, more con- venient to use the equivalent constant expressed in volts. The relation between and 6 is as follows : From equations (6) and (7) w = kb, and from equation (1) w = e, where is expressed in elec- trostatic units, or u volts ......... (8) ELECTRONS FROM SOLID SUBSTANCES 33 Now k is the gas constant for one electron and is equal to 1.36X10" 16 , while e is the electronic charge in electrostatic units. Hence . = u volts, i.e., = 8.6XlO- 5 6volts. (9) The constant < is the electron affinity, values of which for a number of substances are given in the table on p. 29. It can be determined experimentally with a simple device consisting of a filament of the substance to be investigated and an anode placed in its neighborhood, the structure being enclosed in a vessel which can be evacuated to such an extent that the residual gas Temperature of Cathode FIG. 8. has no appreciable influence on the discharge. (The influence of gas will be considered in a later chapter.) Care must be taken that the voltage applied between the filament and the anode is so high that any further increase in the voltage does not appreciably increase the current. The current obtained under these conditions is then the saturation current given by equation (7) . If the current is observed for different values of the filament temperature a curve is obtained such as that shown in Fig. 8. In order to evaluate the constant 6 or we can take logarithms of equation (7). Thus: logio I,\ logio T = logio A - .43436 (10) 34 THERMIONIC VACUUM TUBE By plotting the expression on the left-hand side against a straight line is obtained the slope of which gives 6. We shall have occasion to return to this equation when we come to con- sider efficiency problems connected with the thermionic vacuum tube. It may be remarked here that the constant b can also be determined by photo-electric means. The relation between photo-electric and thermionic phenomena will become apparent when we come to consider the photo-electric effect. 20. Influence of Surface Conditions on Electron Affinity. By applying the theory of images Debije l has shown that it is easier for an electron to escape from a sharp point than from a smooth flat surface. The theory of images involves a purely mathematical process that tells us little or nothing about the nature of the processes going on when a electron escapes from a surface and can be applied only to that part of the process when the electron is co far away from the surface that molecular irregu- larities in the surface can be neglected. We can nevertheless obtain an indication of the manner in which the configuration of the surface affects the electron emission, if we comply with the conditions that govern the application of the theory of images. This theory states that the force of attraction between a charged body and a conductor can be determined by assuming that the force is the same as if the conductor were replaced by another charge which is, in respect to size, shape and position, the optical image of the first charge reflected in the surface of the conductor, but is of opposite sign. Thus a charge e at a distance x from a plane surface would produce an image -\-e at a distance x behind the surface. The force of attraction between the charge e e 2 and the plane surface is therefore T and the work that must be done to remove the charge from a distance XQ from the surface to infinity is : re 2 e 2 4-^=4^' '. which, when expressed in equivalent volts becomes: 300e ^ 1= W 1 P. DEBIJE, Ann. d. Phys., Vol. 32, p. 465, 1910. ELECTRONS FROM SOLID SUBSTANCES 35 the condition being that the distance XQ is largo compared with molecular dimensions. The quantity w\ does not represent the total amount of work which an electron must do to escape from a plane surface. There is still to be added the work W2 done in moving from the interior of the conductor through the interface and up to the point distant XQ from it. Schottky l and Langmuir 2 have made cer- tain assumptions regarding the force of attraction within this region which lead to the result that the work W2 is equal to wi, e 2 so that the total amount of work done is =- . Since the nature of 2x the force very close to and inside the surface is not known and FIG. 9. probably depends very materially on the molecular structure of the material of the conductor, 3 we shall confine our considerations to the force at distances which are large compared with the molecular diameters, and proceed to compute the corresponding part MI, -of the work which an electron must do to escape from a curved surface of radius r. Let the surface be convex toward the electron (Fig. 9). Let the electron e be at a distance a and its image +e\ at a distance a\ from the center of curvature of the surface. Then = r 2 , (12) 1 W. SCHOTTKY, Phys. Zeitsch., Vol. 15, p. 872, 191*. 2 I. LANGMUIR, Trans. Am. Electrochem. Soc., Vol. 29, p. 163, 1916. 3 J. FRENCKEL, Phil. Mag., Vol. 33, p. 297, 1917. 36 THERMIONIC VACUUM TUBE Now the force of attraction between e and -f-ei is: From equations (12) and the geometry of the system, we have, if x be the distance of the electron from the surface : Substituting these values for 'e\, a and ai in (13) the force of attraction becomes: This equation holds for values of x greater than XQ, where XQ is large compared with molecular dimensions. The work which an electron must do to move away from the point XQ is obtained by integrating equation (14) between the limits X = XQ and x=oo. The integration gives: If we take the radius of curvature of the surface so large that XQ is small compared with it we can write equation (15) in the form: The equivalent potential in volts is: This shows that the work of escape of an electron from a curved surface of radius r is less than that from a plane surface by an e 2 amount equal to . It also shows that if the surface is irregular or ELECTRONS FROM SOLID SUBSTANCES 311 contact potential differences must exist between the protru-* sions and the hollows. These potential differences are very small, but if irregularities are close to one another the resulting electrostatic fields may be very large. Thus, if we consider a protrusion and a hollow adjacent to it, each being regarded as spherical surfaces having a radius of curvature of the order of 10 ~ 6 cm., it follows that the electrostatic field tending to drive electrons from the protrusion to the hollow may be of the order of several thousands volts per centimeter. This would necessitate very high plate potentials to overcome these fields and pull all the emitted electrons over to the anode. This result is obtained by the simple application of the theory of images, which unfortunately does not tell us much about the physical processes involved. A similar effect is to be expected when the surface of the cathode contains impurities having electron affinities which are different from that of the material of the cathode itself. Langmuir l has ascribed the lack of satu- ration shown by tungsten filaments contaminated with thorium to the local fields at the surface of the filament, due to the differ- ence between the electron affinities of thorium and tungsten. When the surface of the filament consisted either of pure tungsten or pure thorium the saturation curve was substantially parallel to the voltage axis. But when the surface was a mixture of tung- sten and thorium the thermionic current continually increased with the applied voltage. The oxide-coated cathode is an example of a cathode which generally has an irregular surface. It is obtained by coating a platinum wire or ribbon 2 with oxides of the alkaline earths. The coated filament has a much lower electron affinity and therefore a higher thermionic efficiency than the metals used as sources of thermionic current. Its surface, however, is rough and possibly is not uniformly active thermionically. These filaments do not give such well-defined saturation currents as metallic filaments do. Lack of well-defined saturation currents is generally not a disadvantage in thermionic tubes. It is, in fact, sometimes a distinct advantage, as will become evident from the considerations given in the following chapters. 1 Paper read at Chicago meeting of Am. Phys. Soc., December, 1919. 2 A. WEHNELT, Ann. d. Phys., Vol. 4, 425, 1904. NICOLSON & HULL, U. S. Pat. 1209324, Brit. Pat. 17580, 1915. 38 THERMIONIC VACUUM TUBE 21. Photo-electric Effect. The process of the dislodgment of electrons from solid bodies by means of electromagnetic radiation brings into play the same forces that attend the emission of electrons from hot bodies, and furnishes valuable evidence to show the generality of that characteristic constant of solids which plays such an important part in the operation of thermionic vacuum tubes, namely, the electron affinity. In 1887 Hertz observed that when a spark gap was illuminated with ultra-violet light the discharge passed more readily than when the electrodes were in the dark. Soon after this Hallwachs discovered that the incidence of ultra-violet light on a zinc plate caused it to become charged positively, or when the plate was first charged to a negative potential and then insulated it lost its negative charge when exposed to the light. This has since been found to be a general property of all conductors and could be ex- plained in the light of the electron theory. The energy of the light wave striking the substance stimulates the electrons in the atoms of the substance. They thus acquire sufficient energy to overcome the force of attraction at the surface of the substance and escape with a velocity which depends upon the energy in the light wave and the amount of energy they must expend to overcome the surface force. Thus, if the amount of energy acquired by the electron in the substance from the light is W and the work which the electron must do to overcome the surface force is w, then it escapes from the substance with a kinetic energy. (18) where v is the velocity of escape and m the mass of the electron. It will be understood that of the electrons in the substance those that happen to be near to the surface have to overcome only the surface force, while those that are further in the interior will have to do an extra amount of work in forcing their way out. We can therefore expect electrons to be emitted by the light with velocities ranging from zero to a definite maximum value. This maximum value expressed in volts is the electron affinity. We shall in the following consider only those electrons that have this maximum velocity, and equation (18) will be understood to refer to these maximum values. If a plate is placed in front of the electron emitting substance or cathode, the emitted electrons can be driven back to the cathode by the application of a potential ELECTRONS FROM SOLID SUBSTANCES difference between it and the anode. If the electron emerges from the surface with a velocity v it will be capable of moving against ,an electric field until it has spent its kinetic energy ^mv 2 , where m is the mass of the electron. If the maximum voltage against which the electron can move in virtue of its own kinetic energy is V, then Ve = ^mv 2 . The velocity of an electron is commonly expressed in terms of the voltage V, instead of centimeters per second. Equation (18) can then be written (19) where e is the electronic charge. This voltage can be determined with the arrangement shown in Fig. 10. A is the photo-electric cathode which can be illu- minated with ultra-violet light, and B is the anode. By means, of -wwvwvwvwww t FIG. 10. the potentiometer shown the voltage between A and B can be adjusted to any desired value tending to drive the electrons in the direction B to A. Unless this voltage exceeds a definite amount the electrons emitted from A under the influence of the light will travel all the way across to B in virtue of the velocity with which they are emitted, and the resulting current established in the circuit can be measured with a current-measuring device. If we now measure the current for increasing values of the voltage V, the current decreases until the voltage is large enough to return all the emitted electrons to the cathode before they can reach the anode. By plotting the photo-current against the voltage V a curve is obtained such as that shown in Fig. 11. The voltage is reckoned negative when the receiving plate B is negative with 40 THERMIONIC VACUUM TUBE respect to the emitting plate A. The point at which the curve cuts the voltage axis gives the maximum velocity with which the electrons are emitted from the cathode. Experiment has shown the remarkable result that the maximum velocity of emission is independent of the temperature of the cathode. The maximum velocity of photo-electric emission is furthermore independent of the intensity of the light with which the cathode is illuminated. If the intensity of the light is in- creased only the number of electrons emitted increases but their velocity stays the same, provided that by changing the intensity of the light we do not at the same time change its quality, that Anode Potenfial FIG. 11. is, its wave length distribution. The frequency_of__the incident light is the only factor that influences the Telocity of emission when dealing with one substance. For the same light frequency and different substances, the emission velocity depends upon the electron affinity of the substances. Millikan 1 has shown that if the maximum voltage necessary to keep the emitted elec- trons from reaching the anode be plotted against the frequency of the light the linear relation shown in Fig. 12 is obtained. Thus: (20) where h is a constant and v the frequency of the light falling on the cathode. Referring to equations (18) and (19) it is seen 1 R. A. MILLIKAN, Phys. Rev., Vol. 7, p. 355, 1916. ELECTRONS FROM SOLID SUBSTANCES 41 that W, the energy acquired from the light by the electron in the This w substance is equal to hv, and the constant C is equal to . e extremely important experimental result shows that light energy can be expressed by the product of the frequency of the light and a constant. Indeed, Millikan found that this constant is the same as Planck's constant of action. Furthermore, C has actually been found to be equal to the electron affinity <. We therefore have as the fundamental photo-electric equation: Ye = hv < 23 ) where e=K+V. This expression can be regarded as the effective voltage when the potential difference between grid and cathode is zero. If this potential difference be made equal to E g the effective voltage becomes Ep ' TO '- (24) In this expression E p and E g are the potentials of the anode and grid with respect to that of the cathode, which can be regarded as the zero of potential. Hence, when E g is varied the potential difference between grid and plate also changes. When I first established this linear stray field relation in 1913, I expressed the result by the equation (25) where v is the potential difference between cathode and grid and V that between grid and anode. I also stated that A; is a constant ELECTRONS FROM SOLID SUBSTANCES 45 depending on the grid and d the distance between grid and anode. In testing this relation the grid remained grounded while the potential of the cathode was varied. This made it possible to keep the potential difference V between grid and anode nearly constant while varying the potential difference between cathode and grid. The accuracy with which equation (25) was found to hold is shown by Fig. 14. 1 In the case of the lower curve the 7 2Q 40 60 80 10 Anode -Grid Voltcige FIG. 14 distance d between grid and anode was 6.7 mm., while the upper curve was obtained with d = 2.5 mm. If, instead of plot- ting V as abscissae, we plot , the two curves coincide. rfj It can readily be seen that if we substitute E a for v and E P , the potential of the anode with respect to the cathode for V, the 1 Loc. cit., p. 339. 46 THERMIONIC VACUUM TUBE potential of the anode with respect to the grid, then (24) and (25) give the same result provided that and = /*-! (26) I have since verified this relationship between ^ and the structural parameters of the tube on the basis of an extensive series of experiments carried out in the research laboratories of the Western Electric Company, and have also expressed k in terms cf the mesh of the grid and the diameter of the grid wires. (See Chapter VII, p. 231.) The constant n is a very important constant of the three- electrode tube and, as will be shown later, expresses the maximum voltage amplification obtainable. Expression (24) or (25) can be regarded as the fundamental relationship of the three-electrode vacuum tube. The current in the circuit FPA (Fig. 13) is obviously a function of the expression (24). Hence, if the potential of the cathode be maintained constant, the fundamental expression for the current in a three- electrode tube is (26) where E p and E When # is expressed in volts and i in amperes, we may write this equation: Comparing this constant of proportionality K with C in equation (14) it will be seen that . (18o) Equation (18) shows that as long as the potential difference between the anode and the negative end of the filament is less than the voltage drop in the filament, the anode current varies as the f -power of the anode potential. Except for the fact that here the limitation of current by the voltage drop in the filament has been taken care of, this equation is subject to the same limita- tions as the f -power equations which were derived on the assump- tion that the cathode is an equipotential surface. Case (b) E^E f . In this case electrons flow from the whole surface of the filament to the anode. Hence the current is: 9r \rnjo which gives: (i)^ Ef =K[^-(E-E f )^], . . ... (19) where 1 = length of the filament; r = radius of the cylindrical anode; E f = voltage drop in the filament. PHYSICS OF THE THERMIONIC VALVE 67 Equation (19) may be expanded into the more convenient form: where C=14.65X10~ 6 -, the same constant as appears in the equation (14). The lower signs in the series of (19a) pertain to the case in which the potential of the anode is reckoned with respect to the positive instead of the negative end of the filament. F 1 FIG. 23. This series converges so rapidly that for all values of the anode potential greater than twice the voltage drop in the filament we can write for the current with close approximation. Hf] (20) In deriving these equations, the length of the filament (and that of the cylindrical anode) were put equal to a finite value I. Strictly speaking I should be infinitely long so that the distortion of the field at the ends of the anode can be neglected. This condition can be realized in practice with a device shown schematically in Fig. 23. The anode AA is in the form of a cylinder and the filament is stretched along its axis. In order to insure straight lines of force the guard rings RR r are placed on either side of AA, the filament extending beyond the ends of the anode. The anode and guard rings are electrically connected but the galvanometer G 68 THERMIONIC VACUUM TUBE is inserted as indicated in the diagram, so that it registers only the electron current flowing to the anode. The effective length of the filament is then equal to the length of the anode. The general effect of the voltage drop in the filament when the plate is connected to the negative end of the filament, is to make the space current smaller because the average potential difference between the filament and the plate is smaller than that between the negative end of the filament and the plate, this being the potential difference that is ordinarily measured with a voltmeter. The general effect is shown by the curve OD of Fig. 20. The curve OAB represents the theoretical curve in accordance with the simple f -power equation, and the part AB represents the ideal saturation current which is supposed to be independent of the applied voltage. The characteristic which is ordinarily observed is indi- cated by ODE. For the present we shall consider only the lower part OD of this characteristic. The deviation at voltages greater than the voltage corresponding to the point D is due to the limita- tion of the current by the electron emission from the filament and will be discussed in the next section. The line OAB is computed from the f -power equation (14), the constant C being put equal to 50X10" 6 amperes. If we assume that the voltage drop in the filament is 10 volts, then referring to equation (18a), we find the constant K becomes equal to 2 X 10~ 6 . With the help of equations (18) and (19) we can then compute the current as a function of the potential differences E between filament and plate, by putting #/=10. The values so computed give the value OD of Fig. 20. The percentage deviation of this curve from the theroretical curve OA is quite considerable at the lower voltages. It will be explained in the next chapter that it is desirable to so design thermionic tubes that the saturation current is obtained at the smallest possible voltage. In practice the voltage necessary for saturation seldom exceeds a few hundred volts. Fig. 24 represents two experimental curves plotted on the logarithmic scale and obtained in such a way that in the one case (curve 2) the voltage drop in the filament was effective and in the other (curve I) it was eliminated. To eliminate the effect of the voltage drop in the filament we can, as has been done in taking these curves, resort to a scheme used by von Baeyer 1 in 1909, which consists in connecting the ends of the filament and the 1 0. VON BAEYER, Phys. Zeits., Vol. 10, p. 168, 1909. PHYSICS OF' THE THERMIONIC VALVE 69 plate through a commutator which is so arranged that the filament current and the plate voltage are applied alternatively for short intervals of time, the plate voltage being applied only while the filament voltage is cut off. If the alternations are frequent enough, the filament does not get a chance to cool off markedly during the time that the filament current is cut off. In this way the plate current is measured only while there is no voltage drop in the filament. Iliampere* ro oJ *> -I 30 tD CD O .0 C / o c / o > I c c 9 / / i & J , 1 > 2: ' still offers a great advantage because in such case we could operate the filament at a lower temperature. The power saved in lowering the temperature could then be used in increasing the length of the filament. This would increase the total space current and the characteristic would take the form OHB\. It will be shown later that the steepness of the characteristic is a very important factor in determining the efficiency of thermionic amplifiers, detectors, etc. The curve OH is therefore more suitable than OA\. It is to be seen, therefore, that it is very desirable to use a filament with as low an electron affinity as possible. This is 80 THERMIONIC VACUUM TUBE obtained in the Wehnelt 1 cathode, which consists of a platinum filament coated with an oxide of the alkaline earths. The type of filament used in Western Electric tubes is the result of efforts to reduce the electron affinity. A comparison of Anode Volts FIG. 27. table II for tungsten filaments with the following, which gives the values for a type of Western Electric filament, 2 shows the relative thermionic efficiencies of the two types. TABLE IV p Is s=- P Watts per Cm 2 . Mils per Cm 2 . Mils per Watt. 4 11 2.7 5 35 7 6 80 13 7 160 23 8 300 37.5 9 . 500 55.5 10 750 75 1 A. WEHNELT, Ann. d. Phys., Vol. 14, p. 125, 1904. 2 From measurements of C. J. DAVISSON. PHYSICS OF THE THERMIONIC VALVE 81 The values for p, s and / s given in this table also obey equations (24) and (25) but the constants n and C for this filament have the values: n = 3.59 and C = 2.148Xl(r 2 . It is on account of the high thermionic efficiency that the oxide-coated platinum filament can be operated at such low tem- peratures. These filaments should never be heated above a reddish yellow (which corresponds approximately to p = 8 to 9 watts per cm. 2 ), whereas a tungsten filament can be heated to brilliancy. The experimental verificaton of Richardson's equation for the Wehnelt type of filament presents greater difficulties than in the case of pure metallic filaments. For metallic filaments this equation was verified by Richardson in 1903, 1 and subsequently by several others. Accurate determinations of Richardson's constants for tungsten, molybdenum and other metals were made in the laboratories of the General Electric Company. The earliest experiments that were made to determine the electron affinity for oxide-coated filaments were those of Wehnelt. 2 Richardson's equation has been fully verified for oxide-coated filaments by investigations carried on in the research laboratories of the Western Electric Company. Some of this work is described by H. D. Arnold. 3 The coated type of filament has now been used by the Western Electric Company since 1913, and has been in commercial use in the telephone repeater tubes of the Bell Telephone System since 1914. This filament is sufficiently constant in its behavior to meet the very rigid requirements called for by its use on the long dis- tance telephone lines. It consists of a core of platinum-iridium (6 per cent iridium with other impurities found in commercial platinum-iridium) covered with the oxides of barium and strontium. These oxides are applied alternately and after each application the filament is momentarily raised to a temperature of about 1000 C. The whole process consists of sixteen such applications. After that the filament is baked at about 1200 C. for two hours. If the 1 O. W. RICHARDSON, Trans. Roy. Soc., Vol. A-201, p. 497, 1903. 2 A. WEHNELT, Ann. d. Phys., Vol. 14, p. 425, 1904. For a full discussion of these and similar experiments, see O. W. RICHARDSON, " The Emission of Electricity from Hot Bodies " (Longmans, London). 3 H. D. ARNOLD, paper read at the Chicago meeting of the American Physical Society, October, 1919. 82 THERMIONIC VACUUM TUBE filament is not exposed to moisture or carbon dioxide it does not deteriorate. If kept in vacuum containers they show no deterio- ration over a period of several years. The tubes containing these filaments are completely interchangeable even in repeater circuits where the requirements are held within very close limits. D ower i FIG. 28. The investigation on the thermionic efficiency of the filaments was simplified by a coordinate system devised by Dr. C. J. Davis- son, in which the abscissae represent power supplied to the fila- ment, and the ordinates the thermionic emission. The abscissae of this system are curved, the coordinate lines being so proportioned PHYSICS OF THE THERMIONIC VALVE 83 that if the emission of the filament satisfies Richardson's equation, and the thermal radiation the Stefan-Boltzmann law, the relation between the thermionic emission and the power supplied to the filament when plotted on this chart is a straight line. Such a chart is shown in Fig. 28. The lines represent the average ther- mionic emission for a large number of different filaments. These filaments all have the same area, namely, 95 sq. mm. The further the line lies to the left, the greater is the thermionic efficiency. Each line shows the percentage of tubes that have a higher ther- mionic emission than that indicated by the line. For most pur- poses it is necessary only to insure that the thermionic emission is greater than a certain value. The thermionic efficiency is obtained by dividing the ordinates by the abscissae ($ = j. The broken lines represent the lines of constant thermionic efficiency, the corresponding thermionic efficiencies indicated on this line being expressed in milliamperes per watt. The normal power dissipated in this standard coated filament is from 8 to 9 watts per square centimeter. From this it is seen that the efficiency of these filaments range from about 10 to 100 milli- amperes per watt. The constants of Richardson's equation \I s =AT l/2 e T ) can be determined directly from these lines. The following table gives the constants a and b of Richardson's equation for a number of different substances. The values for the Western Electric oxide-coated filament were obtained by C. J. Davisson from measurements covering about 4000 filaments. 1 The values for the other substances given in the table are taken from a paper by Langmuir. 2 TABLE V Substance. Amps/Cm 2 . b Kelvin Degrees. Oxide coat (W. E. Standard). Tungsten (8-24)Xl0 4 2.36X10 7 (1.94-2.38)X10 4 5.25X10 4 Thorium 2.0X10 8 3.9 X10 4 Tantalum 1.12X10 7 5.0X10 4 Molybdenum 2.1X10 7 5.0X10 4 1 H. D. ARNOLD, loc. cit. 2 1. LANGMUIR, Trans. Am. Electrochem. Soc., Vol. 29, p. 138, 1916. 84 THERMIONIC VACUUM TUBE The thermionic efficiency is determined mainly by 6; the smaller 6 the greater the efficiency. To obtain the electron affinity the equation < = 8.6X10~ 5 X& (Chapter III, equation (9)) can be used. 33. Life of a Vacuum Tube. The life of a tube is determined mainly by two factors: (a) There is always a small amount of ionization by collision even in highly evacuated tubes. The positive ions so formed bombard the filament and this causes excessive local heating. In the three-electrode type of tube the grid acts as a partial screen to positive ion bombardment. The electric field in the region between grid and plate is usually much greater than between grid and filament. Most of the ionization, therefore, takes place between grid and plate and a large percentage of the resulting positive ions go to the grid instead of to the filament, since the grid is always negative with respect to the plate. (b) The rate at which the filament volatilizes increases with its temperature. In the case of the metallic filaments, the vola- tilization causes the filament gradually to get thinner and so in- creases its resistance. If the filament is operated at constant voltage this will cause a reduction in the heating current, and the consequent lowering of the temperature lowers the thermionic emission as well as the thermionic efficiency. If the filament is operated at constant current the voltage increases, resulting in an increase of the temperature of the filament. This shortens the life of the filament. Whether the filament be operated at constant voltage or constant current, both effects are undesirable and must be taken into consideration in estimating the life of the filament. The life of a metallic filament depends also on its diameter. 1 A 5-mil tungsten filament operated at a temperature of 2400 K. has a life of about 4000 hours, while the 10-mil filament operated at 2500 K. has a life of nearly 3000 hours. The thicker the filament the longer the life for the same operating temperature. Or, the same length of life can be obtained by operating the thicker filament at a higher temperature and so obtain a greater thermionic emission, as well as a higher thermionic efficiency, since the thermionic efficiency increases with the temperature. The following table taken from Dushman's paper gives an idea of the effect of the diameter of the filament on its life : 1 S. DUSHMAN, General Electric Review, Vol. 18, p. 156, 1915. PHYSICS OF THE THERMIONIC VALVE 85 TABLE VI Filament Safe Temperature Is per Watts per Diameter, Mils (Life>2000Hrs.). Cm. length. Cm. Length. 5 2475 30 3.1 7 2500 50 4.6 10 2550 100 7.2 15 2575 200 11.3 By " safe temperature " here is meant a temperature which is low enough to insure a life of at least 2000 hours. The quanti- ties given in the third column give the thermionic emission per centimeter length of filament at the corresponding temperature, and the fourth column gives the power that must be expended in maintaining a centimeter length of the filament at that tempera- ture. The thermionic efficiency can be obtained by dividing the values in the third column by those in the fourth. It is seen that the thermionic efficiency of the 15-mil filament is almost twice that of the 5-mil filament when both are operated at such tempera- tures as to give approximately the same life. The coated type of filament retains a constant resistance throughout its life, because the heating current in this filament is carried mainly by the core, while what evaporates is mostly the coating. The nearing of the end of this filament is indicated by an increase in the temperature over sections of its length. These are commonly referred to as " bright spots." This warning is a desirable and important feature, especially where the tube is used as a telephone repeater, because it makes possible a timely replace- ment of the tube without interrupting the service. Tubes containing the standard Western Electric filament have a life of several thousand hours, which depends, of course, upon the temperature at which the filament is operated. Such tubes have been operated in the laboratory for 20,000 hours con- tinuously, during which period the thermionic current remained practically constant. CHAPTER V INFLUENCE OF GAS ON THE DISCHARGE THE discussion given in the previous chapter and the current voltage relations that were obtained were based on the assumption that the residual gas in the device has a negligibly small influence on the discharge. It now remains to show under what conditions this assumption is justified and how these conditions can be realized in practice. It is important to know what are the sources cf gas in thermionic tubes; how the gas influences the discharge and how the c'eleterious effects of gas can be eliminated. There are two principal ways in which the presence of gas in a thermionic tube can affect the discharge. Firstly, gas in contact with the surface of a cathode can change the thermionic emission from the cathode and so change the saturation current, i.e., the total current obtainable from it at a definite temperature. This effect may be referred to as the surface effect. Secondly, the pres- ence of gas in the space between cathode and anode will, if the velocity of the electrons coming from the cathode exceeds a certain small value, depending on the nature of the gas. give rise to the phenomencn cf ionization by collision. This can be referred to as the volume effect. 34. Volume Effect of Gas. Ionization by Collision. In order to explain the effect of ionization by collision on the discharge, we shall assume that we have a characteristic corresponding to that obtained in a perfect vacuum and then see how this characteristic is changed when gas to a sufficiently high pressure is introduced into the tube. We shall also acsume that the gas which is intro- duced is entirely neutral as regards the surface effect; that is, it is of such a nature that its coming in contact with the surface cf the cathode does not change the electron emission from the cathode. In passing from cathode to anode, some of the electrons collide with the molecules of the gas and if they strike the mole- cules with a velocity exceeding a definite minimum amount ioniza- 80 INFLUENCE OF GAS ON THE DISCHARGE 87 tion by collision sets in. The voltage through which an electron must drop to acquire this minimum velocity is called the ioniza- tion voltage, values of which are given on page 22. If the voltage between cathode and anode is slightly greater than the ionization voltage, then, if an electron collides with a gas molecule just before reaching the anode, ionization will result, but a collision in the spa.ce nearer to the cathode will not result in ioniza- tion. In the latter case the electron may be reflected without any loss of energy from the molecule with which it collides, or it may lose part or all of its energy, this energy being transferred to the molecule, or it may combine with the molecule, thus forming a heavy negative carrier. It can readily be seen that if the voltage between .cathode and anode be increased, collision of the electrons with molecules nearer to the cathode may result in ionization, and if the voltage just exceeds twice the ionization voltage, an electron which collides after having dropped through the ionizaticn voltage in moving from the cathode, thus producing ionization, stands a chance of ionizing another molecule with which it may happen to collide just before reaching the anode. For low volt- ages, therefore, it is to be expected that the amount of ionization would increase with the applied voltage. In practice we do not deal with a single electron moving from cathode to anode but with a stream of electrons, and under such conditions it is generally found that ionization sets in at applied voltages less than the ionization voltage. It is, for example, possible to maintain an arc in a gas or vapor by the application of a voltage which is not as great as the ionization voltage of the gas or vapor. This is because it takes a smaller amount of energy to disturb the equilibrium of an atom than it does to completely detach an electron from an atom. Once the equilibrium of an atom has been disturbed the potential energy of the atomic system is increased by an amount equal to the energy given up to the atom by the colliding electron. Such an atom is more easily ionized than the normal atom and therefore the potential differ- ence through which any electron must drop in order to ionize this atom is less than the ionization voltage of the normal atom. 1 The amount of ionization depends also on the pressure of the gas. The pressure of the gas may be so low that the electron does not strike a molecule at all in its flight from cathode to anode. On i H. J. VAN DER BIJL, Phys. Rev., Vol. 10, p. 546, 1917. 88 THERMIONIC VACUUM TUBE the other hand, the pressures may be so high that the electron collides before it has acquired sufficient energy to ionize. The amount of ionization produced in this case depends on whether or not the gas is such that the collisions are elastic. If they are elastic the electrons will rebound from the molecules without losing their energy and may then strike the next molecules with a greater amount of energy than the first. If the collisions are inelastic the electrons lose some or all of their energy on colliding, but the energy which is transferred to the molecules is again radiated from them in the form of light, which causes photo-electric effects in the tube, resulting in a further dislodgment of electrons. 35. Mean Free Path of Electrons in Gases. The chance that an electron has of colliding with a gas molecule in its passage from cathode to anode depends on the mean free path of the electrons in the gas and upon the distance between cathode and anode. The mean free path is the average distance through which an electron can move freely without colliding with gas molecules. The following table gives an idea of the nature of this important quan- tity. The first column gives the number N of electrons, out of a total of 100 starting from the cathode, that can move freely through the distance d given in the second column of the table. The numbers in the second column are expressed in fractions of the mean free path L. 2V d ~L 99 0.01 98 0.02 90 0.1 82 0.2 78 0.25 72 0.333 61 0.5 37 1. 14 2 5 3 2 4 1 4.6 This table snows that if the distance between cathode and anode is equal to the mean free path, only 37 per cent of the INFLUENCE OF GAS ON THE DISCHARGE 89 electrons starting from the cathode will strike the anode without having encountered molecules on their way, and as the ratio of the distance between cathode and anode to the mean free path is increased the number of collisions increases. On the other hand, if the pressure is so low that the mean free path is 100 times the distance between cathode and anode, only 1 per cent of the electrons will collide before reaching the anode. The mean free path increases as the gas pressure is decreased; in fact, it is inversely proportional to the pressure of the gas. It also depends upon the size of the molecules. Thus it is greater for hydrogen than for oxygen. Consequently, since an electron is much smaller than a gas molecule, the mean free path of electrons in gases is greater than the mean free path of the gas molecules themselves. In order to obtain the mean free path of electrons in the gas from the mean free path of the gas molecules in the gas itself, we must multiply by the factor 4V2. If L is the mean free path of the gas molecules at atmospheric pressure (760 mm. of Hg), then the mean free path of elections in that gas, at a pres- sure p is: ~, ,r.; ......' ..-.. . where p is given in millimeters of Hg. The mean free path for most of the common gases is given in tables of physical constants. 1 ' The mean free path of a gas or vapor can be obtained if the coefficient of viscosity is known. The coefficient of viscosity is given by the equation Q -t T 9 f^y\ where rj = coefficient of viscosity; p = density of gas; c = mean molecular velocity; L = mean free path; the quantities being reduced to atmospheric pressure. Now, the pressure P is given by 3 /3P (3) /. C = A/ \ p J l See, for example, "Physical and Chemical Constants," by G. W. C. Kaye and T. H. Laby, 90 THERMIONIC VACUUM TUBE The mean free path for any gas for which the coefficient of viscosity is known can be obtained readily from the known mean free path and coefficient of viscosity of some other gas. For example, from equations (2) and (3) we obtain (4) and therefore if Z/2 is the known mean free path of one gas at atmos- pheric pressure, the mean free path LI for the other gas at the same pressure is given by where M i and MI are the molecular weights of the two gases con- sidered. The mean free path of the electrons in the gas at some other pressure can -then be obtained from equation (1). 36. lonization at Low Pressures. The application of the theory of ionization by collision when the pressure is of such order of magnitude that the mean free path is large compared to the dis- tance between the electrodes is simpler than when the mean free path is of the same order as, or less than, the electrode distance. The relation between ionization current and the pressure is also simpler. Let us consider the case in which the pressure of the gas in the tube is so low that the mean free path is large compared with the distance between cathode and anode. If p is the pres- sure in millimeters of Hg and N the number of gas molecules per cubic centimeter at atmospheric pressure, the number of mole- vN cules per cubic centimeter at the pressure p is |. . i t)U Let us suppose that cathode and anode are both in the form of infinitely large parallel plates, and let the number of electrons moving away from 1 square centimeter of cathode surface per second be n\. In moving from cathode to anode some of these electrons will collide with the gas molecules. If the voltage between cathode and anode be so high that every collision results in ionization, the member of positive ions formed will be equal to the number of collisions, and since the mean free path is large compared with the electrode distance, the chance of an electron colliding more than once on its way to the anode will be extremely small. We can therefore imagine the molecules in the space INFLUENCE OF GAS ON THE DISCHARGE 91 projected on the plane of the anode and compute the ratio of the area covered by the molecules to area of the anode. This will then be proportional to the ratio of the positive ions formed by collision to the number of electrons moving from cathode to anode. Now, the cross-sectional area formed by the ^ mole- o TI T cules is -zr where r is the molecular radius. Hence, if 712 be the number of positive ions resulting from collisions in a column 1 square centimeter in cross-section, and n\ the number of elec- trons moving to the anode per second from 1 square centimeter of cathode surface, we have H2 _ 1 Trr 2 pN n[~k ~760~ or 760/c n 2 , R . P - OA>- - , ..... . . (6) irr 2 N ni where k is a constant which becomes unity if all the molecules in the path of the electron stream are ionized. The pressure p of the gas is therefore directly proportional to the ratio of positive ions to electrons. This linear relation has been observed experimentally by O. E. Buckley 1 and on the basis of this simple relationship redesigned a thermionic gauge for the measurement of pressures below about 10 ^ 3 mm. of Hg. This gauge is described in Chapter X, page 375. 37. Effects of lonization by Collision. When ionization takes place, the characteristic can be influenced in the following ways: (a) The splitting of the gas molecules by bombardment of the electrons, in their passage from cathode to anode, results in the production of more dislodged charges so that the current is increased. This increase in current is small under the conditions prevailing in most thermionic tubes. Thus, if the pressure in the tube is 0.1 micron, 2 the increase in current due to this cause alone is less than 1 per cent. (6) The positive ions resulting from the collisions move toward the cathode and since the total space charge is the differ- ence between that due to the electrons and that due to the positive ions, the presence of the positive ions naturally reduces the total 1 O. E. Buckley, Proc. National Academy of Science, Vol. 2, p. 683, 1916. 2 1 micron = 10~ 3 mm. of Hg. 92 THERMIONIC VACUUM TUBE space charge, and this causes an increase in the current. The extent to which the space charge of the positive ions can reduce the negative space charge of the electrons depends on the number of positive ions compared with the number of electrons in the space at any particular time. It depends, therefore, on the speed with which the positive ions move toward the cathode; the lower the speed the greater will be the density of the positive ions. Thus when the tube contains oxygen the reduction in the negative space charge is greater than would be the case if the tube contained hydrogen at such a pressure that the number of positive ions formed is the same, because the oxygen ions are heavier and move more slowly than the hydrogen ions. (c) The positive ions can, under certain conditions, combine with the electrons at the surface of the cathode and so form a layer of gas on it. This results in a surface effect which will be explained in Section 39. (d) There is still another way in which ionization by collision can affect the operation of the tube. If the voltage between cathode and anode is sufficiently high, the bombardment of the cathode by the positive ions causes an abnormal heating of the cathode. This increases the saturation current because of the increase in the temperature of the cathode. There may also be a direct emission of electrons from the cathode under the bombard- ment of its surface by the positive ions. The undue heating caused by the bombardment wears away the cathode and has a very deleterious effect on the life of the tube. (e) When the velocity of the electrons is less than the value necessary to cause ionization by collision, the electrons attract the neutral gas molecules and so form heavy negative carriers. The ease with which this formation of negative carriers takes place depends on the nature of the gas. Such gases as argon and mer- cury vapor do not readily form negative carriers, while hydrogen and oxygen combine with electrons more easily. The effect of this negative carrier formation is to counteract the reduction in the negative space charge occasioned by the heavy positive ions formed by collision ionization. The positive ions are atoms of the gas from which one or more electrons have been removed. The ions therefore have very nearly the same weight as the gas atoms. The negative carriers, on the other hand, may consist of an atom or molecule to which has been attached an electron. It is also INFLUENCE OF GAS ON THE DISCHARGE 93 possible that the attraction between an electron and the neutral gas molecules can result in the formation of clusters consisting of more than one molecule held together by the electron. These negative carriers, therefore, move as slowly as, and sometimes more slowly than, the positive ions and consequently have a relatively great effect in counteracting the tendency of the positive ions to reduce the negative space charge of the electrons. 38. Influence of lonization on the Infra-Saturation Part of the Characteristic. To confine our attention to this part of the char- acteristic, let us assume that the tube contains gas which has no effect on the electron affinity of the cathode; in other words, it has no effect in either reducing or increasing the saturation current obtainable from the filament at any definite temperature. This condition can be realized, for example, with a tube containing a tungsten cathode and mercury vapor because mercury vapor is neutral as regards the electron emission from tungsten. 1 Let us suppose that we measure the current voltage relation of a tube containing a tungsten cathode and a tungsten anode, and to which is attached an appendix containing mercury which can be main- tained at any desired temperature thus maintaining the pressure of the mercury vapor at any desired value. It is, of course, to be understood that all other gases and vapors have been driven out of the electrodes and the walls of the vessel. It will be appre- ciated that by doing this we do not simulate the conditions ob- taining in practical thermionic tubes, because the gases remaining in the practical tubes seldom, if ever, contain mercury vapor, but do comprise those gases that we are excluding from the experi- ment at present under consideration. For such an experiment it is desirable to use a vapor which can be maintained at any pressure by keeping the parent substance at the corresponding temperature. Let us first suppose the appendix containing the mercury is immersed in liquid air. Under such conditions the characteristic will be that obtained in a high vacuum. Then, to study the effect of the mercury vapor in increasing the current on the infra-satura- tion part of the characteristic we can, instead of using liquid air, maintain the mercury at other temperatures by dipping the mer- cury tube into freezing mixtures or water baths. A set of such characteristics is shown in Fig. 29. The characteristic marked 1 IRVING LANGMUIR, Physik. Zeitsch., Vol. 15, p. 519, 1914. 94 THERMIONIC VACUUM TUBE No. 1 was obtained with the mercury tube immersed in liquid air. The other characteristics were obtained with the mercuiy at temperatures ranging from 7.5 C. to 10 C. The temperatures below C. were obtained by keeping the tube containing the 40 ( 50 60 Anode VolH FIG. 29. mercury immersed in ice and salt freezing mixtures. The following table shows the temperatures of the mercury and the pressures of the mercury vapor corresponding to the set of characteristics shown in Fig. 29. TABLE VII Curve No. Temperature of Hg, C. Pressure of Hg Vapor, Micron. 1 -185 0.000 2 -7.5 0.085 3 0.0 0.18 4 5.0 0.3 5 7.5 0.4 6 10.0 0.5 The pressures of the mercury vapor at these temperatures are obtained from a table given by Knudsen. 1 Referring to this table 1 M. KNUDSEN, Ann. d. Phys., Vol. 29, p. 179, 1909. INFLUENCE OF GAS ON THE DISCHARGE 95 and to Fig. 29, it will be seen that as the pressure of the mercury vapor is increased the current voltage curve becomes steeper and steeper. When the pressure rises to a value of 0.5 of a micron, the current shows a rather sudden increase at about 33 volts (curve 6). Below this pressure there is no sudden increase in current on the infra-saturation part. For a still higher pressure of the mercury vapor, about 2 microns or more, the current increases sharply at about 15 to 20 volts, as indicated by the dotted curve in Fig. 29. At these pressures of the mercury vapor, the formation of the positive ions by collision of the electrons with the mercury molecules neutralizes the space charge of the negative electrons so that the current that can flow through the tube undergoes a considerable increase. For this neutralization of the negative space charge it is necessary, firstly, that the potential difference between cathode and anode be high enough to cause a considerable amount of positive ionization. In the case of mercury vapor, this voltage is of the order of 5 volts or less. Secondly, it is neces- sary that the number of positive ions formed by collision be great compared with the number of negative carriers formed by com- bination of the electrons with the neutral molecules. The for- mation of heavy negative carriers accounts at least partly for the fact that the negative space charge does not become neutralized until the voltage becomes considerably greater than the voltage through which the electrons must drop to produce ionization by collision. Thus, the current does not increase suddenly until the filament-plate voltage reaches about 15 volts or more, although actually a considerable amount of ionization by collision takes place at much lower voltages. The reason why the current does not increase when ionization takes place at these low voltages is because a relatively large number of negative carriers are formed by the combination of electrons with the neutral gas molecules, and these negative carriers tend to neutralize the space charge of the positive ions. Another factor wriich tends to counteract the reduction of the space charge of the electrons is the recombina- tion of the positive and negative charges. The extent to which the current is increased by ionization by collision depends of course not only on the pressure of the gas vapor, but also on the distance between cathode and anode. The important quantity that determines the amount of collision ioniza- 96 THERMIONIC VACUUM TUBE tion is the ratio of the mean free path of the electrons in the gas or vapor to the electrode distance. Since the pressures corre- sponding to the curves shown in Fig. 29 are known, we can from these curves find the ratio of the mean free path to the electrode distance for the maximum pressure at which there is no sudden change in the characteristic due to the presence of the gas. These curves show that this maximum pressure of mercury vapor is about 0.4ju for the tube with which they were obtained. Now, the effects as shown by these curves are much greater for mercury vapor than for the gases that commonly remain as residual gases in thermionic tubes. In order to get an indication of the extent to which the other gases increase the current on the infra-saturation part of the characteristic, we have to distinguish between mercury vapor and such gases in three respects: Firstly, mercury molecules are very heavy compared to the molecules of the ordinary gases, such as hydrogen, oxygen and nitrogen, and, therefore, have a greater effect in reducing the negative space charge. Secondly, the mean free path of electrons in mercury vapor seems to be considerably less than the mean free path of elec- trons in the common gases. Thirdly, such gases as oxygen and hydrogen show a greater tendency to form negative carriers by combining with electrons than mercury vapor. It is also possible that the rate of recombination of the positive ions with electrons is different for different gases. In attempting to obtain an indication of the minimum value of the ratio of mean free path to the electrode distance necessary to give a characteristic which on the infra-saturation part is not influenced to a disturbing extent by the presence of gases other than mercury vapor, the differences mentioned above must be con- sidered. Little is known with regard to the difference in the coefficient of recombination or the rate of formation of negative carriers in different gases and vapors. We can, however, obtain some indication of the maximum allowable pressure of such gases as hydrogen and oxygen by considering only the velocity of the ions and the mean free path of the electrons in the gas. Suppose that the minimum value of the ratio of mean free path to electrode distance for mercury has been determined from a set of curves like that shown in Fig. 29. The extent to which positive ions reduce the negative space charge depends upon the velocity of the ions in the electric field, due to the potential difference INFLUENCE OF GAS ON THE DISCHARGE 97 between anode and cathode and is inversely proportional to it. Thus, if l\ is the mean free path of the electrons in mercury vapor at the maximum permissible pressure, and d the distance between the electrodes, then the ratio of - for any other gas is div where MI and M are the molecular weights of mercury and the gas considered, and vi and v are the corresponding velocities of their ions under the same electro-static field. Take, for example, the case of hydrogen and mercury vapor, since the molecular weight of hydrogen is 2 and that of mercury 200, the permissible ratio of mean free path to electrode distance is one-tenth as great for hydrogen as it is for mercury. This does not, however, mean that when the tube contains hydrogen the pressure can be ten times as high as when it contains mercury vapor; it can, in fact, be still higher because the mean free path of electrons in hydrogen is greater than that of electrons in mercury vapor at the same pres- sure. The relation between the pressure and mean free path is shown by equation (1). If L and LI be the mean free paths of the gas and of mercury vapor at atmospheric pressure, and / and h the corresponding mean free paths at the pressures p and pi, then we have Pi i Substituting the value of - r from equation (7), we obtain: k From this equation the maximum allowable pressure p for any gas can be obtained from the maximum allowable pressure for mercury vapor. In the case of hydrogen, for example, we have L=18.5X10~ 6 cm. at atmospheric pressure. LI, the mean free path of mercury vapor at atmospheric pressure, can be taken to be about 6X10~ 6 cm. 1 If these values be inserted in equa- 1 If the mean free path of mercury vapor is computed from equation (5) by putting its coefficient of viscosity equal to 162X10" 6 (figure given by 98 THERMIONIC VACUUM TUBE tion (8) we find that if the tube contains hydrogen the maximum allowable pressure is about thirty times as high as when the tube contains mercury. When the tube contains oxygen or nitrogen the pressure can be about four times as high as in the case of mercury vapor. For the practical operation of thermionic devices it is necessary that the current over the operating range should not show erratic changes. It will be apparent- from the previous discussions that the pressure necessary to secure a discharge that is not appreciably influenced by gas is of such an order of magnitude that it can readily be obtained. But it is important also to maintain the pressure constant enough to prevent any appreciable changes in the effects of ionizatiori on the characteristic. To secure this the electrodes and walls of the vessel must be freed of gas to such an extent that the heating of these parts during the operation of the tubes does not cause the evolution of enough gas to bring about such pressure changes. The part of the characteristic on which the great majority of thermionic devices operate is the infra-saturation part that we have discussed in the previous pages. The effect of gas on the saturation part of the characteristic will be discussed in the following section. 39. Effect of Gas on the Electron Emission. Surface Effect. It was shown in section 19 that the relation between the satura- tion thermionic current and the temperature of the cathode can be expressed by Richardson's equation: where A is a constant depending on the number of electrons per cubic centimeter of the cathode, b a measure of the work which an electron must do to escape from the cathode, and T the tem- perature of the cathode in absolute Kelvin degrees. If the vacuum in the tube is supposed to be perfect and the electrodes entirely void of gas, the constants A and b of the above equation have definite fixed values that are determined only by the nature of the cathode. Richardson's equation holds for any hot cathode and is KAYE and LAPY) it is found to be 3.5X10" 6 cm. at atmospheric pressure. This value of the viscosity coefficient is obtained by extrapolation and possibly involves a considerable error. It is likely that the value 6XlO~ 6 cm. for the mean free path of mercury vapor is more nearly correct. INFLUENCE OF GAS ON THE DISCHARGE 99 not dependent on the structural dimensions of the device, it being understood that the thermionic current I s is the current obtained from unit area of the cathode surface when the potential difference between cathode and anode is high enough to draw all the emitted electrons to the anode as fast as they are emitted from the cathode. It follows then that if the cathode contains impurities, Richard- son's equation must still hold but the constants A and b will have different values. From the nature of the equation it is seen that while the current changes in proportion to a change in A, a small change in b causes a very considerable change in the current. It has been known for a long time that small traces of gas occluded in the cathode can cause large changes in. the ther- mionic emission. H. A. Wilson 1 has found, for example, that when a platinum wire is freed of the hydrogen occluded in it, the thermionic current drops to a very small fraction of the value obtained from a platinum wire not so treated. J. J. Thomson 2 and O. W. Richardson have pointed out that the effect of the gas occluded in the surface of the cathode is to change the work necessary to detach an electron from the cathode, that is, to change the constant b in Richardson's equation and so produce relatively very large changes in the thermionic current. Thus, if 6 = 5X10 4 (0 = 4.3, see equation (9), Chapter III) and the temperature of the cathode is 2000 K., an increase in b of 25 per cent can decrease the current to approximately -^j of its original value. .Such changes can readily be produced by very small quantities of gas coming in contact with the cathode. The amount of gas that is necessary to produce great changes in the saturation part of the characteristic is often so small that its presence does not noticeably affect the infra-saturation part of the characteristic. This is shown, for example, in Fig. 30. The curves shown in this figure were obtained with a bulb containing two tungsten filaments, one of which was used as cathode and the other as anode. The bulb was not baked during the process of evacuation, so that a small trace of gas and water vapor remained in the tube. It is seen from curve 1 that the pressure of the residual gas was not sufficient to cause any appreciable increase in the current on the lower or operating part of the character- 1 H. A. WILSON, Phil. Trans., Vol. 202, p. 243, 1903. 2 J. J. THOMSON, " Conduction of Electricity through Gases," 2d Ed., p. 202. 100 THERMIONIC VACUUM TUBE istic. As the voltage and current were increased, however, the heating of the bulb by the energy dissipated in the tube caused the liberation of a sufficient amount of gas to give the irregular curve, as evidenced at voltages higher than about 200 volts. The readings were obtained in the order indicated by the arrow. Curve 2 was obtained while the whole tube remained immersed in liquid air. It therefore represents the high vacuum characteristic. Anode Milliamperes FIG. 30 The reduction in the electron emission caused by the presence of gas generally becomes more pronounced when ionization takes place, because this has the effect of directing the flow of gas towards the filament. When the gas is not ionized the electric field has no effect on the motion of its molecules, and the chance of their striking the surface of the filament is determined by he laws of the kinetic theory of gases applicable at low pressures. When ionization by collision takes place, . however, the molecules in the space between cathode and anode become positive ions which are INFLUENCE OF GAS ON THE DISCHARGE 101 directed by the electric field towards the cathode where they recombine with the electrons into neutral gas molecules. When they recombine before reaching the cathode the resulting neutral molecules or atoms have an increased momentum in the direction of the cathode, due to the momentum acquired in the electric field while they were ions. lonization by collision therefore causes more gas molecules to come in contact with the surface of the cathode. It has been found, for example, that the receiver type of three-electrode tubes, containing oxide-coated filaments and that are evacuated sufficiently well to operate very satisfactorily as amplifiers, may still contain a sufficient amount of gas to paralyze the tubes when operated as oscillation generators. (See Chapters VIII and IX.) When the tube is used as an amplifier most of the ionization of the gas takes place between the grid and the anode, and since the grid is negative with respect to the anode, the positive ions formed by collision ionization in this region are attracted to the grid. On the other hand, when the tube operates as an oscillation generator, the grid is subject to large potential variations, so that in this case positive ions are also formed in the space between filament and grid. These positive ions move to the filament and there combine with the electrons to form neutral molecules. If the gas remaining in the tube is of such a nature as to decrease the electron emission when coming in contact with the surface of the filament, this effect can easily become so large that the space current is reduced to practically zero. This accounts for the phenomenon that has been observed that a tube will start to oscillate and after a time, ranging from a fraction of a second to several seconds, the space current will drop to zero and the tube become inoperative. The normal condition of the tube can be restored readily by heating the filament to a higher temperature so as to drive off the gas. Gen- erally it will recover automatically after a period of time depend- ing upon the temperature of the filament. This period may range from a fraction of a second to several seconds or even minutes. The best way to prevent this paralysis of the tube is to evacuate it more thoroughly. Langmuir l has made extensive investigations on the effects of gas on electron emission from tungsten filaments. Langmuir 1 1. LANGMUIR, Phys. Rev., Vol. 2, p. 450, 1913; Phys. Zeitschr., Vol. 15, p. 516, 1914 102 THERMIONIC VACUUM TUBE finds that argon, mercury vapor and dry hydrogen have no direct effect on the emission of electrons from tungsten, but water vapor has a very large effect. Pure dry nitrogen has been found by Langmuir to have no appreciable direct effect in reducing the electron emission when the amount of nitrogen left in the tube is so small that there is no appreciable ionization of the nitrogen molecules. But when the voltage is raised so high that ionization becomes appreciable the nitrogen ions can bombard the filament with sufficient velocity to combine with the tungsten. This causes a decrease in the electron emission from the tungsten. The higher the velocity with which the nitrogen ions strike the tungsten filament the greater seems to be the effect on the electron emission, so that in the presence of nitrogen the current at first increases in the manner shown in the characteristics of most thermionic devices, and then suddenly starts to decrease when the voltage is still further increased. Hence, instead of getting a curve which, for voltages higher than the saturation voltage, becomes substantially parallel to the voltage axis, the curve obtained at these voltages has a negative slope. 40. Influence of Occluded Gases. From the explanations given in Section 38 it follows that the influence of ionization by collision of the residual gases in a tube on the infra-saturation part of the characteristic is generally not disturbing for pressures lower than of the order of one-tenth to one micron. Such a pres- sure is easily obtained. Hence, as far as removing the gas in the space of the tube is concerned, there would be no difficulty in obtaining a sufficiently high vacuum to realize what may be called a " pure electron discharge." What is necessary, however, is to maintain the vacuum in the tube while it is in operation, and it is therefore not necessary merely to remove the gas from the volume of the tube, but also to free the electrodes and walls of the vessel of occluded gases to a sufficient extent. If the electrodes of a device remain cold during operation the occluded gases are not liberated very readily, but when the electrodes become hot during the opera- tion the occluded gases are liberated. In all vacuum devices using hot electrodes it is therefore necessary previously to free the electrodes of gases. An incandescent lamp is such a device and therefore it has always been common practice, in evacuating incandescent lamps, to heat the bulbs and raise the filaments to INFLUENCE OF GAS ON THE DISCHARGE 103 abnormally high incandescence during the evacuating process. In thermionic devices usually only the filament is such that it can be heated during evacuation by passing a current through it. The other electrodes are heated by applying a positive poten- tial to them which is sufficiently high to enable the electrodes to rise to high temperatures by the bombardment, of the electrons coming from the hot filament. The extent to which the electrodes and walls of the vessel must be freed of gas depends on the temperature to which these parts of the tube rise during operation. If, for example, a tube is designed to operate on voltages ranging, say, from 15 to 50 volts, such as is the case with the type of tube commonly used as detector and amplifier in radio-receiving stations, it is not necessary to evacuate the tube so well that it can also operate satisfactorily at much higher "voltages. Such a tube while operating satis- factorily as a pure electron discharge device over the operating voltages stated above, may undergo a sufficient liberation of gas from electrodes to spoil the tube when the voltage is raised to, say, iOO volts or more. Tubes that are to operate on higher volt- ages and currents must have their electrodes more thoroughly freed of gas during the process of evacuation. The way in which the characteristic is influenced by the liber- ation of gas when a tube is subjected to voltages higher than those for which it is designed is shown in Fig. 31. These curves were obtained with a standard Western Electric VTl tube. It contains an oxide-coated filament and is designed to operate on voltages not higher than 100 volts. If the voltage is raised much beyond this value the electrodes become hot enough to liberate some of the gas occluded in them, and the amount of gas liberated increases as the potential difference between filament and plate is raised. This increases the amount of ionization by collision and causes the filament to be bombarded by the positive ions. The bom- bardment of the filament raises its temperature and increases the space current over the value that it would have if there were no positive ion bombardment. When the voltage becomes high enough the current increases rapidly. Such a rapid increase in the current is shown in the case of curve 1 (Fig. 31) to take place at about 400 volts, and in the case of curve 2 at about 300 volts. Tungsten filaments do not seem to be so sensitive to positive ion bombardment. It sometimes happens that the gas liberated 104 THERMIONIC VACUUM TUBE from the electrodes has a very pronounced effect in reducing the electron emission from the cathode and then the current instead of increasing may decrease at the higher voltages. If the voltage is raised to an excessive amount so much gas may be liberated as to spoil the tube permanently. On the other hand, the gas liberated can be cleaned up by the hot filament so that the tube automatically restores itself. This is especially the case with tungsten filaments. 100. 150 ZOO Z50 300 Anode Vq|ts FIG. 31. 350 400 450 50ft If the amount of gas liberated by applying an over-voltage is not excessive the tube will behave like a high vacuum tube on the lower or operating part of the characteristic, even after the gas has been liberated at the voltages corresponding to the saturation part. This is shown, for example, by Fig. 32, which represents a curve also obtained with a VT1 tube. When the voltage was raised to about 250 or 300 volts, the current began to increase rapidly, as shown by the continuous line. The broken line INFLUENCE OF GAS ON THE DISCHARGE 105 shows the currents obtained for decreasing voltage after the voltage had been raised to about 340 volts. It will be seen that on the upper part of the characteristic the currents obtained for de- creasing voltages differ considerably from those obtained for increasing voltages. On the infra-saturation part of the charac- teristic, however, the two curves coincide very well, showing that the amount of gas in the tube is not sufficient to cause any appre- ciable deviation for voltages lower than about 100 volts. Thermionic tubes as they are used to-day perform a large number of different functions, most of which require that the char- acteristic be steady and reproducible. This is, for example, the 10 ,150 ZOO Anode Volts FIG. 32. case where the tube is used as a telephone repeater. In order to insure this the procedure commonly adopted in practice is to apply a potential for about a minute or so, to the plate, which is higher than the normal operating voltages, and then test the tube to see if it performs properly the function for which it is designed. This test is commonly referred to as the " over- voltage test." If the tube is not sufficiently well evacuated the gas is liberated from the electrodes during the time that the over- voltage is applied. If the tube still functions properly after the application of the over-voltage, it means that the amount of gas liberated was not sufficient to have any deleterious effect on the operating part of the characteristic. The difference between the 106 THERMIONIC VACUUM TUBE over- volt age to be used in this test and the highest normal operating voltage depends on the margin of safety that it is desired to secure. 41. lonization at High Pressures. The ionization phenomena encountered in thermionic tubes belong to a class where the mean free path of the electrons in the gas is generally great compared with the distance between the electrodes. The phenomena resulting from the discharge at such pressures that the mean free path is smaller than the distance between the electrodes are more complicated and show the effect of cumulative ionization. In order to show this in an elementary way let us consider what happens when the mean free path is so small that in passing from cathode to anode an electron has a chance of colliding several times with gas molecules. Let the number of electrons start- ing from the cathode be no, and let the number of electrons formed by collision ionization in travers- ing a distance x from the cathode be n. (See Fig. 33.) The total number of electrons arriving at a plane distant x from the cathode is then n+no. FIG. 33. If each electron in moving through unit distance can dislodge a other electrons by collision, the number dislodged in a region of thickness dx at a distance x from the cathode will be* dn=(no+ri)adx. To find the total number N arriving at the anode, we have to in- tegrate this equation between the limits of n = when x = Q, and no~i-n = N when x d, the distance between cathode and anode. This gives: N = n e ad . This equation shows that the number of electrons reaching the anode, and therefore also the current through the tube, increases with increasing distance d between cathode and anode. This is in marked contrast to the discharge in high vacuum thermionic tubes in which, as was shown in the previous chapter, the satura- tion current is independent of the distance between cathode and anode, while the infra-saturation current decreases as the distance between cathode and anode is increased. INFLUENCE OF GAS ON THE DISCHARGE 107 42. Difference between Gas-free Discharge and Arc Discharge. There are other important differences between these two different types of discharge. The mercury arc is an example of a practical device which depends for its operation on ionization by collision, the gaseous medium being mercury vapor in equilibrium with the liquid mercury used as cathode. In a device containing a consider- able amount of gas and cold electrodes the discharge will not pass unless the applied voltage be made so high that the few electrons in the space can cause a small initial ionization. The positive ions so formed bombard the cathode and give up sufficient energy to the cathode to enable the electrons to overcome the force of attraction at the surface of the cathode and so escape from it. The discharge may also be started, as is done in the mercury arc, by bringing the cathode in contact with an auxiliary electrode and then striking the arc by separating them. This furnishes the initial ionization necessary to start the discharge. Thus, while electrons are liberated from the cathode in the pure electron device simply by external heating cf the cathode such as passing a heating current through it, in the gas-filled tube the electrons are liberated by bombardment of positive ions and also by photo- electric effects in the tube. The positive ions formed by collision ionization move toward the cathode and the electrons toward the anode. There is, thus, a predominance of positive space charge in the neighborhood of the cathode and a predominance of negative space charge near the anode. When the conditions are such that an arc discharge passes, the total space charge is small compared with that in the gas-free tube, where the space charge is negative only and has a maximum value near the cathode. The resistance of the arc is therefore lower than that of a gas-free tube. In order to maintain an arc steady it is necessary to connect it in series with an external resistance. The gas-free tube, on the other hand, does not need an external resistance to stabilize the discharge. On account of the frequent collisions in an arc there is also a great deal of recom- bination and this causes a pronounced blue glow in the tube. The gas-free tube, on the other hand, shows no blue glow. If a blue glow does accidentally appear, it is because the tube has been over-taxed and it may cause the tube to become inoperative. Another important difference between a pure electron discharge and an arc discharge is that the latter has a " falling characteris- 108 THERMIONIC VACUUM TUBE tic"; that is, its relation between current and voltage is given by a Curve such as AB (Fig. 34). The gas-free device, on the other hand, has a characteristic similar to OC. The difference between tubes containing these characteristics becomes apparent when we consider the corresponding a-c. resistances. The a-c. resist- ance for small current or voltage variations at any definite voltage is given by the reciprocal of the slope of the characteristic at a point corresponding to that voltage. Since the slope of the curve AB is negative, the arc has a negative resist- ance, while the resistance of a gas-free tube is positive. It is the negative resist- ance of the arc which enables it to produce sustained oscil- lations. It will be shown in Chapter VIII that a device Voltage FIG. 34. containing only two electrodes can only produce sustained oscillations if it has a negative resistance or a falling characteristic. The principle involved in the production of sustained oscillations by the audion or three- electrode thermionic tube is entirely different and depends on the controlling action of the grid on the electron flow from filament to anode. CHAPTER VI RECTIFICATION OF CURRENTS BY THE THERMIONIC VALVE 43. Conditions for Rectification. Let us consider a device on which can be impressed a simple harmonic voltage and let the current through the device be any function f(e) of the voltage, This function can always be expressed in a Fourier series, thus: n n f(e)=lQ+2a n smnx+2b n cosnx, . . . . (1) i i where /o, n and b n are constants. The summation terms of this series are simple harmonic functions, and will therefore vanish when integrated over a com- plete period. On the other hand IQ, being a constant, will be independent of such integration and can be measured with a d. c. measuring instrument. Hence, provided that IQ be not zero, the function f(e) will be such that the device will rectify. The fundamental condition for rectification by any device is therefore: r . . (2) This will be the case either when rf(e)dt = Q or / * f(e)dt=0 .... (3) or when * C JT T f(e)dt (4) Devices which comply with condition (3) are: (1) those which conduct current only in one direction and for which f(e) may be 109 110 THERMIONIC VACUUM TUBE any function of e in the transmission half period as, for example, the thermionic rectifier (Fig. 35); (2) those which conduct current only in one direction and for which f(e) is any finite function of e for all values of e greater than a minimum value e\. The electrolytic rectifier practically complies with this condition; - e + FIG. 35. during the transmission half period it does not conduct unless the applied voltage exceeds its back E.M.F. (Fig. 36.) Devices which comply with condition (4) are: (a) those which conduct current in both directions but for which f(e) is unsymmetrical with respect to the axis of current (Fig. 37); (6) those for which f(e) is a linear function of e, provided the input voltage exceeds a minimum value e\ (Fig. 38). FIG. 36. The three-electrode thermionic detector, or audion, cannot be called a rectifier, as far as the plate current is concerned, because it does not rectify the incoming current. This current only releases energy in the plate circuit which is supplied by the local plate battery, and the characteristic of the device is such that more energy is released during the one-half period than during the other. It will be seen that devices represented by the conditions (3) can RECTIFICATION OF CURRENTS BY THERMIONIC VALVE 111 be made to comply with condition (4) by inserting a local battery in the rectifier circuit so a? to shift the axis of current. But even with this modification they differ from the audion detector because they actually resolve the incoming currents into d-c. e FIG. 37. and a-c. components in the measuring circuit. The three- electrode device or audion therefore differs radically from these other types of radio detectors. A full discussion of the operation of the various types of rectifiers is beyond the scope of these pages. We shall therefore confine our attention to the thermionic rectifier or valve. Tel. Rec. FIG. 39. 44. The Fleming Valve. This device satisfies condition (3) and has a characteristic such as that shown in Fig. 35 (6). It consists of a filament which can be heated to incandescence and a plate, both placed in a highly evacuated bulb. In 1G05 Fleming l recognized the use of the rectifying properties of this device for the indication of high frequency oscillations, and used it as a 1 J. A. FLEMING, Proc. Roy. Soc., Jan., 1905, p. 476; IL S. Pat., 803, 684. 112 THERMIONIC VACUUM TUBE radio detector. The circuit in which Marconi used this device as a radio detector is shown in Fig. 39. 45. Valve Detector with Auxiliary Anode Battery. By our present standard of measurement the two-electrode tube is a very inefficient detector. It can be, and has been used more efficiently by operating on a chosen point of the current-voltage characteristic, thus making it fall in the class of rectifiers given by condition (4) instead of that represented by condition (3). This can be done by inserting a local battery in the circuit as shown in Fig. 40. 1 Tel. foe. FIG. 40. The operation of the device when used this way can be under- stood from the following : By the insertion of the battery E there is established in the circuit FPE a constant direct current which has a finite value even when no oscillations are impressed from the antenna. The current through the device can therefore be repre- sented by a function of the form I+i=f(E+esmpt), (5) where E is the local source of direct voltage, I the direct current due to E and i the superposed a-c. due to e. This can be expanded into a power series: f(E+e sin pt) =f(E)+f'(E)e sin pt e 2 sin 2 pt + e n sin n pi !See LEE DE FOREST, Proc. A.I.E.E., Vol. 25, p. 719, 1906, and J. A. FLEMING, Proc. Roy. Inst., Great Britain, June, 1909, p. 677. RECTIFICATION OF CURRENTS BY THERMIONIC VALVE 113 that is r "(E)^+ . . . +f(E)esmpt f/ffm ^cos2pt -f (E) ~ A + ... (6) If now this be integrated over a complete period the sine and cosine terms vanish. Of the remainder the termf(E) represents simply the direct current established in the circuit FPE by the e 2 battery E } and the series f"(E)--\- . . . represents direct current component established by the incoming oscillations. This series represents second and higher derivatives of the characteristic and hence if / is a linear function, the series vanishes and the device does not rectify. But the characteristic of the thermionic valve is not linear; the derivative series is therefore finite. This series generally converges so rapidly that all the terms except the e 2 first, }"(E), can be neglected, so that the rectified current can be given by the second derivative of the characteristic. It also follows from this that the rectified current is proportional to the square of the input voltage e. As an example let us take an arbitrary case in which the current in the device is proportional to the nth power of the voltage, thus: I = aE n . The rectified current is then given by ~-n(n If, for example, the current varies as the f-power of the applied voltage (n = %) the rectified current is inversely proportional to the square root of the locally applied voltage. If n = 2 the rectified current is independent of the local voltage while for higher values of n, it increases with the local voltage. It is well known that none of these cases applies to the valve when used as a radio detector, but that the rectified current shows a maximum for a definite value of the local voltage. This is due to the fact that the cathode is not an equipotential surface but a filament in which is established a voltage drop due to the heating current. In Chapter IV it was shown that if the voltage drop in 114 THERMIONIC VACUUM TUBE the filament is taken into account the characteristic of the valve can be represented by the two following equations: } E2. This condition is easily satisfied in practice. In Hull's set, for example, the values of LI, 2 and w happen to be such that their product is about 60. However, although this circuit, containing one inductance and two capacities is a decided improvement over the simpler one shown in Fig. 56, it is better to split the inductance and use the circuit of Fig. 59. This circuit has a decided advantage at lower load resistances, even when the inductances LI and L^ are each one-half of the value of LI when r-Tjl L/2 = 0. The percentage ratio of r as a function of log r for these Ur two cases is shown by curves III and IV of Fig. 58. Curve III was computed for the following values: Ci = C 2 = 10- 9 farad, LI = 100 henrys, co = 27rX4000. In curve IV the values were the same except that Li = L2 = 50 henrys. It can readily be seen that a frequency of 4000 is obtained in the filter circuit when the frequency of the voltage impressed at T is 2000 cycles, since by using two tubes as shown in Fig. 59, the condensers are charged up every half period of the voltage in T. Curve IV shows the value of a circuit like that shown in Fig. 59, when it is desired to have a rectifying set which is to operate with large variations in the load resistance. It will be evident that these circuits simply represent a type of wave filter which is supposed to filter out all frequencies except zero, that is, the direct current. The waves obtained in the output of these circuits comprise not only the fundamental frequency that we considered in the above computations, but also a number of harmonics which are generally weak compared with the funda- mental. It will be evident that harmonics must necessarily be present, considering that the wave, which has the form shown in Fig. 53 is not a pure sinusoid. Such a wave can always be ex- pressed in a Fourier series (equation 1). It will also be seen from ?Tjl the nature of the above equations for -^- that the harmonics L P will be damped out more effectively than the fundamental. They were therefore left out of consideration in the above calculations. Another type of circuit that could be used for smoothing out the voltage fluctuations was suggested to me by Mr. T. C. Fry, RECTIFICATION OF CURRENTS BY THERMIONIC VALVE 139 and is a special case of Campbell filter (Fig. 60). It has the ad- vantage that the capacities and inductances necessary are rela- tively small, which is always a good thing when rectifying very high voltages in view of the difficulty of constructing condensers of high capacity for high voltage work. FIG. 60. The characteristic of this filter is seen from Fig. 61, where the current attenuation produced by the filter is plotted against the frequency. The capacities and inductances can be so chosen that the fundamental frequency, , is that which gives infinite ZTT attenuation. This frequency will therefore not be present in the Frequency FIG. 61. load resistance. The filter would transmit lower frequencies than , but such frequencies, except zero, are not present when 2vr represents the fundamental. Hence, for all frequencies below 140 THERMIONIC VACUUM TUBE only direct current is transmitted. The higher frequencies 2-7T will be transmitted and they will be present in the form of harmon- ics. These are, however, so weak that when attenuated to the extent shown by the curve to the right of , their effect in the load ZTT is practically nil. It will be evident from the nature of the attenu- ation curve that when using such a filter the frequency of the input must be adjusted rather accurately to the value determined by the constants of the filter. Figs. 59 and 60 show only two filter sections. If desired, better results can be obtained by adding more sections. Before leaving this subject let us discuss briefly the relative value of a few types of circuits, considering mainly the arrange- ments of the valves irrespective of the type of filter used in the output circuit. The circuit shown in Fig. 59 is arranged to make use of both half waves. The voltage fluctuation at the condenser C\ will therefore be of double the frequency of the wave supplied through the transformer T. The potential of points A and B (Fig. 59) will always be 180 out of phase, but only when they are positive with respect to will the voltage be effective in charging up the con- densers. If the potentials of A and B be represented by the broken lines A' and B' (Fig. 62) the potential fluctuation at the condenser FIG. 62. will be represented by the curve CD, which possesses a fundamental whose frequency is twice that of the waves A' and B'. This is an advantage because it follows from equation (32) that the higher the frequency, the more effectively will the fluctuation be smoothed out by the filter. On the other hand this circuit has the disad- vantage that the voltage impressed on the valves is only half that supplied by the transformer. In order to use the full transformer voltage we could resort to the arrangement shown in Fig. 55, replacing r by the filter and load resistance shown in Fig. 59. RECTIFICATION OF CURRENTS BY THERMIONIC VALVE 141 Fig. 63 shows a circuit whereby the transformer voltage 1 can be doubled. When the transformer voltage is such that D is at a positive potential with respect to 0, an electron current will flow in the direction of the arrow through the valve AD, thus charging the condenser C such that A is positive with respect to 0. But during this half period no current will flow through DB. During D rL FIG. 63. the next half cycle current flows only through DB, charging B negatively with respect to 0. The potential difference between A and B (if the condensers did not discharge themselves) would therefore be twice the transformer voltage. What actually happens is that the one condenser discharges through the load while the other is being charged. Hence if the broken line (Fig. 64) FIG. 64. represents the potential of the point D with respect to 0, the curves A 'A' and B'B 1 will represent the potentials of A and B respect- ively with regard to 0. The potential difference between A and B is therefore obtained by adding the curves A' and B f and is given by EE. Thus, although the condensers are charged only in alternate 1 H. GREINACHER, Verb. d. D. Phys. Gesell., Vol. 16, p. 320, 1914. 142 THERMIONIC VACUUM TUBE half periods, the voltage fluctuation in the circuit leading to the filter is double the frequency of the impressed voltage, while the mean voltage on the filter is approximately twice the impressed voltage. It will be observed from the above discussion that there are various ways in which thermionic valves can be used for increas- ing frequency. For laboratory work it is often necessary to have a source of fairly high constant voltage supplying very small currents, such as would be needed, for example, in the study of photo-electric phenomena, ionization of gases by radium or X-rays, measurement of the intensity of X-rays with the ionization chamber, etc. For such purposes the thermionic valve could be used to replace the rather troublesome high voltage batteries frequently used in university laboratories, which consist of a large number of min- iature storage or dry cells. In fact, the high voltage desired could be obtained from any standard storage or dry cell battery of a few volts, which forms part of the equipment of any physi- cal laboratory, by connecting the primary of the transformer to the low voltage battery through an interrupter. This could, for example, be done by using a small Ruhmkorff coil with an ordi- nary hammer break. Since the desired current is small the valves could be designed to operate with very small power expenditure in the filament. It must, however, be remembered that when using the device for the purposes mentioned, the load resistance is usually very high, and hence, in order to prevent the condensers from discharging through the valves during the blocking half peri- ods, the valves should be designed to have the lowest possible electrostatic capacity and the frequency of interruption of the primary current should not be very high. 51. The Thermionic Valve as a Voltage Regulator. The rapid increase in the saturation thermionic current with increase in the filament temperature, or filament heating current, as is shown by Richardson's equation, can be utilized to control the voltage of the generator of varying speed. A scheme whereby this can be done, and which was devised by H. M. Stoller, is shown in Fig. 65. Here the tube is used to regulate the voltage supplied by a wind-driven generator such as has been used on airplanes. The generator is designed to supply a high voltage for the plate circuit of thermionic tubes and a low voltage for heating the RECTIFICATION OF CURRENTS BY THERMIONIC VALVE 143 filaments. D and M are the differential and main field windings of the generator. The thermionic valve is inserted as indicated High Voltage () Common Voltage FIG. 65 FIG. 66. at V. The characteristics of such a valve are shown in Fig. 66. Suppose, now, that the speed of the generator is so low that the 144 THERMIONIC VACUUM TUBE current flowing through the filament of the valve is 1.2 amperes. With this filament current the thermionic current through the valve and the differential winding is small and practically the full voltage is obtained. If, now, the speed of the generator increases, the filament current of the valve increases, but this causes a pro- portionately much greater increase in the thermionic current which flows through D. Thus Fig. 66 shows that a small change in the filament current of from 1.2 to 1.4 amperes causes a five- 100 4,000 6,000 Revolutions Per Minute FIG. 67 10,000 12,000 fold increase in the thermionic current. This causes a decrease in the field flux of the generator, thus restricting the increase in the output voltage. The regulation obtained with such a device is shown in Fig. 67. HH and LL represent the high and low output voltages as a func- tion of the speed of the generator, and it will be seen that although the speed changes from about 4000 to over 12,000 R.P.M., the voltage output remains practically constant. -,:-- CHAPTER VII THE THERMIONIC AMPLIFIER EXCEPT for the derivation in Chapter III, of a few fundamental relationships that govern the discharge in three-electrode devices, we have so far considered only the simple type of device containing two electrodes. The physical principles underlying the thermionic tubes discussed in the previous chapters are applicable also to the three-electrode type of thermionic tube which it is our purpose to treat in this and the following chapters. This device consists essentially of a highly evacuated vessel, containing a thermionic cathode, usually in the form of a filament which can be heated by passing a current through it, an anode and a discharge-controlling electrode which generally takes the form of a wire mesh or grid, and placed between the cathode and anode. This third electrode can, however, be of any form, since a controlling effect on the discharge can be obtained by so positioning a conductor with respect to the path of the discharge that potential variations applied to it will cause variations in the current flowing between cathode and anode. The controlling electrode may, for example, be in the form of a plate placed on the side of the cathode opposite to that of the anode or in the form of a wire or a plurality of wires galvanically connected and placed in the plane of the cathode parallel to that of the anode. The theory of operation of the device to be given in the following applies to these various struc- tures, but will be explained with particular reference to the case in which the auxiliary or discharge-controlling electrode takes the form most commonly used in practice, namely, a grid placed between cathode and anode. This was suggested by Lee de Forest. 1 Originally he used the device, which he called the " audion " as a radio detector. It has since developed, however, that its use is not by any means limited to this field, it being now 1 U. S. Patents No. 841387, 1907; No. 879532, 1908. 146 THERMIONIC VACUUM TUBE used extensively also as amplifier, oscillation generator, and in a large number of widely varying applications. Fig. 68 shows a commercial type of thermionic amplifier. 52. Action of the Auxiliary Electrode. It was shown in Chapter III, page 42, that the relation between the electron current to the anode or plate, and the potentials applied to the grid and plate with respect to the filament, can be expressed in a simple way by making use of the writer's linear stray field relation : (1) which means that if the grid and filament be at the same potential, a potential difference E p between filament (or grid) and plate, _^ < causes a stray field to act through the openings of the grid which is equivalent to the field that would be produced if a potential difference equal to were applied directly between the filament and a plane coincident with that of the grid. The small quantity e represents an intrinsic potential difference be- tween the filament and the system constituted by the grid and plate. The constant /x depends on the structure of the device (see p. 226). If we now apply a potential differ- ence Eg directly between filament and grid, the effective voltage in the tube is obtained simply by adding E s and E tt , and the current can be expressed as a function of this sum, thus FIG. 68. Before discussing this relationship, let us look more fully into the functions of the two quantities E s and E . To simplify matters somewhat we shall neglect the effect of the small quantity e. In Fig. 69, the distribution of the field intensity in the region THE THERMIONIC AMPLIFIER 147 between cathode and anode of a three-electrode device is repre- sented by means of lines of force. The anode is assumed to remain at a constant positive potential with respect to the cathode, the potential of which we can call zero. The three diagrams shown refer to the cases in which the potential of the grid is positive, zero and negative. Looking upon the intensity of the field as the num- ber of lines of force passing through unit area, it will readily be seen in a general way how the potential of the grid affects the flow of electrons from the cathode. But before considering the flow of electrons it must be pointed out that the diagrams in Fig. 69 represent the distribution of field intensity only for the case in which the space between cathode 6 FIG. 69. and anode is free from any dislodged electric charges. As soon as charges are introduced, such as electrons moving from cathode to anode, some of the lines of force proceeding from the anode will end on the electrons, and hence the density of the lines of force, i.e., the intensity of the field or the potential gradient, will be greater near the anode and less near the cathode than indicated in Fig. 69. This space charge effect can be made, clearer by representing the field intensity as shown in Figs. 70 and 71. Fig. 70 shows the case in which there are no electrons in the space, such as would be the case if the cathode were cold. BP repre- sents the potential of the anode, that of the cathode being zero. The potential gradient (or field intensity)' is given by the slope of the lines PaO, etc. It is easily seen that the field between 148 THERMIONIC VACUUM TUBE cathode and grid is the resultant of E s and E g . The lines PaO, PbO and PcO therefore represent the distribution of field intensity for the three cases in which E s +E g is greater than, equal to or less than zero. If, now, the cathode be hot enough to cause a copious emission of electrons from it, the field intensity is no longer a linear function of the distance between cathode and anode, but can be represented in a rough way by the curves shown in Fig. 71. If E,+E g >0, the field distribution can be represented somewhat by the curve OaP. If E 5 +EofO, the field between the cathode and the equivalent grid plane is negative and the emitted electrons are FIG. 70. FIG. 71. returned to the cathode. The curvature of the lines 06 and Oc is due to the initial velocities of the electrons (see Fig. 21). The lines of force proceeding from the anode that reach through the grid represent the stray field due to E s , which therefore tends to draw the electrons through the grid and throw them on to the anode. By varying the potential E g of the grid the intensity of the field between the grid and cathode is varied in such a manner that the effect of E g is similar to that of E s , and whether or not electrons will flow away from the cathode depends on the resultant value of E s and E g . Now, E s is always positive and therefore E,+E g will be positive (1) when E g is positive, and (2) if E g is nega- tive and less than E,. ' (1) When Eg is positive some of the electrons moving away THE THERMIONIC AMPLIFIER 149 from the cathode are drawn to the grid (see Fig. 69), while the rest are drawn through the openings of the grid to the anode under the influence of E s . The relative number of electrons going to and through the grid depends upon the mesh of the grid, the diameter of the grid wires and the relative values of E s and E a . When, for example E s is large compared with E g the number of electrons going to the grid is comparatively small, but for any fixed value of E, the grid current increases rapidly with increase in Eg. Hence, for positive values of E g current will be established in the grid circuit FGE g (Fig. 72). (2) If, however, E g is negative and less than E s , as is generally the case, nearly all the electrons drawn away from the cathode pass to the plate, practically none going to the grid. In this case the resistance of the grid circuit is practically infinite for low frequen- FIG. 72. cies. The electrostatic capacities between the electrodes causes the impedance between filament and grid to have a value depending on the output circuit. For the present we shall neglect this effect, which is usually small, and later on investigate the conditions under which it can manifest itself to a marked extent. If, now, an alternating E.M.F. be impressed on the grid circuit so that the grid becomes alternately positive and negative with respect to the filament or cathode, the resistance of the grid circuit FGE g which is usually referred to as the input circuit, will, if the frequency is not too high, be practically infinite for the half cycle that the grid is negative and finite but variable for the positive half cycle. If, on the other hand, the alternating E.M.F. be superimposed upon a constant negative grid potential, which is so chosen with respect to the value of the impressed alternating voltage that the grid always remains negative with respect to the filament, the resistance of the input circuit is infinite. 150 THERMIONIC VACUUM TUBE It can now be seen in a general way how the device functions as a relay. Any variation in the grid potential changes the in- tensity of the field between filament and grid, resulting in a corre- sponding change in the number of electrons moving from fila- ment to plate. Hence potential variations set up between filament and grid cause variations in current in the output circuit PE b r , the power developed in the load TQ being greater than that expended in the input circuit. 53. Current-voltage Characteristics of the Thermionic Ampli- fier. Returning now to a consideration of the expression for the current (2) it is to be noticed in the first place that since this equation contains two independent variables, E p and E ff , the three-electrode device possesses two families of characteristics, or the complete charac- teristic can be represented by a surface. The current as a function of the filament-plate voltage E p can for various negative values of filament-grid voltage E g be represented by a series of curves such as those shown in Fig. 73. It will be noticed that each of these curves is similar to the current-voltage characteristic of the simple two-electrode thermionic valve discussed in Chapter IV. The main difference is that in the three-electrode tube the current is limited not only by space charge and the voltage drop in the filament, but also by the grid. For the same potential on the plate the current in the three-electrode tube will therefore be smaller than in a simple valve. This follows directly from quation (2). The relation between I p and E ff for various values of E p can be expressed by a set of curves similar to those shown in Fig. 73. Fig. 74 shows such a set of characteristics. The ordinates repre- sent current to the plate and not necessarily the emission current, i.e., total current from the filament. When the grid becomes posi- tive it takes current and so can distort the I p , E g curves. A set of grid current curves for various plate potentials is shown in Fig. 75. For the higher plate potentials these curves show a maximum. This is due to secondary electron emission from the grid by the impact of electrons coming from the filament (see p. 47) . At the E lower plate potentials the stray field given by is smaller, and THE THERMIONIC AMPLIFIER 151 fewer electrons are attracted to the plate. The secondary electron emission is then also less marked, so that the I g E g curve shows a rapid increase of I g with increasing *E g . So far it has not been possible to derive the equation of the whole characteristic theoretically with sufficient accuracy. For 150 Anode Volts FIG. 73. the operating range of the characteristic, when the tube functions as an amplifier, the plate current can be expressed by the equation. 1 (3) where 2E P and 2E g are the filament-plate and filament-grid 1 H. J. VAN DER BIJL, Phys. Rev., Vol. 12, p. 180, 1918. 152 THERMIONIC VACUUM TUBE voltages. If, for example, an alternating e.m.f. e sin pt be impressed on the grid circuit the equation takes the form: sn (4) Grid Voltb. FIG. 74 This equation was determined empirically and is subject to certain limitations. In the first place, it does not apply to the horizontal part of the characteristic which gives the saturation current, but only to that part which obtains when the filament is hot enough to emit more electrons than are needed for the current convection through the tube. This is the condition under which the amplifier operates, because here the plate current can be THE THERMIONIC AMPLIFIER 153 varied by varying any of the applied voltages. Another condition for equation (4) is that the grid should not become sufficiently positive to distort the characteristic. Under these conditions I have generally found this equation to hold sufficiently well, to a first approximation at least, and have been using it in connection with work on the amplifier tube. The above equation does, how- ever, not hold sufficiently accurately for purposes of radio detection, since this is determined by second order quantities. 15 20 25 30 35 40 0.4 FIG. 75. Latour 1 has derived some equations for the " relay effect " of audion tubes. He starts from the general functional expressions for the plate and grid currents: I f =F(E p} Eg) and I g =f(E g , E p ). In the expansion of these equations he neglects all quantities of the second and higher order, thus assuming that the current and voltage variations are very small, or that the characteristic is linear over the operating range. 1 M. LATOUR, Electrician, December, 1916. 154 THERMIONIC VACUUM TUBE Vallauri 1 also assumes a linear characteristic by expressing the equation for the plate current in the form: I p = aE +bE P +c. It will be shown later that it is important to distinguish between the characteristic of the tube itself and that of the tube and exter- nal circuit combined. The latter can by taking special precau- tions be made practically linear. The characteristic of the tube itself can, however, not be regarded as linear over the range over which most amplifiers operate. The curvature of the characteris- tic cannot be neglected because it introduces distortion which, unless properly taken care of, makes it practically worthless as a telephone repeater, for example, on long telephone lines. When treating the tube as an oscillation generator the curvature of the characteristic can be neglected, because the oscillation current is established in an oscillation circuit which is usually tuned suf- ficiently sharply to eliminate the harmonics caused by the curva- ture of the characteristic. Equation (3) gives the characteristic of the tube itself; that is, E p and E g are the potentials of the plate and grid with respect to the filament, and are not necessarily equal to the plate and grid battery voltages. E p is, for example, only equal to the plate battery voltage E b when the external resistance TQ is zero (Fig. 72) . When TO is not zero the potential drop established in ro by the cur- rent in the plate circuit causes a decrease in E p , and it can readily be seen that if the current be varied, by varying the grid potential, E p becomes a function of the plate current. This effect will be discussed more fully when we come to consider the characteristic of the tube and circuit (Section 58). Langmuir 2 has expressed the equation for the characteristic as I p =A(E p +kE Y /2 . The extent to which the characteristics of practical tubes depart from the f-power relation was discussed in Chapter IV. In the case of the two-electrode tube the main cause of the devia- tion is the voltage drop in the filament. This has a greater 1 G. VALLAURI, L'Elettrotecnica, Vol. 4, 1917, Electrician, Vol. 80, p. 470, 1917. 2 I. LANGMUIR, Proc. I.R.E., p. 278, 1915. THE THERMIONIC AMPLIFIER 155 effect at the lower than at the higher voltages. In three-electrode tubes the limitation of current by the grid accentuates this devia- tion. Thus, referring to equation (3), the constant ;u is generally greater than unity and, therefore, although the plate voltage (E \ +.#0+ e) is low, so that the voltage drop in the filament has a relatively greater effect in causing a deviation from the | -power relation. As an example, suppose that ^=100 volts; M = 5; the voltage in the filament E/=lQj and E g +e = Q. Then the effective voltage is only twice the voltage drop in the filament. Under such conditions the deviation from the f -power relation is considerable. It is for this reason that the quadratic equation (3) is generally found to be more serviceable at least for that range of the characteristic over which the tube operates as an amplifier. The quantity e, which depends on the intrinsic potential difference between the filament and the system constituting the grid and plate, is usually small, but may, in some types of tubes, vary considerably. For tubes operating with high effective voltages e can generally be neglected. But when the effective voltage is low, as in the detector and small amplifier tubes, variations in e can, if not corrected for, cause deviations in the exponent of the effect- ive voltage. The important thing about the tube equation is that the cur- rent can be expressed as a function of (Ep+^Eg) 1 . Referring to equation (3) and Fig. 74, we see that the current is finite for negative values of the grid potential, and is reduced to zero only when H- E g =- p?+e )=E S (5) This linear relation and equation (3) can be verified experi- mentally when the constants ^ and e are known. These constants 1 This expression for the effective voltage in a three-electrode tube was established experimentally by the author and published in 1913 (Verh. d. D. Phys. Gesell., Vol. 15, p. 330, 1913). See also p. 44. The same expression has also been used by SCHOTTKY (Archiv. f. Elektrotechnik, Vol. 8, p. 1, 1919. BARKHAUSEN (Jahrb. d. drahtlosen Tel. & Tel., Vol. 14, p. 27, 1919) and others. See also W. H. ECCLES (Rad. Rev., Vol. 1, p. 69, Nov., 1919). 156 THERMIONIC VACUUM TUBE can be determined by methods which do not involve the exponent of equation (3). Let us assume a general exponent /3, thus: Assuming the general case in which both E p and E are variable, we have: dl p= 3l p dE p dl p dE g SEpdEffdEg' Now Hence /IT /w. \ 0-i/f ,77? \ -_ (6) Since the current can be varied by varying either one or both of the independent variables E p and E g , we can make these varia- tions in accordance with the condition that the current I p remains constant; for example, the current can be first increased by increasing E p and then brought back to its original value by increasing the negative grid voltage E g . The relation between the variations in E p and E necessary to keep the current con- stant, can be obtained by putting I p = constant in equation (6). Then we have either = . ....... (5a) or These equations are therefore independent of the exponent of (3). Equation (5a) obviously states the condition that the current has the constant value zero, and shows that the stray field poten- tial E s is simply equal to the absolute value of the grid potential which is necessary to reduce the plate current to zero. Referring to the above equations for the partial derivatives of IP, it follows that a change iii the grid potential produces ju-times as THE THERMIONIC AMPLIFIER 157 great a change in the plate current as an equal change in the plate voltage. Equation (7) can be interpreted to mean that a potential varia- tion 5E g = e g impressed between the grid and the filament is equiv- alent to introducing an E.M.F. in the plate circuit which is equal to fjLe g . This result is of fundamental importance and has been found of great value in the solution of many vacuum tube problems. 1600, 1400 J 1200 1000 1-8 ZA- Grid FIG. 76. Integrating equation (7) we get E' P = E p +nE g ........ (8) While equation (5a) gives the relation between E p and E g necessary to neutralize the stray field and keep the current zero, equation (7) gives the relation necessary to keep the current constant at any convenient value. The verification of these relations is shown in Fig. 76. l The slope of these curves is equal to the constant /z. 1 H. J. VAN DER BIJL, Phys. Rev., Vol. 12, p. 171, 1918. See also Fig. 14, p. 45. 158 THERMIONIC VACUUM TUBE The characteristic equation (3) was verified as follows: The tube was inserted in a circuit such as shown in Fig. 72, with the exception that the generator in the input circuit and the resist- ance ro were omitted. A convenient negative potential was applied to the grid, so that no current could be established in the grid 600 800 circuit, and the current in the plate circuit observed as a function of the plate voltage E p . Since ro was zero.Ep was always equal to E b) the plate battery voltage. The grid being kept at a constant negative potential E g with respect to the filament, current could pi not be established in the plate circuit until the + e became M greater than E . The characteristic obtained is shown in Fig. 77. THE THERMIONIC AMPLIFIER 159 From the value of the plate voltage for which the current is just reduced to zero we get E4 ,5 I V o 40 80 160 IQQ 240 280 FIG. 78. and since & could be determined as explained above, this equation could be used to give e. Once /z and c are known the observed current can be plotted as a function of the expression for arbitrary values of E p or E g . Some curves obtained in this way are shown in Fig. 78. If we obtain a number of characteristics such as those shown 160 THERMIONIC VACUUM TUBE in Fig. 74, which show the relations between the plate current and grid potential for a number of different plate potentials and plot the logarithms of I p against the logarithms of the effective voltage ( -f- Eg] the observed points for all the characteristics should, x M according to equation (3), lie on one straight line. This can be done by subtracting the applied grid potentials from the grid potential which is just necessary to reduce the current to zero, and plotting on logarithmic paper the values so obtained against the observed currents. (Note that the value of the grid potential pi necessary to reduce the current to zero is .) The disadvantage of such a procedure lies in the uncertainty of the voltage at which the current becomes zero. However, the logarithmic plot of the curves of Fig. 74, and which is shown in Fig. 79 indicates a substan- tially good verification of equation (3). The slope of this lumped logarithmic line is almost exactly 2. 54. Amplification Constant. The constant ju appearing in the above equations is one of the most important constants of the audion or three-electrode tube. It will be shown later that /-c is the maximum voltage amplification obtainable from the tube. This constant is also very instrumental in determining the current and power amplification and can therefore be referred to as the ampli- fication constant. This constant plays an important part in all functions of the tube, as will be shown later when we come to consider its use as a radio detector, modulator, oscillation gen- erator, etc. It will be noticed that since it appears in the stray field relation (equation (1)), which is a pure potential relation, the amplification constant is a function only of the geometry of the tube. It depends, for example, on the mesh of the grid, diameter of the grid wire and the distance between grid and plate. It can be determined from E P E curves shown in Fig. 76 and by methods which will be described later. In practice it is generally found that // is not quite constant, its value decreasing somewhat at lower voltages. For the operating range of voltages commonly employed its value does, however, not vary much. (See Fig. 125.) 55. Plate Resistance and Impedance. The resistance of a tube is due to the work which the electrons emitted from the cathode must do in moving from cathode to anode. Let us consider the case of a single electron emitted from the cathode. In moving THE THERMIONIC AMPLIFIER 161 through the cathode surface it has to do an amount of work equivalent to the electron affinity and in moving from cathode to anode it has to do work in overcoming the contact potential difference between cathode and anode. This may sometimes assist the electron in moving from cathode to anode. (See Chap- ter III.) The total amount of work it has to do to overcome these o rcs CD ^ -K t * - ZO 30 40 FIG. 79. forces is generally small and never amounts to more than a drop of a few volts. If these were the only forces exerted on a large num- ber of electrons escaping from the cathode the application of a small voltage between cathode and anode would almost immediately give rise to the saturation current, and the resistance of the tube would for all values of current less than the saturation current be very low. This is, however, not the case, since the electrons 162 THERMIONIC VACUUM TUBE in the space exert a mutual repelling force on one another. This is the space charge effect explained in Chapters I and IV, and causes by far the greatest expenditure of energy on the part of the electrons in moving to the anode. This expenditure of energy causes the heating of the anode. The true d-c. resistance of the tube is, of course, given simply by the ratio of the total amount of work done to the square of Tjl the current, i.e., by j^. The a-c. resistance on the other hand, is IP given by the slope of the plate current characteristic, and since the characteristic is non-linear the a-c. and d-c. resistances are not the same. Referring to Fig. 80, the d-c. resistance at a voltage E p is FIG. 80. given by the reciprocal of the slope of the straight line OC, while the impedance of the tube is given by the ratio of the alternating voltage e p between filament and plate to the alternating current i p in the plate circuit. Now, the flow of electrons in the tube shows no lag, and for frequencies low enough to make the effect of the electrostatic capacity of the tube itself negligibly small, the condensive reactance thus being also practically infinite, the /> /^/7 impedance is simply given by -^=-r (see Fig. 80), and is then lp CLO of the nature of a pure resistance. For most tubes used at present this approximation is satisfactory for frequencies up to the order of several hundred thousand cycles per second. For a tube like that shown in Fig. 68, for example the filament-plate capacity is of THE THERMIONIC AMPLIFIER 163 the order of a few micro-microfarads. Now we have ^-~ e p dE P when e p and i p are very small. But in practice we generally do not deal with very small current variations. To obtain an expression for a-c. resistance for finite variations we must evaluate the partial derivative ^- from the equation of the characteristic and integrate it over a complete cycle of variations, thus: ,, For frequencies at which the electrostatic capacity of the tube cannot be regarded as negligibly small, we have in effect a condenser in shunt with the tube resistance. If x is the reactance due to the capacity of the tube the plate impedance Z p can be obtained from the admittance Y p : where p rf+4 (10) (11) To evaluate expression (9) let us assume a general exponent for the characteristic equation: Then where Hence . . . . (12) oinE y n - 2-jriJL 1 r -j, ( 1+ i sin ^ n-l Now the maximum value e of the input voltage is never greater than E y ; for distortionless amplification e must always 164 THERMIONIC VACUUM TUBE be less than E y (see Section 60). Referring, for example, to Fig. 81, it will be seen that E y is the intercept cd when E g = or fd when E g = cf. Taking the latter case it will be seen that the maximum value of the input voltage e should not exceed the value fd otherwise we would be working beyond the point d, and then the lower peaks of the output current wave would be chopped off Grid Voltage FIG. 81. thus introducing harmonics. Furthermore, since the maximum value of sin pt is unity and its odd powers vanish on integration the expression in the parentheses can be expanded into a series, the integral of which converges sufficiently rapidly to enable us to compute the resistance, for all practical values of n, from a few terms of the expansion. The integrated series is: THE THERMIONIC AMPLIFIER 165 (n-1) . . . (n-4)/ e \ 4 1 _ssessed by the tube is capacitive and is due to the electrostatic capacity between the electrodes. It is, therefore, in effect, a capacity shunted across the plate resistance. The capacity of v>rdinary tubes, is, however, so small (of the order of a few centi- meters) that this parallel reactance can be regarded as practically, infinite for frequencies ranging up to several hundred thousand cycles per second. Hence, for this range of frequencies the THE THERMIONIC AMPLIFIER 173 dynamic characteristic of the tube coincides with its static char- acteristic. (2) If the external resistance r (Fig. 72), instead of being zero, has a finite value and is non-inductive, the dynamic charac- teristic still coincides with the static characteristic, but they are different from the characteristic of the tube itself, being given by Figs. 84 and 85 instead of those shown in Fig. 74. The effect of the external non-inductive resistance on the characteristic of the output circuit, when an alternating potential is impressed on the grid, can be explained as follows: Referring FIG. 86. to Fig. 86, let the three parabolic curves represent the characteris- tics of the tube itself, the middle one of which, let us say, is the one obtained when the plate-filament voltage has a definite value E p . The other two are the characteristics for higher and lower values of E p . Let the tube be inserted in the circuit shown in Fig. 72. Let the constant grid battery voltage E tt be so adjusted that the direct current in the plate circuit, as measured with A, is mo. Now, on account of the voltage drop in TO, due to the current I p in it, the plate-filament voltage is E p = E b rol p . If I p be varied by impressing an alternating potential on the grid, E p varies accordingly since E* is constant. Thus, if the negative grid poten- tial is decreased the plate current increases. This causes E p to decrease to the value, say, corresponding to the lower characteris- tic shown in Fig. 86, and the current instead of increasing to a', 174 THERMIONIC VACUUM TUBE as it would if E p remained constant, increases only to a. For the same reason, when the negative grid potential is increased the cur- rent decreases only to b instead of to &'. The characteristic there- fore straightens out and takes the shape given by boa, instead of b'oa'. Referring to equation (20), t will be seen hat if we represent the alternating plate voltage and current by e p and i p) respectively, we have e p = i p ro. The plate current and plate voltage are there- fore 180 out of phase. The plate current is, however, in phase with the grid potential, so that the grid and plate potentials differ in phase by 180. FIG. 87. (3) Let the plate circuit now contain reactance as well as resistance, that is, let it contain an impedance Zo=ro+jxo. Here we have e p = i p Z^ but on account of the reactance XQ in the plate circuit the phase difference between the plate and grid potentials may differ from 180. When this happens the dynamic character- istic of the plate circuit takes the form of a loop. To explain this we can make use of the theorem stated on page 157, that a voltage e g applied between filament and grid is equivalent to an electromotive force ne g impressed on the plate circuit, where M is the amplification constant of the tube. The phase relations are shown in Fig. 87 for various values of the angle = tan~ 1 of the external impedance. Let the plate current be represented THE THERMIONIC AMPLIFIER 175 by i p in the direction OQP. The voltage drop i p r p , in the tube, due to its plate resistance, is given by OQ. The drop i p Zo in the external impedance ZQ is given by Qa. Thus, in the case in which the angle is 45, i P ZQ=Qa2, and is the vector sum v*o and ipXo, the total driving E.M.F., ^e a in the plate circuit is in this case given by Oa^. Now e p is equal to i p Zo and is given by Oc2, Grid Volfs FIG. 88. which is parallel to Qaz. The phase difference between e v and peg or e g is therefore equal to the angle a^Oc^ which is 157.5. This is for the case in which the external impedance Z is numeri- cally equal to the plate resistance r P (OQ = Qd2), and has an angle of 45. Referring now to Fig. 88, let the negative grid battery voltage 176 THERMIONIC VACUUM TUBE be equal to MS, so that we operate around the point of the tube characteristic A OB, which corresponds to the plate potential which obtains when the alternating potential impressed on the grid is zero. Tne other two tube characteristics are for the maxi- mum and minimum potentials which the plate acquires when an alternating potential e sin pt is superimposed on the constant negative grid potential E g = MS. If we now plot the plate cur- rent as a function of the varying grid potential e ff , considering at the same time that e g and the alternating plate potential e p are 157.5 out of phase, we obtain the loop shown in Fig. 88. The loop is, of course, due to the reactance in the external circuit, because there is no lag within the tube. This loop is not an ellipse, but has a curved axis CD, the general slope and curvature of which depends upon the angle between e g and e p , which in turn depends upon the angle $ of the external impedance. As <> decreases the loop nar- rows down, its axis straightens out and rotates in a clock-wise direction until, when is zero, that is, when the external circuit contains only non-reactive resistance, the loop degenerates into the line EF, which is the non-reactive dynamic characteristic boa shown in Fig. 86. It will be observed that if the angle 6 between e g and e p is 157.5, the axis of the loop very nearly coincides with the approximately straight line EF obtained when 6 is 180. The angle 6 depends not only on 0, the angle of the external impedance ZQ, but also on the value of this impedance compared with the plate resistance r P . Thus if is 90 then i p Zo is given by Qct4, and if ZQ is numerically equal to r p , the angle a^Oc* between e a and e p is 0= 135. But if Z =3r P , the angle 8 is about 160. In this case also the axis of the dynamic characteristic coincides very nearly with the line EF which is obtained when 0=180. It is important to note the conditions that must be secured to make the axis of the dynamic characteristic approach a straight line. While the curvature of the characteristic enables the thermionic tube to perform certain very important functions, such as detection and modulation of oscillating currents, it is nevertheless an undesirable feature when the tube operates as an amplifier. It follows from the explanation given in Section 57 that unless the characteristic is straight the output current wave is not an exact enlarged reproduction of the wave impressed on the input. This causes distortion when amplifying telephonic cur- THE THERMIONIC AMPLIFIER 177 rents, and to avoid it the amplifier must be operated under such conditions that its characteristic is substantially linear. Now, it will be shown later that when operating the tube as an ampli- fier, maximum power amplification is obtained when the external impedance is numerically equal to the plate resistance of the tube. If this equality is preserved and the angle of the external imped- ance is not greater than about 45, the axis of the characteristic is, as we have seen, substantially linear over a considerable range of input voltage. In practice the conditions are often even better, because the angle of the external impedance is often much less than 45. This is, for example, the case where the tube is operated as a telephone repeater; the secondary of the output transformer feeds into a long line of comparatively high resistance, so that the angle of the effective impedance into which the tube works is very small. In cases where the angle of the external impedance is neces- sarily large, we can still secure a practically linear axis for the dynamic characteristic by making the external impedance larger than the plate resistance. We would therefore gain in quality of transmission at the expense of amplification. But the necessary sacrifice in amplification would not be large. Although maximum amplification is secured when the external impedance is equal to the plate resistance, the decrease in amplification is small even when the external impedance is twice as large as the plate resist- ance (see Fig. 112). If the necessary precautions be taken to secure the conditions necessary to make the axis of the dynamic characteristic substan- tially linear, we can extend the theorem deduced on page 157 from the stray field relation: A voltage e g applied between filament and grid establishes a current in the plate circuit which is given by ...... ' (22) where ju is the amplification constant of the tube r p its plate resist- ance and ZQ the external impedance in the plate circuit. If the conditions are not such as to make the characteristic linear this equation is still true as far as the fundamental frequency is concerned, but the curvature of the characteristic introduces harmonics which would necessitate the addition of terms of higher order of smallness to equation (22). 17$ THERMIONIC VACUUM TUBE The theorem embodied in eauation (22) is of fundamental importance and is instrumental in the solution of many vacuum tube problems. We shall have occasion to make extensive use of it in what follows. t 60. Conditions for Distortionless Amplification. Distortion- less amplification is obtained if the amplified current in the output circuit is, for the whole range of frequencies which it is desired to transmit, an exact enlarged reproduction of the input current. Distortion can be produced in two ways: (1) When currents of different frequencies are not amplified in the same proportion; (2) when the amplification is not independent of the input voltage. (1) As far as the first effect alone is concerned, the amplifica- tion will be distortionless if the whole circuit is non-reactive. The circuits commonly used in connection with the tube are not non- reactive, but the necessary transformers and condensers can always be so chosen that for the operating range of frequencies the total impedance is not unduly affected by the frequency. As far as the tube itself is concerned it is to be noted that the capacities between the electrodes introduces a reactance effect. Of these we distinguish between the capacity between filament and plate, and the effective input impedance as measured between the filament and grid. When the amplification is expressed in terms of the potential actually applied to the grid, the only inter-electrode capacity that comes into consideration is the capacity between filament and plate. This is so small that when the amplification is expressed in this way it is found to be independent of the fre- quency for frequencies ranging up to several hundred thousand cycles per second. The power amplification is usually expressed in terms of the ratio of the power developed in the external output circuit to the total power impressed on the input. In this case the effective reactance due to the inter-electrode capacities depends on the circuit used, as will be explained in Sections 69 to 71. Under the conditions under which amplifiers are mostly operated, the electrode capacities usually have a very small effect. The general effect, however, is to decrease the amplification when the frequency becomes very high. (2) The second condition for distortionless amplification will not be satisfied unless the axis of the dynamic characteristic of the output circuit is linear over the operating range of voltage. As was shown in the previous Section, this can be secured by THE THERMIONIC AMPLIFIER 179 making the external impedance in the output circuit sufficiently large. It is important to note that another condition for distortionless amplification is that the input voltage must be kept within certain limits determined by the d-c. plate and grid voltages and the struc- ture of the tube. Let us assume that the external impedance is sufficiently large to straighten out effectively the characteristic. The question now is what range of input voltage can be employed without overtaxing the tube. If the input voltage is so large that the grid becomes sufficiently positive to take appreciable current, the positive halves of the output wave can be reduced in the man- ner explained in Section 57. This reduction is more marked the larger the external impedance in the output circuit, because the extent to which the grid can become positive without taking appre- ciable current depends on the potential difference E p existing between filament and plate at the moment that the grid is positive and on the structure of the tube. Remembering that the stray field between filament and grid, due to the potential difference E p , tends to draw the electrons through the openings of the grid, it will be seen that the larger E p the higher must be the positive grid voltage to overcome the stray field and attract the electrons to the grid. Now the external impedance has the effect of decreas- ing the plate-filament potential difference when the flow of electrons from plate to filament through the impedance is increased, that is, during the half .cycle when the grid is positive. This reduces the stray field and consequently increases the flow of electrons to the grid. This is the effect that gives rise to the bend C in the dynamic characteristic shown in Fig. 86. If we say that g is the positive potential with respect to the filament which the grid can acquire without taking appreciable current, we can state that one condition for distortionless amplification is e<- | E g +e | + \g | (23) 4* where E g is the voltage of the grid battery, e the peak value of the input voltage, and e the intrinsic potential difference between filament and grid. Another condition is that the peak value of the input voltage must not exceed the value given by mn (Fig. 86), otherwise the negative peaks of the output current wave will be chopped off. 180 THERMIONIC VACUUM TUBE Now sn is given by -, where E' p is the potential difference between filament and plate at the moment when the grid has its maximum negative value, and sm is the voltage E a of the grid battery. We therefore have the two conditions: I E g +e P + I M (24) or when the tube is working at full capacity, that is, when operating over the whole range of the characteristic. e=- I E g +e I + \g I = (25) 61. Amplification Equations of the Thermionic Amplifier. We shall now derive quantitative expressions for the amplification produced by the three-electrode thermionic tube. It will be recognized that when operating as a power amplifier the tube derives the extra power from the d-c. battery inserted in the plate circuit. The energy of the plate battery is released by the influence of the grid potential on the current in the plate circuit and the amount of power released depends almost entirely on the influence of the grid potential. , In deriving the following equations we assume that the grid is maintained sufficiently negative with respect to the filament to prevent any appreciable current convection between filament and grid; that is, the tube will be assumed to operate within the limits defined by equations (24) and (25). We shall also assume that the impedance conditions in the plate circuit are such as to make the characteristic of the plate circuit substantially linear over the operating range of voltages. These conditions can very nearly be satisfied in practice even when the circuit constants are so adjusted as to give a maximum degree of amplification. Under these conditions the alternating current i v in the plate circuit is related to the alternating potential e a , applied to the grid, by equation (22) THE THERMIONIC AMPLIFIER 181 where r p is the plate resistance and ZQ the external impedance. This equation enables us to derive the amplification equations in a very simple manner. 62. Voltage Amplification. Consider first the case in which the tube is used as a voltage amplifier. The voltage developed in the impedance ZQ is eo=i p Zo, which according to equation (22) becomes: r p +Z ' and the voltage amplification is therefore == = r p +Z ' (26) It must be noted that e g is the a-c. potential difference actually established between filament and grid. It will be seen that // increases as ZQ is increased and asymptot- ically approaches the maxi- mum value /* when ZQ becomes infinitely large compared with r p . The constant which de- pends on the structure of the tube and determines the stray field, is therefore simply the maximum voltage ampli- fication obtainable from the tube. When a tube is to be used as a voltage amplifier it should therefore be designed to have as high a value of /* as possible. Fig. 89 shows a Western Electric voltage am- plifier. The amplification con- stant ju of this tube is 40. A voltage amplification of several hundred fold is not hard to obtain, it being simply necessary to design the tube accordingly, since ju is a struc- tural constant. In using tubes however, necessary to consider FIG. 89. as voltage amplifiers it is, also the other factors that 182 THERMIONIC VACUUM TUBE influence the voltage amplification. For example, it follows directly from equation (26) that the external impedance should be made several times as large as the plate resistance of the tube. Now, for the same amount of filament surface the plate resistance increases approximately as the square of /z (see equation 15) and may acquire such a high value as to necessitate an impracti- cably high external impedance. It is, therefore, often necessary, when increasing //, to increase the amount of filament surface so as to reduce the plate resistance as much as possible. It is, of course, also possible to decrease the plate resistance by increasing the d-c. plate voltage, provided we do not operate beyond the minimum saturation voltage. Referring now to equation (26) let ZQ=TQ-}-JXQ', the voltage amplification is then given by (27) Suppose the tube is inserted in the circuit shown in Fig. 90, and that it is desired to obtain the voltage developed between FIG. 90. the ends A and B of the impedance ZQ. This voltage CQ can be measured by connecting an electrostatic voltmeter between A and B. 1 The secondary of the transformer T can be wound to have as high an impedance as possible, thus impressing the highest possible voltage e g on the grid for a given voltage in the primary ofT. Let us now consider the two extreme cases in which ZQ is (1) a non-inductive resistance TO (zo=0) and (2) a practically pure 1 A thermionic tube can be used as an electrostatic voltmeter in the manner shown in Section 114. THE THERMIONIC AMPLIFIER 183 reactance XQ (ro=0). In the first case the voltage amplification is given by (28) The relation between and is shown by curve II of Fig. 91 Cg T p from which it is seen that reacnes about 90 per cent of its e, maximum value M when r = 10 r p . (In computing these curves u was taken equal to 10.) I "5 o t 6 CO n h r p FIG. 91. If ZQ is a pure reactance XQ, the voltage amplification is given by e o_ (29) Curve I of Fig 91 shows the relation between and . It is e g r p seen that there is a distinct advantage in making the tube work into a reactance, the voltage amplification rising to about 90 per cent of its maximum value when XQ is numerically only twice r p . It is, however, advisable to make the reactance as large as possible in order to minimize distortion due to the curvature of the charac- teristic. The use of a reactance instead of a resistance has another 184 THERMIONIC VACUUM TUBE advantage. If Zo is a pure resistance and several times greater than the plate resistance, a considerable portion of the voltage of the plate battery is lost in ro, so that to secure the necessary potential difference between filament and plate it would be neces- sary to use a rather high plate battery voltage. This can be avoided by using instead of a pure resistance a choke coil which has a comparatively small d-c. resistance. On the other hand, the value of the tube as a voltage amplifier lies in the fact that it can be operated in a non-inductive circuit, and in this respect it performs an important function, in that it serves the purpose of producing high degrees of amplification with very little distortion. Unlike the transformer, for example, it furnishes a voltage-amplifying means that is independent of frequency unless the frequency is very high. And, as a matter of fact, it can also be used to produce power amplification that is practically independent of frequency. When several tubes are used in cascade formation in multi- stage non-inductive amplifier sets, all but the last tube should be used as voltage amplifiers, because the tube is a potential operating device. It works best as an amplifier when its grid does not take appreciable current; that is, when the tube operates within the limits defined by equations (24) and (25). The input power consumed by the tube is therefore usually very small, and all that is necessary is to make the input voltage applied between filament and grid as high as possible. It must be pointed out that unless it is necessary to use a non-inductive circuit it is best to operate all tubes in a multi- stage amplifier set as power amplifiers, and use voltage step-up transformers between the tubes. Consider, for example, the circuit in Fig. 92. (The circuits shown here do not include details that are necessary to give best operation in practice. They are merely skeleton circuits intended to illustrate the points under consideration. Complete circuits will be discussed below.) If the tube A were to be used as a voltage amplifier, it would be necessary to make ZQ several times as large as r p . This does not, however, give maximum total amplification, because when using transformers we have to consider the power, and maximum amplification is obtained when Z Q =r p , T 2 being used as a voltage step-up transformer. This can be shown as follows: The power THE THERMIONIC AMPLIFIER 185 in ZQ will be a maximum for maximum voltage e' g impressed on the input of the second tube B. Now, the voltage eo in ZQ is given by: where ju is the amplification constant of tube A. Now, the voltage ratio of the transformer T% is -y^ Hence, the voltage impressed on tube B is: e '< = (r p +ZQ) (30) FIG. 92. It is in all cases desirable to make Z\ as large as can possibly be done in practice. Hence, regarding Z\ as fixed and differen- tiating e'g with respect to ZQ and equating to zero, it will be seen that e' g is a maximum when Zo=r p , and this, it will be shown in the next paragraph, is the condition for maximum power in ZQ. 63. Power Amplification. The three-electrode thermionic tube can be used to amplify power, and in this property lies its great usefulness. It is its amplifying property that enables it to be used also as an oscillation generator. There are other types of amplifiers, such as, for example, the arc which amplifies in virtue of its negative resistance characteristic and therefore operates on an entirely different principle. But the thermionic amplifier, or audion, has certain marked advantages over other types. Unlike the arc it does not depend for its operation on ionization by col- lision of residual gas, and in fact operates satisfactorily only when the vacuum is so high that ionization by collision plays a negligibly small part in current convection in the tube. The discharge is therefore steady and reproducible. When using the device as a 186 THERMIONIC VACUUM TUBE telephone relay, for example, steadiness and reproducibility are conditions that must be complied with, and this is also true of many other cases where amplifiers are used. It is furthermore capable of amplifying currents of frequencies ranging all the way up to several million cycles per second, and if properly designed it can be made to produce an extraordinarily high degree of amplifica- tion. I have for example, obtained with a specially designed tube, a power amplification of 3000-fold. An equation for the power amplification can be obtained directly from the equations deduced above. Let us consider the circuit shown in Fig. 90. It is desired to amplify the power in the transformer T which may be at the end of a section of tele- phone line or may, for example, be connected in the output of the generator G. Let the a-c. potential impressed on the grid be e ff . Then the alternating current i v in the output circuit FPABis v where r p is the plate resistance. The voltage CQ in ZQ is and hence the power in ZQ is _A*VZ COS where cos < is the power factor. In order to get the power amplification it is necessary also to know the power expended in the input. The grid current does not bear a simple relation to the operating parameters, but to get an indication of how current in the grid circuit affects the amplifica- tion, we can expand the obvious functional relationship, I =f(E p , Eg) into a Taylor series, thus: }-8l g =f(E p +dE p , THE THERMIONIC AMPLIFIER 187 second and higher order quantities being neglected. By making the following substitutions: 8E g =e g , we get: Putting = /*i, the input power becomes, if we neglect the power 6g consumption in the input transformer: Hence the power amplification becomes: = e 0p cos <> = M cos e ff i ff ( This equation shows how the power amplification is affected by the grid conductance g , the amplification factor p and the reflex mutual conductance g n . For a perfectly unilateral amplifier the output circuit has no effect on the input and then g n = 0. Conditions can readily be realized in practice which make both g n and g g negligibly small. 2 Conditions under which they become appreciable will be discussed in Section 69. If we neglect these quantities the input resistance is infinite and the power loss in the input indeterminate. We can, however, shunt the input 1 This equation is equivalent to that derived by Latour. (Electrician, Dec., 1916.) 2 When there are reactive effects, as, for example, when the output circuit is reactive, we should, strictly speaking, consider the mutual admittance and reflex mutual admittance instead of simply the mutual conductances, because under these conditions the grid potential and plate current are out of phase. The mutual admittances are then complex quantities involving the mutual conductances and the mutual susceptances. (See Fig. 87.) When the circuit constants are so proportioned that the axis of the dynamic char- acteristic is substantially linear, which is the condition for distortionless transmission, the angle of the mutual admittance is so small that we can, to a first approximation, neglect the mutual susceptances. 188 THERMIONIC VACUUM TUBE with a resistance r a (Fig. 90), as was suggested by H. D. Arnold, and so proportion its value that the input transformer works most efficiently. The power expended in this resistance can then be taken as a measure of the input power. In telephone repeater circuits this resistance usually has a value of about 600,000 ohms. Equation (32) then becomes: cos or putting Zo=ro+jx , the power amplification can be expressed as: (33a) Let us first consider the case in which ZQ takes the form of a non- inductive resistance (zo=0). The power amplification is then simply given by (34) and it will be seen by differentiating rj with respect to ro and equating the derivative to zero, that the power amplification is a maximum when ro=r P . For the general case in which the reactance X Q is not zero, we note that = tan -1 and cos the grid must be made more negative with respect to the filament. If the necessary grid voltage is E' g , M is given by (39) A convenient and rapid means of measuring /i is shown in Fig. 97. 1 E\ is a battery of small dry cells of about 10 or 20 volts. By closing the key K opposite potentials are applied to the grid and FIG. 97. plate, their values depending upon those of r\ and r%. Since a potential applied to the grid produces ju-times the effect of a potential applied to the plate, it is evident that no change will be produced in the reading of the current meter by closing K if =M- For convenience in measurement r-z is given a fixed value 7*2 of 10 ohms and n consists of three dial rheostats of 1000, 100 and 10 ohms arranged in steps of 100, 10 and 1 ohms each. The rheostats are marked in tenths of the actual resistances, so that the setting of the dials gives n directly. A similar method has also been described by J. M. Miller, 2 who use,d a source of alternating current instead of the battery 1 H. J. VAN DER BIJL, Proc. I.R.E., Vol. 77, p. 112, 1919. 3 J. M. MILLER, Free. I.R.E., Vol. 6, p. 141, 1918. THE THERMIONIC AMPLIFIER 195 Ei. The meter is replaced by a telephone receiver and the resist- ances n and r2 are adjusted until the tone in the receiver is a mini- mum. The use of an alternating current has the advantage that it also allows a simple determination of the plate resistance of the tube. 66. Measurement of the Plate Resistance. We have seen that the characteristic of the amplifier can to a first approximation be given by equation (3), in which the exponent is 2. For such a characteristic the plate resistance is the inverse slope of the /, 1^-curve and is given by equation (15): r^^-Tr 1 - v ..... (15) By multiplying numerator and denominator by the expression in the parentheses we can express r p in the simpler form (40) or, neglecting the small quantity e and putting E g = 0, We can, therefore, obtain a fair estimate of the plate resistance by simply observing the plate current for the plate voltage at which it is desired to obtain the resistance. It will be noted that the plate resistance, by which we mean the a-c. resistance, is half the d-c. resistance. It is also to be noted that while the amplifica- tion constant /z is a geometrical constant, the plate resistance depends not only on the structure of the tube but also on the values of the plate and grid voltages. If can, however, be fully specified for all operating plate and grid voltages by determining it as a function of the plate voltage, the grid voltage being kept zero. The relation between r p and E p can be represented by a curve like that shown in Fig. 98. Now, the resistance at any specified plate voltage E p and a grid voltage E g other than zero can be obtained by applying the stray field relation given in equation (1), from which it follows (neglecting e) that the effective plate voltage 196 THERMIONIC VACUUM TUBE is now Ep+v.E g . 1 All that is necessary, therefore, to obtain the plate resistance from the curve in Fig. 98 for any values E p and E g is to read off the resistance at an abscissa equal to E p +vE . In regard to Fig. 98 it should be noted that the resistance char- acteristic drops in virtue of the increase in slope of the plate current characteristic. Let us consider the curve shown in Fig. 99, which represents the relation between the plate current and the effective plate voltage E v = (E p -\-^E g ). If this voltage has the value given by ob the direct current in the plate circuit will be repre- sented by bb'. Let the grid voltage now be varied so that E v oscillates between oa and oc, ab being equal to be. The plate resistance is then the reciprocal of the slope of the line a'c', and if Effective Plate Voltage FIG. 98. the characteristic is parabolic it follows directly from the proper- ties of the parabola that a'c' is parallel to slope of the curve at the point corresponding to the direct voltage E ir = ob. In the case of the parabolic characteristic the plate resistance is therefore simply given by the slope of the characteristic. If E v oscillates between oc and od the plate resistance is smaller since the slope of c'd' is larger. If now E r is so large that it oscillates between od and of the resistance increases. This is shown by the broken part of the resistance characteristic in Fig. 98. In this case the resistance is no longer given by the slope of the curve at the point corresponding to the mean value of E v . If E v oscillates over the whole range oe the resistance is greater than in the case 1 This applies for positive values of E g only as long as the grid is not suf- ficiently positive to take an appreciable current. THE THERMIONIC AMPLIFIER 197 where E v oscillates over the range cd and the amplification will be less. This drop in amplification when the input becomes very large can of course always be avoided by operating at a higher plate potential E p and increasing the saturation current by in- creasing the temperature of the filament. Methods have been devised whereby the plate resistance can be measured dynamically with comparative ease. It is therefore a o c cf e Effective Plate Voltage FIG. 99. a simple matter to obtain a curve like that shown in Fig. 98. The following method was published by J. M. Miller. 1 Consider the circuit shown in Fig. 100. It will be recognized that with the key K\ open and Ki closed the circuit is the same as Fig. 97 except that the meter is replaced by the telephone receiver T and a source S of alternating current is used instead of the battery 1 Loc. cit, 198 THERMIONIC VACUUM TUBE EI. The circuit therefore gives a means of measuring /*, which can be done by adjusting r\ until the tone in the receiver T vanishes. To measure the plate resistance r p let the key K\ be closed. If e g be the alternating voltage applied between filament and grid the alternating current in the circuit FPrq is, by equation (22), ** and the voltage in 7*0 is therefore M 9 Now it will be observed that if A is positive and B negative, the electron current to the plate will be increased if the effect of the applied grid voltage exceeds the opposite effect of the voltage simultaneously applied to the plate. The currents in TQ and r\ are therefore in phase. Hence, by adjusting r until the potential drop in it is equal A ~ ^MA/WV FIG. 100. to that in n, the tone in the telephone receiver can be reduced to a minimum. If this is the case we have But e ff = Ir 2} hence the plate resistance is: (42) from which r p can be computed. Miller puts ri=r 2 to obtain a simpler equation. But even so the method involves a calculation. A very valuable simplification hitherto unpublished was suggested by G. H. Stevenson. Suppose we adjust n for minimum tone in THE THERMIONIC AMPLIFIER 199 T when KI is open. Then M = , and it will be seen from equation (42) that with this relation between r\ and 7*2 it would not be possible to obtain a balance with KI closed. But if r% be doubled, which can be done by opening K^ thus adding a resistance equal to T2, and 7*0 be now adjusted, with K\ closed, to give minimum tone in T 7 , then r p = r$. This is the simplest method of measuring the plate resistance. By giving 7*2 a fixed value of, say, 10 ohms and calibrating n in the manner explained with reference to Fig. 97, we obtain a comparatively simple circuit which enables us to read the amplification constant and the plate resistance directly in terms of r\ and ro. 67. Direct Measurement of the Mutual Conductance. Once the amplification constant and plate resistance are known the mutual conductance can be obtained from equation (18) (18) and it is therefore hardly necessary to measure it directly. How- ever, since the mutual conductance is a good indication of the figure of merit of a tube, we shall briefly describe a few methods whereby it can be measured directly. Referring to equation (17) it can be seen that the principle of any method of direct meas- urement of the mutual conductance is to apply a potential differ- ence between filament and grid by passing a current through a resistance shunting the grid and filament and balancing this cur- rent against the resulting current in the plate circuit. There are various ways in which this can be done. The circuit arrangement of a method proposed by S. Ballantine l is shown in Fig. 101. The coils 1 and 2 are so connected that the currents i\ and i% flowing in the directions of the arrows tend to neutralize each other's effect in the secondary of transformer T 7 ., If t\ and fa be the inductance due to the coils 1 and 2, respectively, and Ri be so adjusted that the tone in the receiver is a minimum, then * 1^1 =$2(2. Ballantine assumes that 12 = from which he then obtains, r P 1 S. BALLANTINE, Proc. I.R.E., Vol. 7, p. 134, 1919. 200 THERMIONIC VACUUM TUBE since e g =iiRi, (42) The assumption made is, strictly speaking, justifiable only when the impressed oscillations are very small, because the current- voltage characteristic of the circuit is not linear unless the external impedance in the plate circuit (i.e., the impedance of coil 2) is large. On the other hand, if it is large the current i 2 cannot be expressed by the above simple equation, but is given by equation (22), namely: r P +Z 2 (22) where Z 2 is the impedance of coil 2. The mutual conductance of the tube is then given by : that is, by ti Z 2 . t 2 fJL (43) (44) For a simplification of this dynamic method I am indebted to an hitherto unpublished suggestion of Mr. H. W. Everitt which is THE THERMIONIC AMPLIFIER 201 shown in Fig. 102. 1 It consists in replacing the transformer T by two non-inductive resistances r\ and r^ the telephone receiver being connected directly to them as shown. The effect of the FIG. 102. external resistance is shown in the following table, which gives observations obtained by Everitt. The second column gives the values that would be obtained with equation (42), and the last 1 r 2 r\ TzRl T Z 100 1,000 1.33X10-3 1.09X10-3 1.37X10-3 1.39X10-3 2,100 0.86X10-3 1.34X10-3 10,000 0.37X10-3 1.43X10-3 column the corrected values according to equation (44). The true value of computed from separately observed values of /x and r p r p is, for the plate voltage used in these experiments, 1.31X10" 3 . The values in the last column are not quite in agreement with this value, since the method is not very accurate, but they are grouped around a mean value. The values given in the second column are distinctly influenced by the external resistance, the deviation from 1 This modification was also suggested by Ballantine and given in an addeni- dum to his paper, which appeared about four months after the reading of the original paper at a meeting of the Institute of Radio Engineers. 202 THERMIONIC VACUUM TUBE the true value increasing with it. When the external resistance is so large that it must be taken into consideration the method becomes tedious and has no advantage over obtaining - from r P separate determinations of ju and r P by the method explained with reference to Fig. 100. A simple d-c. method of measuring the mutual conductance, due to E. V. Appleton l is of interest. The circuit arrangement is shown in Fig. 103. When the key K is open the galvanometer G indicates the normal plate current. When K is closed the poten- tial difference fy applied between filament and grid is I\R\, where FIG. 103. This causes a change in the plate current 7i is the current in R\. equal to Now it will be seen that / and I\ flow through the galvanometer in opposite directions. Hence if R\ be adjusted until the galvano- meter reading shows no change, then or _ _ Se g ~Ri (45) The plate circuit does not contain any external resistance, except that of the galvanometer, which is small. This equation is, 1 Wireless World, Vol. 6, p. 458, 1918. THE THERMIONIC AMPLIFIER 203 strictly speaking, correct only when the potential applied to the grid is small, in which case we can put = so that 5e g r v (46) It will be evident from the foregoing that the mutual con- ductance is, like the plate resist- ance, a function of the d-c. plate and grid voltages. As in the case of the plate resistance the effect of the plate and grid voltages can be explained with reference to a curve like that shown in Fig. 99, except that here the abscissae would repre- sent the effective grid voltage, E= ^ . effective instead of the plate voltage, E v = It is evident that 68. Circuit for Measuring Amplification Constant. Plate Resistance and Mutual Conduc- tance. A set which makes possi- ble the quick measurement of all three quantities, ju, r p and g m was devised by H. W. Everitt. It consists of the combination of three circuits shown in Fig. 104. For a certain setting of the keys on the box the circuit arrangement is that shown by circuit I (Fig. 104). As was explained above, when r<2 is so adjusted that the tone in the receiver is a minimum, then Tel, Rec. FIG 104. 7*2 (47) 204 THERMIONIC VACUUM TUBE The resistance r\ has a constant value of 10 ohms and r 2 is cali- brated to read tenths of ohms, so that the reading of r 2 gives /* directly. Now, to measure r p the circuit is transformed into circuit II by the simple operation of throwing over a multiple-contact key. This is done without changing the setting of r 2 that gave the value of n in circuit I. It is seen that r 2 is now transferred to the grid circuit and is replaced by a constant resistance rs = 1000 ohms. Referring to this circuit and applying equations given in the previous sections, the voltage drop across r^ is es = If ii is the current in the grid circuit, Hence es = When R i is so adjusted that the tone in the receiver is a minimum, the voltage drop e 3 in r 3 is equal to the voltage drop i\r 2 in the resistance r 2 . Hence, putting 63 =iir 2 we get: Now since r 2 has the same value that it had in circuit / and ri = 10 ohms, we have from equation (47) r 2 = fj.ri = 10/z. Hence "" 3 * 10 10 But since rs is a constant resistance of 10 ohms the last two terms vanish. Furthermore, rs = 1000 ohms, so that the plate resistance is given directly by v r p = lOOfli (48) The dials of Ri are marked 100 times their actual ohmic resistance so as to make the set direct reading. Next, to measure the mutual conductance g m = a second THE THERMIONIC AMPLIFIER 205 multiple-contact key is operated which transforms the circuit into III (Fig. 104). The resistance r% is the same as that used in circuits I and II. It was shown in Section 67 that if r is small compared with the plate resistance of the tube then By making r^Rz an even multiple of 10, we have - r p For the chosen values of r and #2, namely 100 and 1000 ohms, n = 5, and since the dials of r^ are marked in tenths of ohms : (50) [r2\ being the reading indicated on the dials. The measurement of the tube constants with this set is a very quick and simple operation. The complete set is shown in Fig. 105. It includes a tone source, such as that described on page 223. The tube to be tested is inserted in the socket as indicated. The transformation of the circuits is accomplished with the keys 2 and 3. A and B represent the resistances r^ and R\ of Fig. 104. 69. Influence of the Electrode Capacities. The amplification equations derived in sections 61 to 63 express- the quantities considered in terms of the potential variations actually applied to the grid. When considering the power supplied to the input circuit it is necessary to determine to what extent the electrode capacities can influence the results. The potential variations impressed on the grid when the power is supplied to the input circuit can be influenced by the electrostatic capacities between the electrodes of the tube. The capacities between grid and plate effects a coupling - between the output and input circuits, so that the tube is not a perfect unilateral device. The extent to which the output circuit reacts on the input depends on the constants of the circuits. The solution of the network involving the electrode capacities was given by H. W. Nichols l and by J. M. Miller. 2 1 H. W. NICHOLS, Phys. Rev., Vol. 13, p. 405, 1919. 2 J. M. MILLER, Bureau of Standards, Bulletin No. 351. THERMIONIC VACUUM TUBE Fig. 106 represents the equivalent network of the tube and cir- cuit. (7, F and P denote the grid, filament and plate. This cir- cuit represents the condition that the grid is kept at a negative potential with respect to the filament, so that there is no con- vection current between them. The resistance to the convection current between filament and plate is represented by r p and is in FIG. 105. shunt with the capacity C 2 between the filament and plate. Z ff represents the impedance as measured between filament and grid and is the effective input impedance. Remembering that a poten- tial e a impressed on the grid introduces an E.M.F. equal to ne y in the plate circuit, the input impedance Z ff can be obtained by including in the plate circuit a fictitious generator giving ^e a as indicated in the diagram and solving the Kirchoff equations for the network. THE THERMIONIC AMPLIFIER 207 Unless the frequency is very high (over a million cycles per second) we can neglect the capacity 2 between filament and plate, since it is shunted by the plate resistance which, is then low compared with the impedance due to 2. The equation given by Nichols for the effective input impedance is: 7 = _J " where W= ^_ ; co is 2?rX frequency, and ,;' is the imaginary unit V 1. The other quantities are indicated in Fig. 106. ^v * *: FIG. 106. For most tubes used at present this equation is applicable for frequencies up to about a million cycles per second. Let the external output impedance take the general form Z Q =r Q +jx Q . Then equation (51) can be transformed into: _ ae+bd ad-bc ^ ' = -r g +jx g where the coefficients have the values (53) c = a)*r P ro(J iL 3 -1- wx (L i -t- c 3 -t-M^ 3; It will be seen from inspection that the effective input im- pedance will generally comprise a resistance r g which may be positive or negative, and a reactance x g which is capacitive. 70. Case 1. Low Frequencies: co<10 6 . In this case we can neglect co-terms where they occur in the same expression with terms containing co in a lower order, e.g., neglect co 2 in comparison with co. 208 THERMIONIC VACUUM TUBE Let the output impedance be inductive XQ=LQU- Evaluation of the coefficients (53) gives for the input resistance: and for the input reactance : and therefore the effective input capacity is: (55) (56) Now, Ci is the electrostatic capacity between filament and grid. The effective input capacity is greater than the electrostatic capacity by the amount shown by equation (56). The increase depends on the electrostatic capacity between grid and plate, and on the resistance in the output load. It also depends en the amplification constant //. It will be recognized that this equation contains the expression for the voltage amplification as a function of the external output resistance (see equation 28). The effective input capacity therefore increases with the output lead resist- ance in the manner indicated by Fig. 95, page 192. Miller 1 has measured the effective input capacity as a function of the external output resistance. The following table shows the agreement between his observed and computed values for the case of a VT-l tube. Input Capacity. r , Ohms. Computed. Observed. 27.9 8,000 51.4 49.0 16,000 64.5 61.5 49,400 78.9 76.1 97,000 84.2 84.3 139,000 86.1 87.6 1 Loc. cit. THE THERMIONIC AMPLIFIER 209 Equations (54) and (55) show that the effective input resist- ance is for low frequencies ( < 10 6 ) independent of the frequency, but depends, among the other circuit constants, on both resistance ro and inductance LO in the external output circuit. The input reactance, on the other hand, is inversely proportional to the fre- quency and depends on the resistance TQ, but not on the inductance in the output. From equation (55) it follows that the amplification given by the tube would decrease as the frequency is increased. But this tendency to distort is in itself not due to power consumption in the input, but is occasioned by the decrease in the input grid potential, due to the lowering of the input reactance. The power consumed in the input is determined by the equa- tion (54). This equation contains a negative term in the numer- ator and therefore if the output inductance LO is large enough, the input resistance can be negative. Under these conditions the tube would tend to produce oscillations or " sing " through its internal capacities. This tendency to sing is frequently a source of annoyance in amplifier circuits. Miller has computed the relation between r g and the output inductance LQ. In amplifier circuits we are usually more inter- ested in the external output impedance than in the output induct- ance. Fig. 107 shows the relation between the effective input rp resistance r Q and the ratio - - of external output impedance to r P plate resistance for various angles = tan~ 1 of the output r o impedance Zo=ro+jLo. For a pure inductance in the output (ro=0), equation (54), reduces to the simple form _ ( . 2 ' and is therefore always negative . As the angle decreases, the negative value of r g decreases and finally becomes positive. The curves in Fig. 107 were computed with the following values of the constants: r p = 5Xl0 3 ohms Ci = 5XlO- 12 farad; C 3 = 15 X10- 12 farad; M = 5; co = 2X10 4 . 210 THERMIONIC VACUUM TUBE These are approximately the constants of a type of tube that is commonly used for amplifying telephonic currents. FIG. 107. The corresponding input reactances. x a are shown in Fig. 108. The input reactance is therefore generally much larger than the input resistance. FIG. 108. 2.5 3.0 3.5 It can be seen from the above equations that if the output reactance is capacitive, then the input resistance is always positive This is also the case when the output is a pure resistance (zo=0). THE THERMIONIC AMPLIFIER 211 Under these conditions the tube would absorb power from the input. But for ordinary frequencies this power absorption is negligibly small. The power absorbed in the input can be obtained as follows: Let us impress an alternating potential e g on the grid. Then the grid current is * = ^ = _^_ Z. r g +jx g > the condition being that the grid is at all times negative with respect to the filament, so that there is no convection current between filament and grid. The power absorption is therefore due entirely to the reaction of the output on the input circuit. This power is: or P p 2 f a Va For co < 10 6 we can neglect rf in comparison with 97^- and write (58) Substituting the values of r ff and C g from equations (54) and (55), for the case of a pure resistance in the output (Lo=0), we obtain P 9 = <**e*rjCtfK(l+nK), .... (59) where K = p . This shows that the only inter-electrode capacity that is effective in causing input power loss is Ca, the capacity between grid and anode. In order to obtain the order of magnitude of P g for a common type of tube, we can insert the values for the constants given on page 209 into equation (59). When ro=r p (the condition for maximum power output), K = %. Putting e g = 5 volts, we get: P, = 4.8X10- 17 Xco 2 watt. For a tube of the type considered, and for telephonic fre- quencies (co<2X10 4 ), the ratio of output to total input power 212 THERMIONIC VACUUM TUBE is about 300, and for an input voltage of 5 volts the power in the output is about 30X10" 3 watt. The total input power is there- fore about 1 X 10" 4 watt. For co = 2 X 10 4 , the power P g consumed in the effective grid resistance is about 2X10~ 8 , which is still very small compared to the total input power which, in normal operation of a tube, is consumed in the input transformer, and in the high resistance usually bridged across filament and grid, as shown in Fig. 90, page 182. Of course, the power consumption by the effective grid resistance can become quite large when the frequency is high, since it increases with the square of the frequency within the frequency range considered. At extremely high frequencies the effective grid resistance again becomes negligibly small, as will be seen from the following. 71. Case II. High Frequencies. When the frequency is very high, we cannot neglect the capacity 2 between filament and plate because the impedance due to 2 can obviously become com- parable with or even lower than the plate resistance r p with which it is in parallel. (See Fig. 106.) In this case the effective input impedance is given by _ac-\-bd .be ad ~^+d?^~ J #+d?' where the coefficients now have the values: (60) and x Q can be L to or ~ . Since co is large we can neglect the co-terms of lower order in comparison with those of the succeeding and higher orders. This gives: r g = Q i r, _ ) then R = r and X = x . Summing the E.M.F.'s in the two branches we have ..... (66) ' . '(67) From (67) and (62) we obtain directly or r 2 =-r ? , Z . ,. . . . (68) smh ad + cosh ad 1 The values of r^ necessary to give any desired attenuation d can thus be obtained directly from a table of hyperbolic functions. In deriving equation (68) we made use of equation (62), which holds for a circuit of zero reactance, while in the receiver shunt circuit the reactance is not zero. The values of r% obtained will therefore not be correct unless the angle of the impedance ZQ is small or .the attenuation large. If the angle of ZQ is not greater than about 45 the values of TI given by equation (68) are suf- ficiently accurate for current attenuations greater than those produced by 6 miles of standard cable (d>6). For smaller atten- uations or if the impedance ZQ has a large angle the values of r2 obtained from (68) can be corrected as follows: Suppose it is desired to compute a receiver shunt giving a maximum attenua- tion of 30 miles of standard cable and allowing the attenuation to be varied in steps of 1 mile each. This shunt, we shall suppose, is to operate with a receiver having a large angle, say, 70. We can use equation (68) to obtain an idea of the range of values of r 77\ alog e (2 sin J 1 Loc. cit. 230 THERMIONIC VACUUM TUBE When the diameter of the wire is small compared with the distance between adjacent wires, --is small, aud we can write approxi- mately: 60 50 o o c o 10 where (78) a log p -.456 cm. r - .01 cm. L 4 6 H umber of Wires Per Cm. FIG 120. to p= distance between grid and plate; a = distance between adjacent grid wires; r = radius of grid wire. This equation does not give as good results as the empirical equation that will be given below (equation 79). But for values THE THERMIONIC AMPLIFIER 231 of ju ranging from about 2 to 20, equation (78) can be used for designing tubes with a sufficiently high degree of accuracy for most practical purposes. The extent of the agreement between cal- culated and observed values is shown in Figs. 120 and 121. The points indicate observed values, while the smooth lines represent equation (78). Each point represents the average of a number of tubes. The deviation at the higher values of ju where the wires are close together, is inherent in the equation which was derived on the assumption that the distance between successive wires is large compared to the thickness of the wires. HV . 1 3 la n=7.88 r~ .01 per cm. cm. / jf s6 / 6 L o ~C_ c 10 / ^ / /* - ) .Z .3 .4 .5 Distance Between Plate and Grfo^Cm. FIG. 121. On account of the accuracy with which tubes must be designed for telephone repeater purposes, the author carried out an exten- sive series of measurements in 1914, to establish an empirical for- mula relating the tube constants with its structural parameters. The equation which was found to give the best results is: M = Cprn 2 +l, (79) where p = distance between plate and grid; r diameter of grid wires; n = number of wires per unit length. 232 THERMIONIC VACUUM TUBE C is a constant which for the parallel-plane type of tube (see Fig. 68) has a value of 80. Since this equation is non-dimensional, C is independent of the system of units used in expressing the tube dimensions and is independent of the size of the tube structure. It will be recognized that this equation is the same as that given on page 44 where d = p and k = ~ ^ 70 6C Z p = . 4 76 cm. 1 50 40 PP.. 3 17cm. . 238 cm. ./p - 158cm. 4 6 8 10 12 14 Number of Grid Wires Per Cm. FIG. 122. Equation (79) has been determined from measurements made on a large number of carefully constructed tubes in which not only the quantities given in the equation were varied, but also the istance between filament and plate, and the distance between Slament and grid varied over a wide range. The constant is, however, independent of these latter two distances, as the equa- tion shows. This is in accordance with Maxwell's result which also states that the stray field between filament and grid is inde- THE THERMIONIC AMPLIFIER 233 pendent of the distance between them. (See Equation 75.) Equa- tion (79) is more accurate than the theoretical equation (78) and therefore has been used by the Western Electric Company for the design of substantially all its tubes. The accuracy with which this equation holds is shown in Fig. 122, where /x 1 is plotted as a function of n, the number of wires per centimeter length of the grid for various distances p between grid and plate. The curves are computed from equation (79), while the circles and crosses repre- sent the observed values of /* 1. The radius r of the grid wires in these tubes was 1.02X10" 2 cm. The relation between /x and r is shown in the following table, which also contains values to indicate the range over which distances of the grid and plate from the filament were varied. The agreement between observed and computed values is, as will be seen from the table, quite good for values of - ranging to about 0.3. The thickest grid wire used in these tubes had a radius of 2.54X10" 2 cm. It is usually desirable to use thin wires, unless Amplification Constant /*. p+f / P n r Observed. Calculated. (eq. 79) .635 .158 .475 5.12 .0102 10.8.. 11.1 .635 .158 .475 5.12 .0191 18.0 19.0 .635 .158 .475 5.12 .0254 25.8 26.1 .318 .158 .158 8.26 .0102 8.4 9.8 .397 .158 .238 8.26 .0102 14.7 14.5 .476 .158 .317 8.26 .0102 20.2 18.7 .556 .158 .397 8.26 .0102 23.2 23.0 .635 .158 .476 9.84 .0102 42.0 38.5 .635 .158 .476 6.7 .0102 18.1 18.3 .635 .238 .397 8.26 .0102 24.6 23.1 .635 .317 .317 8.26 .0102 16.5 18.6 .635 .397 .238 8.26 .0102 14.0 14.5 .635 .476 .158 8.26 .0102 11.0 9.8 .635 .158 .476 11.4 .0102 50.5 51.5 p = distance grid and plate in centimeters; / = distance grid and filament in centimeters; n= number of wires per centimeter; r= radius of grid wire in centimeters. 234 THERMIONIC VACUUM TUBE requirements of rigidity necessitate the use of heavy wires, such as is the case when the grid is in the form of a helix, supported only at the ends, or sometimes even at one end only. King in the paper referred to above has also given an equation for M for the three classes of cylindrical structures shown in Fig. 123. His argument applies particularly to the case in which the grid wires are parallel to the axis of the structure, but the resulting p* o o equation applies almost equally well when the grid is a helix. The equation is: (80) 2-jrnr where n number of grid wires per unit length; r = radius of grid wires; PP, Po = radii of anode and grid. As in the case of parallel-plane structures, /x does not depend on the distance between filament and grid. The negative sign in equation (80) is to be used for the type of tube shown in Fig. 123C. Equation (80) gives a reasonably good agreement with observed values of /i. With the help of the equations given above, it is possible to determine beforehand the tube dimensions required to give the desired value of JJL. 76. Calculation of Plate Resistance. The plate resistance can in general not be determined with such simple equations as those which make possible the calculation of ju. But in designing tubes it is necessary to make the ratio , where r p is the plate r p resistance, as large as possible. For any given value of M it is therefore desirable to make r p as small as possible. THE THERMIONIC AMPLIFIER 235 o Now r p can be decreased by decreasing the distance p+f between filament and plate. On the other hand fj, increases with increasing distance p between grid and plate, but is independent of the distance / between filament and grid. Hence, in order to keep M large and r p small, / should be kept as small as possible, i.e., the grid should be close to the filament. The plate resistance depends, furthermore, on the size of the electrodes. It is within certain limits inversely proportional to the area of the anode as well as that of the cathode. It will be evident that there are limitations to increasing the area of the anode. For example, if the cathode is a single straight filament and the anode a plane parallel to the filament, there would be a limit to the size of the anode beyond which any further increase in its size would not contribute appreciably to a reduction in the resistance. On the other hand, the resistance can be reduced very much by using two plates, one on either side of the filament, as is mostly done. If the cathode consists of more strands of filament, the anode area can, of course, be further increased to advantage. If the anode is cylindrical, an increase in its diameter would increase the distance between fila- ment and anode in the same proportion as the anode area is increased. Considering a surface element of the anode, the resistance is proportional to the square of the distance between the cathode and the anode element. But for a cylindrical anode the area can be increased only by increasing the radius in the same proportion, so that the resistance increases linearly with the area of the anode; or, what is the same thing, it increases linearly with the radius. In this connection, we may note an interesting relation between cylindrical and parallel-plate tubes, which was pointed out by R. W. King. Suppose a cylindrical structure, having a thin filament stretched along the axis of the anode (Fig. 124) be unfurled so that the anode becomes a plate having a width equal to 2irp v . Let the filament be replaced by a surface equal to the anode area and at a distance p p from it. Assuming the cathode to be an equi-potential surface, the space current per unit area of the FIG. 124. 236 THERMIONIC VACUUM TUBE parallel plane structure is given by equation (9) Chapter IV. Hence the current for this tube is given by PP where I is length of the structure (perpendicular to the paper). That is 7=14.65X10- 6 W/*. PP This is the same equation that applies to the cylindrical tube (see equation (14), page 60). The two structures, therefore, give the same space current. As regards the effect of the area of the cathode, there are also certain limitations. If the area of the cathode be increased by increasing its diameter, the resistance will not be reduced propor- tionately because of the density of the space charge of the electrons in the neighborhood of the filament. The total saturation current will, of course, be greater, but will only be obtained at a higher voltage. The better way to increase the area of the cathode is to increase its length. However, this generally means an increase in the voltage drop in the filament, due to the heating current, and this in itself increases the plate resistance, due to the limitation of the current by the filament voltage. (See Fig. 20, page 61.) King has also derived equations for the space current as a function of the structural parameters for both cylindrical and parallel-plane structures, on the assumption that the current can be taken to vary as the f-power of the effective voltage. Since K the effective voltage +E g is generally not large compared with the voltage drop in the filament, the limitation of space current by the latter must be taken into account, in which case the current will be governed by equations (18) and (19) of Chapter IV. If the voltage drop in the filament be neglected the computed cur- rent will in general be considerably larger than the observed cur- rent. 77. Types of Thermionic Amplifiers. The number of different types of thermionic tubes now in use has become so large that no attempt will be made to describe or even mention all. The purpose in describing any is merely to give the reader a quantitative idea THE THERMIONIC AMPLIFIER 237 of characteristics of tubes used in practice. At the outset it may be stated that tubes are used ranging from a type that consumes for its operation a small fraction of a watt, to types that give several thousand watts' output in the form of alternating current. This widely varying range is occasioned by the widely differing condi- tions to be satisfied, depending on the purpose for which the tube is to be used. If the tube is to operate as an amplifier with the tele- phone receiver connected directly in its output circuit, the output power necessary need not be more than a very small fraction of a watt one millionth of a watt is quite sufficient to give a very loud tone in most well-constructed receivers. If, on the other hand, the tube is to be used as a telephone repeater, inserted at a point on the telephone line about midway between the sending and re- ceiving stations, the tube must give a sufficient amount of pow r er to give clearly audible speech in the receiver after the telephone currents have been attenuated by the line between the repeater and the receiver. Then, again, if the tube is used to amplify modulated high-frequency oscillations, for example, before being impressed on an antenna for radio transmission, it must obviously be capable of giving a much larger output power, the magnitude of which depends upon the distance over which transmission is to take place, and can range all the way up to several kilowatts. When the necessary power is too large to be handled by one tube, a number of tubes can be used in parallel. In designing tubes for amplification purposes several factors have to be taken into consideration. It is, for example, necessary to consider the output power that is necessary. To obtain best operation the plate resistance of the tube should be made equal to the impedance into which the tube works. If this is not possi- ble or desirable from the point of view of tube construction, a transformer could be used in the output circuit to match the tube resistance on the one side and the line impedance or the imped- ance of the recording apparatus on the other. It is also possible to use two or more tubes in parallel, thus reducing the total plate resistance. Referring to equation (31) it will be seen that the output depends also upon the input voltage e g and the amplifica- tion constant fi. The input voltage must be kept within the limits defined by equations (24) and (25). Furthermore, n and the plate resistance must be so chosen that the amplification has the desired value. This is usually as large as possible. 238 THERMIONIC VACUUM TUBE There are thus a number of requirements to be satisfied and they differ with different operating conditions. The following tubes represent a few standard types. The tube characteristics are specified sufficiently fully by giving the value of /z, the filament constants, the relation between plate current and plate voltage, S.8 il '5.4 5.Z 40*IO J \ E-0 g- 1.3 100 120 140 cu 4-0 60 80 Anode Volfs-Ep FIG. 125. and the relation between plate resistance and plate voltage, over a range of operating plate voltages. The slope of the T v plate current-grid potential characteristic can then be obtained directly from the known values of /* and r v . The tube shown in Fig. 68, page 146 represents a modern type THE THERMIONIC AMPLIFIER 239 of telephone repeater manufactured by the Western Electric Company and used on the lines of the Bell Telephone System. The overall length of the tube and base is about 4 inches. The plates are of nickel and their edges are turned up to prevent warp- ing due to the high temperature to which they rise when bom- 10 8 6 5 4 5 2 I ii.o |.i .5 o / 1 o / i / \ 1 < > A A L 9 1 f 1 / 3 o .1 i 8 f / / I f 10 iO 40 50 60 80 100 20C Anode Volts FIG. 126. barded by the electrons during the process of evacuation. It contains an oxide-coated platinum filament operating on a normal filament current 1.3 amperes, the voltage being 7 volts. When operated as a telephone repeater the d-c. plate voltage is 160 volts, and the grid is maintained negative with respect to the filament by a battery of 9 volts. The characteristics are shown 240 THERMIONIC VACUUM TUBE in Fig. 125. The plate resistance is shown here and in the follow- ing curves as a function of the plate potential, the grid potential being zero. To obtain the plate resistance for any grid potential other than zero, all that is necessary is to add pE a to the plate potential and read the resistance from the curve at the value of plate potential equal to the value so obtained. Thus, since ju is about 5.6, the plate resistance at a plate potential ^=160, and grid potential E =$ is that corresponding to an abscissa of 160-9X5.6=100 volts, namely, 5000 ohms. The minimum amplification required of this tube is 25 miles of standard cable, which corresponds to a power amplifica- tion of 230. (See table on page 219.) The logarithmic plot of this tube's charac- teristic is shown in Fig. 126. The slope of the line is close to 2, indicating a parabolic relation between current and voltage over the operating range. Fig. 127 shows a type of tube, com- monly known as the VT-1, that is suitable for use either as detector or amplifier and is designed to operate on a plate voltage of about 30 volts when delivering power directly to a telephone receiver. Its operat- Length: 10 cms. are shown in Fig. FIG. 127. Western Elec- ing filament current and voltage are 1.1 trie Receiving Tube, amperes and 2.5 volts, and its amplifica- tion constant is 6. Its other characteristics 128. The logarithmic plot of the charac- teristic is shown in Fig. 129. The slope of this line is also close to 2. The minimum amplification at 30 volts on the plate is 24 miles of standard cable. This tube was manu- factured by the Western Electric Company for use as an aero- plane radio receiver. The aeroplane radio transmitter tube resembles in its structural features the one shown in Fig. 68 but was designed to operate on plate voltages ranging from 275 to 350 volts instead of 160 volts, the voltage of the telephone repeater. The evident rugged construction of these tubes was found necessary to enable them to withstand the rather severe vibration to which they are subjected on an aeroplane. In the case of the receiver tube (Fig. 127) the filament, plate and grid are sup- THE THERMIONIC AMPLIFIER 241 ported from the top by means of a block of lavite. The lower part of the plate forms a collar which fits tightly round the re- entrant tube. The double plates and grids are each stamped in one piece from sheet metal, thus facilitating quantity production. A tube of simple construction manufactured by the General Electric Company is shown in Fig. 130. The anode consists of a nickel cup about -f? inch in diameter and -3% inch high, and is 4.5 4.0 > ^ j I / Fif. Amps =1.2 Grid Volts = / 35,000 30,000 V 1 _ 3.0 _ 2.5 ,, 2.0 1.5 1.0 6.5 Q , ' I , is twice as large as the plate THE THERMIONIC AMPLIFIER 253 resistance of the tube to which it is connected, the voltage ampli- fication is about 90 per cent of its maximum value p. If, however, L is a practically pure reactance, it is desirable to make it more than twice as large as the plate resistance, in order to make the phase difference between grid and plate potentials as near as 180 as possible, thereby straightening out the tube characteristic and minimizing distortion. (See Section 59.) The circuit shown in Fig. 142 is so arranged that both tubes can be operated from the same plate battery. The grids can be maintained negative with respect to their adjacent filaments by means of grid batteries (not shown) or by connecting them to convenient points on the FIG. 143. filament rheostat Rf. The resistance r should be large, preferably of the order of one or two megohms, and merely serves the pur- pose of maintaining the grid of the second tube at the desired d-c. potential. Instead of using the inductance L and condenser C, a step-up transformer can be inserted between the tubes, as shown in Fig. 143. When this is done both tubes should be operated as power amplifiers (see page 184). The primary impedance of the inter-tube transformer should therefore be equal to the plate resistance of the first tube and its secondary should be wound to impress the highest possible voltage on the grid of the second tube. The thermionic tube makes it possible to obtain high degrees of amplification with non-inductive circuits by means of an arrangement suggested by H. D. Arnold. 1 Fig. 144 shows a 1 U. S. Patent 1129943, 1915. 254 THERMIONIC VACUUM TUBE non-inductive amplifier. Instead of the inductance L a non- inductive resistance r is used. If the grid battery E g were omitted the grid of tube B would be at the same potential as the plate of tube A. The grid of B would therefore be positive with respect to its filament by an amount equal to the potential differ- ence between filament and plate of tube A. To avoid this the negative voltage E g is applied to the second grid to give it the appropriate negative potential with respect to its filament. This non-inductive type of amplification circuit is a very important contribution made possible by the thermionic tube, because it enables us to produce almost any degree of amplification without the use of transformers. In many instances transformers are undesirable. This is, for example, the case when dealing with FIG. 144. currents of very low frequency, such as are used on telegraph lines and especially on submarine telegraph cables. Transformers for such frequencies are unpractical, being costly and inefficient. Besides, they distort the wave form which it is very desirable to preserve. Even when dealing with currents of frequencies cov- ering the audible range, transformers produce distortion which in some cases is very serious. This can, for example, happen in the transmission of music. When speech is transmitted through a system having a transmission band ranging from a few hundred to about 2000 cycles per second, the speech is still perfectly intelligible and, in fact, a smaller frequency range often suf- fices. Transformers that are used on telephone lines have a fairly flat frequency characteristic and are very satisfactory for speech transmission. But for the transmission of music a much wider range of frequencies is necessary. It is known that to preserve THE THERMIONIC AMPLIFIER 255 the quality of many musical tones, the system must be capable of transmitting with equal facility frequencies ranging up to several thousand cycles per second. In all such cases the non- inductive amplification circuit is of value. Care must, of course, be taken to eliminate the distortion produced by the curvature of the characteristic of the tube itself. In ordinary circuits, such as that shown in Fig. 139, trans- formers and coils are used for convenience to serve definite pur- poses. The output transformer T% is, for example, inserted to match the impedance of the line or device into which the tube works with the impedance of the tube. This secures maximum power amplification. The input transformer likewise matches the impedances and has a very high secondary impedance because of the high input impedance of the tube. Referring to equation (32) (page 187), it will be noticed that the power amplification rj is directly proportional to the input resistance r ff . Hence, if the tube is to amplify currents from a low impedance line and the input transformer TI were omitted, the amplification would be very small. To overcome this Arnold suggested using voltage ampli- fier tubes to step up the input voltage. These tubes then feed into tubes having an impedance sufficiently low to be connected directly to the output circuit. This can be done by designing tubes to have a low plate resistance or using a number of tubes in parallel. Telephone transformers that are commonly used on the input side of vacuum tubes have voltage step-up ratios ranging from about 18 to 40. Voltage amplifier tubes having an ampli- fication constant ;u=40 are commonly used. It follows from equation 28, page 183; that if the resistance r (Fig. 144) is made five times as large as the plate resistance r p of the tube A, the voltage amplification produced by this tube is 33. It can, there- fore, take the place of the input transformer. The voltage can, of course, be amplified still more by increasing the number of tubes in the cascade series. Fig. 144 shows the filaments connected in parallel to a common battery. They can, of course, also be operated in series from a common battery. Which ever is the more desirable depends upon the filament battery available. Both arrangements are used where tubes are operated in parallel to give increased output. But when the filaments are connected in series and the grids in 256 THERMIONIC VACUUM TUBE parallel, provision must be made to counteract the difference in potential between the successive grids and filaments, due to the voltage drop in the preceding filaments. This is done by the inser- tion of appropriate grid batteries. In designing multi-stage amplifier circuits, it is very important to make sure that all the tubes operate in accordance with the limit equations (24) and (25). In all cases the voltages impressed on the inputs of the tubes must be as high as possible, irrespective of what the input power may be, because the power developed in the output depends primarily on the input voltage. Now, when using a tube as a voltage amplifier it must be designed to have a large amplification constant /z. This, according to equation (27) produces a large voltage amplification. But, referring to equation (25), it is seen that the larger the value of /x the smaller is the input voltage e g that can for constant plate battery voltage E b be impressed on the input without causing distortion. When it is necessary to use a multi-stage amplifier set the input voltage on the first tube is generally so small that // for the first tube can be -pi quite high and the plate voltage not large, because -- need not be larger than about 2e , where Et, is the voltage of the plate battery. But the voltage impressed on the second tube after being amplified by the first tube is then very much larger and the second tube must be capable of handling this increased voltage. If the first tube, operating on a definite plate battery, is just capable of handling the voltage impressed on its input, then, in order to handle the amplified voltage, the second tube must be designed to have a lower /* or otherwise must operate on a higher plate voltage than the first, so that it operates on a characteristic having a larger intercept on the axis of grid potential. (See Fig. 74, page 152.) This often necessitates heating the filament of the second tube to a higher temperature to increase the range of the characteristic. Such considerations show the important part played by the structural parameters of the tube. In some multi- stage amplifier sets it is possible to use several like tubes in series operating on the same plate voltage; that is, when the input volt- age is much smaller than the limiting voltage that the first tube can handle. For example, if the amplification constant M is 40, and the plate voltage is 120 volts, the intercept of the IpEg-curve is equivalent to 3 volts. If E =1.3 volts, the input voltage can THE THERMIONIC AMPLIFIER 257 therefore have a maximum value of about 1.5 volts, since the grid can generally be allowed to become slightly positive. If this is the input voltage on the first tube, the succeeding tubes must have lower amplification constants or must operate with higher plate voltages. But if the input voltage on the first tube is, say, 5X10~ 5 volt, it can be amplified 30,000 times before it becomes too large to be handled by this type of tube operating under the conditions specified above. If each tube with /z = 40 operates with an external resistance equal to four times its plate resistance, it produces a voltage amplification of 32. It would therefore take three such tubes in series to produce a voltage amplification of 30,000, and all three tubes can operate under the above conditions. It may be remarked that if a is the voltage amplification produced by one tube, the total amplification A produced by n tubes is A = a n . Instead of using a large number of tubes in cascade to produce a high degree of amplification, use could be made of a " feed-back" arrangement, due to R. V. L. Hartley, 1 which is of special advan- tage when large amplification is to be produced with a few tubes in a non-inductive circuit. It will be evident that in any ampli- fying system the power developed in the output, which is larger than that in the input, can be greatly increased by feeding a small portion of the energy in the output back to the input, thus ream- plifying that portion. This increases the output power and also the portion fed back to the input, and in this way the original input power can be amplified to almost any desired extent depend- ing on the portion fed back and the limits of the tube characteristic. Thus, suppose unit power be applied to the input of an ampli- fying system, the normal amplification of which is a-fold. The power in the output is then a. Let a fraction s of the output power be fed back to the input, so that the power returning to the input is as. The portion remaining is a (1 s). The fraction as amplified again into the output becomes a?s. Of this, a portion a?s X s = a?s 2 is again fed back to the input, leaving a 2 s a 2 s 2 = a?s (1s) available in the output. This process is repeated and we get in the output an amount of power given by the sum of a series of which the (n+l) th term is a(l-s)a n s n . Thus, if A is the total output power: A=a(l-s)^l+as+a 2 s 2 + . . . aV . . . ). 1 R. V. L. HARTLEY, U. S. Patent, 1218650. 258 THERMIONIC VACUUM TUBE If the fraction as is less than unity the series is convergent, its sum being , so that the total output power becomes: A = " ( and the total amplification produced is A^ 1-s a I as n = = Since as = fr-Cr < 1( VACUUM TUBE AS AN OSCILLATION GENERATOR 275 We have seen above that the condition for oscillation in the case of a two- electrode device is that the resistance of the device must be negative and equal to -^-. This is the effective resistance (_y 7* of the oscillation circuit, so that when it is added to the equal and opposite resistance of the device the total resistance of the circuit, and therefore the damping, is zero. From equation (10) we see that in the case of a three-electrode tube the resistance of the tube need not be negative as long as the first term -^ is large enough. \jT This term involves the amplification constant /* and therefore indi- cates directly that the ability of the audion to produce oscilla- tions lies in its amplifying property. In order to give an interpretation to this condition (equation (10) let us write it in the form: Cr 1 or Cr jr4& (11) It will be recognized that g m = is the mutual conductance of T p the tube as defined in the preceding chapter. For very small oscillations the mutual conductance is given by the slope of the plate current grid potential characteristic, while for large oscil- lations it can be taken to be approximately equal to the slope of the line joining the points of maximum and minimum current on the characteristic. Now, it will be recognized that as the intensity of the oscillations increases, the slope of this line becomes less and less. Equation (11), on the other hand, states that for oscillations to be sustained the mutual conductance must be greater than a quantity involving the constants of the external circuit. The right-hand side of equation (11) is also of the dimensions of a conductance and can also be represented by a line having a slope depending on the values of these constants. Sup- pose this line has a definite slope given by OA, Fig. 154. The oscillations will, therefore, increase in intensity, the current vary- ing over a greater and greater range of the characteristic 1 until the 276 THERMIONIC VACUUM TUBE mutual conductance as given by the line BC joining the points of maximum and minimum current becomes parallel to OA. If the mutual inductance between the plate and grid coils were decreased, the slope of the line representing the right-hand side of equation (11) would increase, say, to OA', and then the oscillations would be weaker, the plate current varying over such a range that the mutual conductance is equal to the slope of the line OA'. Grid. Volfs - + FIG. 154. Whether or not the tube will oscillate depends not only on the coupling between the output and the input coils, but also on a number of other quantities. One of the important quan- tities is the amplification constant /* Fig. 155 shows how /z in- fluences the operation of the device as an oscillator. The line OB gives as a function of /*, and CD gives the expression of equation (11) as a function of /-t. We shall refer to this quantity VACUUM TUBE AS AN OSCILLATION GENERATOR 277 as go. This equation states that g m must be at least equal to go; hence, for the constants of the circuit chosen in this particular case, all values of M lying to the left of the broken line are impos- sible values. The effect of the plate voltage can be shown in a similar way. It follows, for example, from the considerations given in Chapter 10 FIG. 155. VII, that the mutual conductance is approximately proportional to the plate potential, provided the filament temperature is high enough to insure that by increasing the plate potential we do not enter into the saturation region. We can, therefore, replace r v and r p by E P and some arbitrary constants. We then obtain 278 THERMIONIC VACUUM TUBE an expression g m = go where g m is directly proportional to E p and go is a linear function of E p . These relations when plotted as shown in Fig. 156 intersect at the point A. The condition for oscillation is that g m must be at least as large as go. We see, therefore, that the tube will not oscillate until the plate voltage reaches a certain minimum value which is fixed if the other quantities, such as the coupling, etc., are fixed. These considerations show that it is desirable to make the 50 20 30 40 Plate Volts FIG. 156. 50 mutual conductance of the tube as large as possible. This was also found to be the case when using the tube as an amplifier. (See equation (36), Chapter VII). The oscillation frequency as given by equation (9) is deter- mined not entirely by the inductance and capacity in the oscilla- tion circuit, but depends also on the plate resistance of the tube and the resistance in the oscillation circuit. Since, however, the ratio --is usually very small, the frequency can generally be r VACUUM TUBE AS AN OSCILLATION GENERATOR 279 taken to be very closely equal to that given by the simple oscilla- tion circuit; namely, (12) It will be recognized that the solution of the circuit shown in Fig. 153 does not indicate directly what the amplitude of the oscil- lations is. This quantity is, however, determined indirectly by the condition for oscillation. On account of the curvature of the characteristic, the mutual conductance of the tube decreases as the amplitude of the oscillations increases, in the manner explained above, until the mutual conductance reaches its minimum value. The amplitude of the oscillations in the plate circuit can then be determined from this limiting value and the characteristic of the tube. Usually, however, such a determination is not necessary. 83. Relation between Mutual Conductance of Tube and that of Plate Circuit. In the above equations, represents the mutual r-p conductance of the tube itself. This is also the mutual conduct- ance of the plate circuit, provided the external impedance in the plate circuit is negligibly small compared with the resistance of the tube. When this is not the case, the dynamic characteristic of the plate circuit does not coincide with the characteristic of the tube itself, but differs from it to an extent depending on the rela- tive magnitudes of the external impedance and the plate resistance. If the external circuit is non-reactive, the dynamic characteristic of the plate circuit is the curve of noC shown in Fig. 86. If the external circuit is reactive, the dynamic characteristic of the plate circuit takes the form of the loop such as that shown in Fig. 88. In this case the quantity concerned is not a pure conductance but a complex quantity, and what we have to deal with then is the mutual admittance. In most oscillation circuits, however, the reactance is so small at the oscillation frequency in comparison with the total resistance that the angle can generally be neglected. It can readily be seen that the mutual conductance of the cir- cuit is less than that of the tube alone, because when the current in the external circuit is increased by an increase in the potential of the grid, the voltage drop in the external impedance causes a decrease in the plate potential, so that the resultant increase in plate current is less than would be the case if the external imped- 280 THERMIONIC VACUUM TUBE ance were zero. The relation between these two mutual con- ductances can be obtained as follows: The alternating plate cur- rent is given by Putting Z =r +jx we get P,Qo /* + M V where Y' m = g'mjb is the mutual admittance of the plate circuit. Generally the imaginary component is small in comparison with the resistance component, so that we can use the simple equation: 4-= 1 +-. ........ (14) 9 m Qm M This relationship can be expressed in a somewhat different form. Since i p ro=e p , we get directly from equation (13): The condition for oscillation can also be expressed in terms of the mutual conductance of the plate circuit instead of the mutual conductance of the tube itself. This was, for example, done by Hazeltine. 1 The quantity g in Hazeltine's equations is not the mutual conductance of the tube, but the mutual conductance of the plate circuit. 84. Phase Relations. The phase relations that exist in vacuum tube oscillator circuits have been investigated by Heising and explained with the help of vector diagrams. 2 We shall not discuss this phase of the subject beyond what is necessary for an understanding of the fundamental phenomena of such circuits. The main condition is that the plate current and grid potential must be as nearly in phase as possible. The phase relations be- tween the various quantities are shown in Fig. 157 and can be explained with reference to Fig. 152. Ib represents the steady direct current supplied by the battery E b through the choke coil. We can regard this current as constant, 1 L. A. HAZELTINE, R.I.E., Vol. 6, p. 63, 1918. 2 R. A. HEISING, Journal of A.I.E.E., Vol. 39, p. 365, 1920. VACUUM TUBE AS AN OSCILLATION GENERATOR 281 although in actual practice it is only approximately so unless the choke coil has a very large inductance. I P represents the instan- taneous value of the plate current and / the instantaneous value of the current in the branch containing C and Z/2 in parallel. This current multiplied by the instantaneous plate-filament voltage and integrated over a complete cycle, represents the a-c. power supplied by the tube. As much power is drawn from the tube as Grid Potential Anode Current Anode Potential ' Output Current FIG. 157. is dissipated in the oscillation circuit when the steady condition is reached. Referring to Fig. 157, the lines marked represent the ordinates of zero voltages and currents. The grid is maintained at a nega- tive potential E c . When the alternating grid potential is zero, the plate current is equal to 7&. When the grid potential oscillates, as indicated, the plate current oscillates in phase with the grid potential. The plate potential oscillates around the mean value Ei,, but is 180 out of phase with the grid potential if the 282 THERMIONIC VACUUM TUBE external circuit is non-reactive. The current 7 in the branch cir- cuit is the difference between direct current I b drawn from the battery and the plate current I P . It is therefore 180 out of phase with the plate current and oscillates around zero. We have assumed that the grid always remains negative with respect to the negative end of the filament. If the grid becomes positive during a part of the cycle, it takes current which generally means a loss of power occasioned by heat dissipation in the grid circuit. On account of the curvature of the characteristic, the current wave in the plate circuit, due to a sinusoidal voltage impressed on the grid circuit, is not a pure sinusoid but is distorted. This introduces harmonics. They can, however, be effectively tuned ii -* ^ * FIG. 158. out in the oscillation circuit so that most of the energy in the oscillation circuit will be due to the fundamental. It must be recognized that the harmonics cause a waste of power. These considerations apply in general to the fundamental, the effect of harmonics being neglected. 85. Colpitts and Hartley Circuits. The circuit shown in Fig. 152 is only one of a large number that can be used with a vacuum tube oscillator. It was chosen there for its simplicity, although it is not the most commonly used type of circuit. Two circuits that are frequently used are those shown in Figs. 158 and 159, known as the Colpitts and Hartley circuits, respectively. The main difference between these circuits is that in the one the coup- ling between output and input circuits is capacitive and in the other it is mainly inductive. If we neglect the effect of the elec- trostatic capacities between the electrodes of the tube, the oscil- VACUUM TUBE AS AN OSCILLATION GENERATOR 283 lation circuits are C\C 2 L, for the Colpitts circuit, and LiL 2 C, for the Hartley circuit. The effect of the inter-electrode capacities will be considered below. The conditions for oscillation for these circuits have been given by Hazeltine, Heising l and others. Taking, for example, the case of the Hartley circuit, the condition for oscillation can be expressed by: gm= (L 2 +M)Lu(L!+M) - (L 2 +M)]> * ' ' (16) where g m = mutual conductance of the tube, M = mutual inductance between L\ and L 2 , FIG. 159. From this equation it follows that there is a certain relation between the voltages established in the plate and grid coils, which makes the tube oscillate most readily. Since the conditions for oscillation state that the right-hand side of equation (16) must not be greater than #,. it follows that the tube will oscillate most readily when this expression is a minimum. Putting =n, we find e g 1 Loc. cit, 284 THERMIONIC VACUUM TUBE where A; is a constant. This is a minimum for M Cr (l+n) 2 Qm ~ L njL-n M+2' (17) (18) For tubes having a high value of M, therefore, LI should be approx- imately L2. If M is low, on the other hand, the best condition can necessitate making Z/2 considerably smaller than LI. 86. Tuned Grid-circuit Oscillator. This type of circuit which is commonly used in the reception of radio signals, is shown in Fig. 160. If it is assumed, as before, that the grid is maintained FIG. 160. at a sufficiently high negative potential to insure that there is no appreciable convection between filament and grid, the condition for oscillation for this circuit can also be easily obtained. The potential e g applied to the grid is given by (19) and the electromotive force induced in the plate circuit through the tube, on account of the effect of the grid potential on the current is ne a . There is another electromotive force induced in the plate circuit, namely, Mpi, and is due to the mutual react- ance of the grid circuit on the plate circuit through the coils LI and L2. The electromotive force induced on the oscillation cir- VACUUM TUBE AS AN OSCILLATION GENERATOR 285 cuit, due to the current i p in the plate circuit, is Mpi p . Equating these E.M.F/s in the circuits, we get for circuit /: , ..... (20) and for circuit II : (21) Eliminating i p from these two equations, the equation for i becomes : (LiL 2 - M 2 )p*i + (r*Li +rL 2 )p 2 i+ (rr P C+L 2 - 0, . (22) which is of the form p*i+Ap*i+Bpi+Di = 0. This is a cubic equation and has one real and two complex roots. The condition which makes the damping zero is D = AB. That is: In most circuits rL 2 can be neglected in comparison with r p L\ With this approximation the condition for oscillation becomes: The right-hand side of this equation contains two terms, one of which is directly proportional to M, and the other inversely pro- portional to M . There appears, therefore, to be an optimum value for the mutual inductance between the input and output which makes g m a minimum. 1 87. Effect of Inter-electrode Capacities Parasitic Circuits. We have assumed in the above that there is no reaction of the plate circuit on the grid circuit through the tube itself. In some types of circuits the capacities between the electrodes cause the circuits to behave differently, from what is to be expected. The simple circuit shown in Fig. 160 can, for example, be drawn in the manner shown in Fig. 161, where the capacities between the electrodes of the tube are indicated Ci, C 2 and 3. Such a circuit, therefore, has more than one degree of freedom, a number of oscillation cir' 1 S. BALLANTINE, Proc. I.R.E., Vol. 7, p. 159. 286 THERMIONIC VACUUM TUBE cults being added to the main oscillation circuit CL\. Of these parasitic circuits, the most important one in the diagram shown is the circuit formed by the capacity Cs between grid and plate, and the inductance Z/i and Lz in series, the total inductance being Frequency FIG. 162. Li+L,2+2M. The effect of the capacity Ca is to make the fre- quency of osciUation different from that which would be obtained from a simple circuit CL\. The reactance-frequency curve of the VACUUM TUBE AS AN OSCILLATION GENERATOR 287 circuit CLi is shown by the curve marked X\ (Fig. 162). For frequencies lower than that corresponding to the point A, this cir- cuit has a positive or inductive reactance. The effective react- ance, due to the coil LI and its coupling with the oscillation circuit Z/iC, is given by the curve X%. At frequencies below A, the total reactance is inductive, and oscillations will occur at such a fre- quency that the inductive reactance is equal to the capacitive reactance due to the capacity 3 between grid and plate. The oscillation frequency is, therefore, that corresponding to the point F instead of the point A, as would be the case if the effect of the grid-plate capacity were negligible. This circuit, therefore, be- haves somewhat like a Hartley circuit in that the plate coil Z/2, and the oscillation circuit L\C, together, act like an inductance in r 9 FIG. 163. parallel with a capacity. In the Hartley circuit, the capacity between grid and plate is simply in parallel with the oscillation circuit capacity C. This circuit is, therefore, more suitable for use at high frequencies. 88. Regeneration. The effect of the inter-electrode capacities can cause a tube to produce oscillations even when there is no mutual inductance M between the output and input coils. It was explained in Chapter VII, Sections 6971, that on account of these capacities there is an effective impedance between fila- ment and grid, which depends not only on the capacities between the electrodes but also on the constants of the output circuit. This impedance can generally be represented by a resistance r g and a reactance due to the effective input capacity C g . The input circuit can, therefore, be drawn as shown in Fig. 163. The im- 288 THERMIONIC VACUUM TUBE pedance of the circuit formed by C in parallel with r c and C a in series is: The real component r is (26) The first term of the denominator in this equation is usually negligibly small compared with the second, so that the total resistance of the circuit is: If oscillations are impressed on this circuit, the rate at which they would die out depends, of course, on the value of the total resist- ance. If r g is negative, the total resistance will be reduced; that is, there will be a smaller consumption of power in the input cir- cuit and the tube will give a greater amount of amplification. If r a is negative and the effective resistance to the right of AB is equal to the resistance ri, i.e., if the total resistance of the circuit is zero, the circuit will produce sustained oscillations. We can take expression (27) as a measure of the damping, 6, due to the resistance in the circuit. The increase in amplification, due to a reduction in this resistance results in the effect that is sometimes referred to as " regeneration." A measure of the regenerating effect is given by -. Now, it was shown in Chapter VII that r a o is positive when the external plate circuit is non-reactive or con- tains only capacitive reactance. If, on the other hand, the reactance in the plate circuit is inductive and the angle of the impedance in the plate circuit is large enough, then r a is negative. In Fig. 164 are plotted curves showing the relation between the regenerative effect and the ratio of the external impedance in the plate circuit to the plate resistance. The values of r a and C , used in computing these curves, were obtained from equations (54) and (56) of Chapter VII. The quantity T was computed 5 VACUUM TUBE AS AN OSCILLATION GENERATOR 289 with the values so found and with arbitrarily assumed values of rij as indicated in the curves. The curve for ri = 5.4 ohms stretches to infinity, indicating that over the range of the ratio rp from about .8 to about 1.2, the tube produces sustained oscil- T v lations, due to the reaction of the plate circuit on the grid circuit through the electrostatic capacities of the tube. .3.0 An interesting result shown by these curves is that the max- imum regenerating effect is obtained when the external impedance in the plate circuit is equal to the plate resistance. This, it will be remembered, is also the condition for maximum power amplification derived in Chapter VII, for the case of the simple amplifier. 290 THERMIONIC VACUUM TUBE According to expression (27) the regenerating effect becomes greater the smaller the capacity C in the oscillating circuit. J. M. Miller 1 has computed curves giving the signal strength as a function of the inductance in the plate circuit. These curves are similar to those shown in Fig. 164, except that they are more symmetrical. They have the same general form as a curve giving experimental results published by Armstrong. 2 89. Complex and Coupled Circuits Meissner Circuit. Com- plex circuits can be reduced to simple circuits by the addition of the reactances of the separate branches. Thus, the circuit shown in Fig. 160 constitutes a complex circuit if the capacity between grid and plate becomes effective in determining the frequency of the oscillations. The reactances of the branches I and II are indicated by the curves X\ and X% of Fig. 162, while the reactance FIG. 165. due to the capacity 3 between grid and plate is indicated by X%. The frequency of the oscillations is determined by the value of these reactances which makes the total reactance of the circuit zero. In general, a complex circuit such as that shown in Fig. 165 can be regarded as a simple circuit in which the oscillation circuits LiCi and LiCi act as inductances or capacities, according as the reactance between grid and plate is capacitive or inductive. The reactance-frequency curve of a parallel oscillation circuit like L\C\ has a shape such as the curve X\ in Fig. 162. Now, if the react- ance between grid and plate is capacitive or negative, the total 1 J. M. MILLER, Bureau of Standards Bulletin 351. 2 E. H. ARMSTRONG, Proc. I.R.E., Vol. 3, p. 220, 1915. VACUUM TUBE AS AN OSCILLATION GENERATOR 291 reactance can only become zero at a frequency F, which is lower' than the natural oscillation frequency A of the simple parallel circuit LiCi or L^C^ From the curve it is seen that at frequencies below A the reactance of the simple circuit L\C\ is inductive (positive), so that the complex circuit shown in Fig. 165 can be represented by the simple circuit of Fig. 166. This is a Hartley circuit. If, on the other hand, the reactance between plate and grid were inductive, the frequency of oscillation of the circuit will be such as to make the sum of this inductive reactance and the reactances of the branch circuits I and II equal to zero. This would require that the reactances of these branch circuits be capacitive and therefore the frequency of oscillation will be higher than the natural frequency of the circuits I and II separately. o 0> o o o FIG. 166. In this case the total circuit reduces to one like that shown in Fig. 166, except that instead of the two inductances, we have two capacities, and instead of the capacity 3, we have an inductance. In other words, the complex circuit is reduced to a simple Colpitts circuit. Coupled circuits can be treated in much the same manner. The Meissner circuit shown in Fig. 167 is an example of a coupled circuit. 1 The two oscillation circuits are LiZ^Ca and LC. The effects that can be obtained with such a circuit by varying the constants of the oscillation circuits have been discussed by Heising in the paper cited above. The reactance-frequency curves of such a circuit are shown in Fig. 168, where X\ represents the reactance of the circuit LiZ^Cs, and X% the reactance due to 1 A. MEISSNER, " Electrician," Vol. 73, p. 702, 1914. 292 THERMIONIC VACUUM TUBE coupling with the oscillation circuit LC. The sum of the two reactances is indicated by the curve X. It is seen that there are three frequencies for which the total reactance is zero. The tube will not oscillate at the frequency F because this represents an unstable condition, but it can oscillate at the two frequencies Fi and 7^2. Usually, however, it oscillates at only one frequency. By suitably adjusting the coupling between the oscillation circuit LC, or choosing the constants of the circuits, the reactance-fre- quency curve of the combination can take such a form that the three frequencies practically merge into one. This can be done by making the coupling loose, or by making the total inductance i ^mmm} f \M FIG. 167. large compared to 3. This is usually the case with most tubes when the desired frequency is not very high. 90. Circuits Comprising a-c. and d-c. Branches. The circuits shown above indicate only the a-c. branches. These are the only branches that need to be considered in determining the conditions for oscillation and the frequency. In practice we also need d-c. sources of power supply, and it is often necessary to separate the a-c. and d-c. circuits. This can be done readily by applying the simple and well-known rule to 'separate the d-c. from the a-c. branches by means of inductances and capacities. In doing so, however, it is necessary to adjust these inductances and capacities to such values that they do not appreciably influence the behavior VACUUM TUBE AS AN OSCILLATION GENERATOR 293 of the oscillation circuit proper, or introduce parasitic circuits that would result in a loss of power. Fig. 169 shows, as an example, the Hartley circuit as it is com- monly used in practice. The plate battery E b is inserted directly in the circuit connecting the plate to the inductance L^ It is usually not necessary to separate the direct and alternating cur- rent in this branch of the circuit. The capacity C s and resistance R s are used here instead of a battery to maintain the grid at an FIG. 168. appropriate negative potential with respect to the filament. This means of maintaining the grid negative operates only when there is a convection current between filament and grid; that is, when the grid becomes positive during part of the time that the a-c. potential on the grid is positive. When the grid becomes positive it attracts electrons, and current flows through the resistance R s . During the rest of the cycle there is no flow of electrons from fila- ment to grid. There is, therefore, established a rectified current 294 THERMIONIC VACUUM TUBE through the resistance R s , and this lowers the potential of the grid with respect to the filament. 4 FIG. 169. Fig. 170 shows a Colpitts circuit as it can be used in practice. In this case the resistance R s is replaced by a choke coil Chi. The alternating and direct current in the plate circuit are sep- arated by means of the choke coil Chz and the capacity C&. The FIG. 170. inductance of this choke coil is usually chosen as high as possible, or at least so high that its impedance is several times the plate resistance of the tube. The capacities C s and C 6 are chosen sufficiently large so that they do not appreciably affect the opera- tion of the oscillation circuit LC\Cz. VACUUM TUBE AS AN OSCILLATION GENERATOR 295 91. Effect of Grid Current. In deriving the conditions for oscillation above, it was assumed that the grid is at all tunes maintained sufficiently negative with respect to the filament to prevent any convection current' from flowing between filament and grid. In practice this is usually not the case. The grid usually becomes positive to an extent depending on the adjustments of the circuit constants. Thus, when using the condenser and resistance to maintain the grid negative, as shown in Fig. 169, the grid must become positive during part of the cycle. The rectified current through R s maintains the grid at a steady nega- tive potential, and the value of this potential will be greater the greater the grid current becomes. Hence, the fraction of a period during which grid current flows, that is, the amount of grid cur- rent, will be determined by the rate at which it leaks off through the resistance R s . Now, the grid and plate potentials are approx- imately 180 out of phase. This is shown, for example, in Fig. 157, which was drawn for the case in which the plate is connected to a non-reactive circuit. The amount of current flowing to the grid depends not only on the grid potential but also on the potential of the plate. The higher the plate potential the more readily will the electrons be drawn through the openings of the grid, and the smaller will be the grid current. But if the plate becomes less positive at the same time that the grid becomes more positive (as shown in Fig. 157), there is a tendency for the grid current to become much greater, and if the potential variations impressed on the grid become so great that the maximum positive grid potential becomes equal to or perhaps greater than the simul- taneous minimum plate potential, then the grid can rob the plate of so much current that the characteristic representing the plate current as a function of the grid potential becomes apparently saturated at a current value which is lower than the actual satura- tion current at the temperature of the filament. This effect is shown in Fig. 171 which represents the static characteristics of the tube for various fixed values of the plate potential. When the tube operates in an oscillation circuit, which is so adjusted that the reactance in the plate circuit is practically zero, the dynamic characteristic of the plate circuit is represented by the curve AOB. The normal grid potential, when the tube does not oscillate, is represented by the value E c . When oscillating, the plate poten- tial decreases when the grid potential increases and vice versa, 296 THERMIONIC VACUUM TUBE so that the characteristic is given by A OB instead of the static characteristic A'O'B'. At B the plate and grid potentials become comparable, and the plate current begins to decrease. This plate current is less than the emission current; that is, the current represented by the total number of electrons leaving the filament. The point B represents the maximum potential that the grid can acquire without causing too much waste of power. The mutual conductance of the plate circuit can be repre- sented by the slope of the straight line joining A and B. The instantaneous value of this quantity is zero at B and A, and has a B' A' Grid Potential FIG. 171. maximum value at 0, but the mean value which is determined by the integrated slope of the curve is finite. 92. Output Power. The value of the grid potential at which the bend B in Fig. 171 occurs, depends on the resistance of the external plate circuit. The current in this resistance r causes a potential drop which reduces the potential on the plate, since the voltage of the plate battery remains constant. The larger this resistance the greater will be the decrease in the plate potential when the current in the plate circuit increases, and the sooner will the bend in the characteristic occur. Also, the greater the external resistance, the smaller will be the slope of the dynamic VACUUM TUBE AS AN OSCILLATION GENERATOR 297 characteristic. Fig. 172 shows the dynamic characteristics for a number of different values of the external plate resistance ro. The characteristic OB is obtained for the largest, and OE for the smallest external resistance. If the tube operates, for example, in a circuit like that shown in Fig. 152, the impedance of the parallel circuit L 2 r and C is given by , .coL 2 (l-co 2 CL 2 )-coCr 2 Z = (l-co 2 CL 2 ) 2 +co 2 C 2 r 2 ~~ (l-co 2 CL 2 )-co 2 C 2 r (28) The resistance or real component of this impedance at the L 2 resonance frequency is given by ro=. The characteristics Or Gnd FIG. 172. OB, OC, etc., correspond to different values of this resistance. The maximum power output in each case is obtained when the grid potential rises up to the value indicated at the bend. If, now, the output for each of these resistances ro be plotted as a function of this resistance, we obtain a curve such as that shown in Fig. 173, which shows a maximum for a particular value of the external resistance ro. This resistance is equal to the plate resist- ance of the tube. From the maximum value given in Fig. 173, the ratio of the inductance to the capacity of the oscillation circuit can be determined, which gives the maximum output power. In general, maximum output power does not necessarily mean THERMIONIC VACUUM TUBE J maximum efficiency. This will become evident from considera- tions in the next section. 93. Efficiency. The efficiency of the oscillator can be ex- pressed by the ratio of the power supplied to the oscillation circui t to the power drawn from the source of plate voltage (battery, generator, etc.). Strictly speaking, the overall efficiency should take account also of the power expended in heating the filament. In high power oscillators this power can usually be neglected, as will become evident from the following considerations. Of External Resistance FIG. 173. the power drawn from the source of plate voltage E, part is dissi- pated at the plate and serves no useful purpose. This we shall refer to as P p . The remainder, P , of the power drawn from the plate battery, is delivered to the oscillation circuit. If we neglect the power expended in heating the filament, the efficiency can be expressed as: Efficiency = ^=- where P b represents the power supplied by the plate battery and is equal to the product of the direct current I b and direct voltage Eb in the plate circuit. VACUUM TUBE AS AN OSCILLATION GENERATOR 299 J For a fixed value of the efficiency, the power drawn from the plate battery is a measure of the power supplied to the oscillation circuit. This can be increased either by increasing the plate cur- rent or the plate voltage. In the former case, the filament area or the filament temperature, or both, must be increased and then the power expended in heating the filament may become com- parable with, or even greater than, the power in the plate circuit. If, on the other hand, the power in the plate circuit be increased by increasing the plate battery voltage, instead of the current, the power expended in heating the filament becomes relatively smaller and smaller. It will be evident that even if the saturation current obtained from the filament remains relatively small, the power can be increased to almost any desired value by sufficiently raising the voltage of the plate current supply. Of course, in doing so the operating point of the characteristic rises to higher current values and may even fall on the saturation part of the characteristic, but this can be prevented by increasing the nega- tive potential on the grid or increasing the value of the amplifica- tion constant ju. As was explained in Chapter VII, the plate potential necessary to give any chosen value of plate current increases as ju is increased. The limitation to increase in power by this means is not inherent in the tube, but is determined almost entirely by the available source of high voltage direct current. The plate voltage is usually supplied by one of three means: Battery, d-c. generator, or vacuum tube rectifying system, such as those explained in Chapter VI. Batteries are costly and are seldom used for high-power tubes, while high-voltage d-c. gene- rators are at present inefficient. Vacuum tube rectifying systems have been used successfully and are capable of giving very high voltages but care must be taken to smooth out the rectified cur- rent wave, and the extent to which it is smoothed out by means of filters, for example, depends on the resistance of the load in its output. If satisfactory d-c. generators could be made to give from 10,000 to 20,000 volts, it would be possible to get several kilowatts output power from tubes that are relatively inexpensive and simple to make. In considering the efficiency, we shall neglect the power dis- sipated in heating the filament. Let Ej,, Eg, Ip be the instantaneous plate and grid potentials and plate current, and E b , E C) h, the corresponding d-c. values 300 THERMIONIC VACUUM TUBE when the alternating components are zero. Let e p , etc., be the corresponding R.M.S. values, and e' P the maximum a-c. values. From the curves shown in Fig. 157, it follows that Ep = E b +e' p smpt, ....... (29) and referring to Fig. 152, we see that I p = I b -I = I b -i' sinpt (30) The power dissipated at the plate is given by 1 C^ Pp = 2~ I E p l p dt (31) or, putting in the values from the above two equations and integrat- ing: 6 V 1 P^_p n /Q0\ ^r*i> *o \3*) The power dissipated at the plate is therefore equal to the power supplied by the plate battery minus the power supplied to the oscillation circuit, and the efficiency is (33) This is never greater than 50 per cent and becomes equal to 50 per cent if the plate current oscillates over the whole range of the characteristic and the maximum value of the alternating plate potential is such as to reduce the plate potential to zero at the moment when the grid has its maximum positive potential. Under these conditions e' p =Eb, and i' ' = /&. This expression was derived on the assumption that the values of E p and I p are always within the limits of the characteristic. There is, however, another way in which the tube can be operated, which gives higher efficiency. This can be done by so propor- tioning the plate and grid potentials that the plate current flows only during a small part of the cycle. Taking, for example, the case in which the plate and grid potentials are so adjusted that the operating point does not lie on the characteristic, but is sit- uated beyond the intersection of the characteristic with the axis of the grid potential as indicated at A (Fig. 174) , it will be seen VACUUM TUBE AS AN OSCILLATION GENERATOR 301 that the plate current flows only during a part of the half period during which the a-c. component of the grid potential is positive. During the time that the plate current is zero, the power dissipated at the plate is, of course, zero. When current flows to the plate the potential of the plate decreases on account of the voltage established in the external resistance. If the current could become so large that the potential of the plate is reduced to Grid Pofenf-ial FIG. 174. practically zero, the power dissipated at the plate is again nearly zero, so that the total power dissipated at the plate becomes very small. In the extreme case in which the current at a given grid potential rises suddenly to such a high value that the plate poten- tial is almost immediately reduced to zero, the total power dis- sipated at the plate would become zero and then the efficiency would be 100 per cent. This is, of course, a theoretical limit which never obtains in practice. The plate potential would hardly ever drop down to zero because when it drops so low as to become about equal to the simultaneously occurring instantaneous value of 302 THERMIONIC VACUUM TUBE the grid potential, the electrons coming from the filament would be diverted to the grid and the plate current would .decrease, so that in general the plate potential would not at any time become lower than the grid potential. The increase in efficiency, when operating the tube somewhat I Power Dissipated at Plate Output fowzr FIG, 175. in the manner described above, can be explained with reference to the curves in Fig. 175. These curves are drawn for the con- ditions that current to the plate flows only during part of a cycle, and that the plate potential when the current is a maximum is reduced to a small value. For such an irregular set of curves the simple analysis given above, and which led to equation (33), VACUUM TUBE AS AN OSCILLATION GENERATOR 303 cannot readily be applied. But the efficiency can still be expressed by the equation ^- ^ (34) JEjdt+jEpIjli In Fig. 175, the horizontal dotted lines represent the axes of zero values. The plate current is represented by the curve just above the plate potential curve. The output current is repre- sented by /, and indicated by the curve below the plate potential curve. This current has a mean value indicated by the dotted line. The plate current I P flows only during the period indiaated by MN. During this period the plate potential drops and the power dissipated at the plate, which is given by J E p lpdi, is rep- resented by the area A. The output power, on the other hand, is given by J E p ldt, and is represented by the difference between the shaded areas B and C. This power, for the conditions chosen, is greater than the power dissipated at the plate, the efficiency for the values chosen here being about 70 per cent. Fig. 176 shows oscillograms of the currents and voltages taken under such conditions that the plate current remains zero during about half of a complete cycle. For this I am indebted to Mr. J. C. Schelling. The photograph shows two sets of curves taken on the same film, /o represents the current in the oscillation cir- cuit and is 90 out of phase with the plate current I P . The grid current I g is in phase with the plate current and the grid potential, and these quantities are nearly 180 out of phase with the plate potential E p . J. H. Morecroft l has computed the efficiency for a number of assumed shapes of the plate current wave. These curves are shown in Fig. 177. Below the figure are indicated the power dissipated at the plate, the output power and the efficiency for each of the assumed shapes of the plate current waves. In the last case, where the current wave is assumed to be rectangular, the efficiency rises to a value of 82 per cent. This represents the best condition as far as output power and efficiency are con- cerned, but in general the output power decreases as the efficiency increases because this assumed shape of wave is not obtained in 1 Transactions of A.I.E.E., 1919. 304 THERMIONIC VACUUM TUBE Ig. Grid Current Jo, Oscilla- tion Current Ip, Plate Current Ep. Plate Potential Eg, Grid Potential Ip, Plate Current FIG. 176. VACUUM TUBE AS AN OSCILLATION GENERATOR 305 practice. In practice it is therefore necessary to compromise between efficiency and output power. The importance of high efficiency becomes apparent when considering that the limiting factor in a tube is the amount of power that can be dissipated at the plate. This is limited by the factors discussed in Section 31. If we write rj for the efficiency, we see from equation (34) that the output power is given by Since P P is a fixed quantity for a given tube, the output power could be made very large by making 77 large. For example, if Efficiency -39% Efficiency =62%, FIG. 177, the efficiency could be as high as 90 per cent, and if the plate is capable of dissipating, say, 500 watts, then the output power would be about 4.5 kw. This would not require a very large tube. The total area of the plates that would be necessary for a dissi- pation of about 500 watts ranges from about 50 to 100 sq. cm., depending on the material used for the plates. When using a tube in this manner, it is necessary to remember that when the tube stops oscillating, for example, when the oscillation circuit is detuned, the total power supplied by the plate battery will be dis- 306 THERMIONIC VACUUM TUBE sipated at the plate and may cause the liberation of too much gas, or even melt the plates. It is therefore necessary to insure that whenever the oscillations should stop, the plate battery be imme- diately cut out, or its voltage be sufficiently reduced. 94. Method of Adjusting Coupling between Output and Input. In order to obtain the best operation with a tube, it is necessary to adjust properly the coupling between the output and input circuits. In most circuits this is readily done by making use of any of well-known means of changing the mutual reactance. In some circuits, however, changing the coupling also changes the oscillation frequency. Fig. 178 shows, for example, a Col- FIG. 178. pitts circuit; that is, a circuit in which the coupling between input and output is capacitive. The coupling is changed by changing the condenser 2, but it will be seen that this at the same time changes the frequency of the oscillation circuit LCiCz. This is usually taken care of by inserting another condenser C a , the capacity of which is then so adjusted as to bring the fre- quency back to its original value. Such a circuit requires two adjustments when it is necessary to change the coupling while keeping the frequency constant. A circuit which avoids this double adjustment has been described by R. A. Heising. 1 This circuit is shown in Fig. 179. The oscillation circuit is given by LC\C2 and the mutual reac- tance between the output and input is varied by varying the con- tact Q. This adds an inductive reactance to the capacitive 1 Loc. cit. VACUUM TUBE AS AN' OSCILLATION GENERATOR 307 reactance, thereby changing the mutual reactance between the output and input circuits. It will be recognized that if the plate is connected to the point Q', the circuit is the same as that shown in Fig. 178, with the capacity C a omitted. This means of adjust- ing the coupling does not appreciably change the oscillation fre- quency. 95. Influence of the Operating Parameters on the Behavior of the Oscillator. It will be realized that there are a large number of factors that determine the operation of a vacuum tube oscillator. The most important of these factors are the filament current, d-c. plate and grid potentials, plate and grid coupling and oscillation circuit resistance. When it is a mere matter of obtaining an C * FIG. 179. alternating current by means of the vacuum tube, very few adjustments will serve the purpose. It will usually be found that the tube starts oscillating immediately on closing the plate and filament circuits. If it fails to oscillate a slight increase in fila- ment current or plate voltage, or both, will set the tube oscillating. If, on the other hand, it is desired to obtain maximum power out- put at the maximum efficiency consistent with it, the adjustments have to be made carefully, but with a little practice the whole operation reduces to a simple one. Some of the operating para- meters are fixed by the limits of the tube and circuit. For exam- ple, the tube may be designed to operate on a certain range of filament current and plate battery voltage. This automatically fixes two parameters. The manner in which the behavior of the oscillator is influenced by these various parameters can be explained with reference to the following diagrams. These represent in a 308 THERMIONIC VACUUM TUBE general way, what can be expected with commonly used types of tubes. The nature of these curves could be expected to vary some- what with different types of tubes. 1 One of the most important variables is the filament current. The influence of the filament current on the operation of the tube can be understood by lef erring to Figs. 17 and 18, that were discussed in the beginning of Chapter IV. Fig. 17 gives the relation between the output current and the plate or anode voltage. When using the tube as oscillator, we operate over the sloping part OA of the characteristic. The three sets of curves shown are for different values of the filament current. Fig. 18, on the other hand, gives the relation between the anode current and the temperature of the filament or the fila- ment current. But the sloping part of this characteristic repre- sents a temperature of the filament which is so low that the plate potential is sufficiently high to draw all the electrons away to the plate as fast as they are emitted from the filament. The condition which may be characterized as temperature saturation is repre- sented by the horizontal poition CD of the curve, and obtains when the number of electrons drawn to the plate is less than the total number emitted. The part CD of Fig. 18, corresponds to the sloping part of OA of Fig. 17; hence, for a given d-c. plate potential it is necessary that the temperature of the filament be so high that we operate on the horizontal part of the plate current, filament current characteristic. If this is not the case, the varia- tion in output current with the variation in the grid potential is too small to produce oscillations. The dependence of the oscilla- tion current and the plate current upon the filament current is indicated in Fig. 180. If the filament current is below a certain value given by A, the tube does not produce sustained oscillations. Filament currents below this value correspond to the saturation part of the curve giving the plate current as a function of the plate potential. If the filament current is raised beyond the value indicated by A, the tube starts oscillating and the oscillation current increases until, when temperature saturation is obtained, it shows no further increase with increase in filament current. In order to secure the best operation, therefore, the filament cur- rent should not be less than the value indicated by B. On the 1 A variety of experimental curves have been obtained by Heising with a standard VT-2 type of tube and published in the Journal of the A.I.E.E., May, 1920. VACUUM TUBE AS AN OSCILLATION GENERATOR 309 other hand, the filament current should not be increased much beyond this value because that would shorten the life of the tube. If the tube is operated with a resistance R s in the grid circuit, as indicated in Fig. 169, for example, the value of the oscillation current obtained depends on this resistance, in the manner shown in Fig. 181, where the lowest curve represents the highest leak resistance R s in the grid circuit. The oscillation current is less for the higher resistance, but the horizontal part of the curve Filament Current FIG. 180. starts at a lower filament current. On the other hand, if the oscillation current be plotted as a function of the filament current for various values of the plate potential, a set of curves is obtained similar to that shown in Fig. 181, except that the lowest curve would represent the case for the lowest plate potential, so that although the output can be increased by increasing the plate bat- tery voltage, the horizontal part of the curve is reached at a higher filament current. The filament current at which the bend in the curve occurs can be taken to represent the safe temperature of the filament. It will be seen then that the safe temperature 310 THERMIONIC VACUUM TUBE increases with increase in plate potential and decreases with increase in the grid leak resistance. By making use of these two variables, plate potential and grid leak resistance, a com- promise can be effected to give the best output for the longest life of the filament. The relation between the oscillation current and plate poten- tial is shown in Fig. 182. 1 The tube starts oscillating at a plate potential depending on the adjustments of the circuit. If the plate voltage be raised, the oscillation current increases almost Filament Current FIG. 181. linearly with it. As the grid leak resistance is increased, the slope of this line becomes less and the oscillation current for given plate potential becomes less. The value of leak resistance R s that gives satisfactory operation usually lies in the neighborhood of 5000 to 10,000 ohms. When a grid battery is used to maintain the grid at an appro- priate negative potential, the tube behaves differently from the manner explained above, where the negative grid potential was maintained by means of the grid leak resistance R s . For example, with a battery in the grid circuit the oscillations will usually not 1 R. A. HEISING, loc. cit. VACUUM TUBE AS AN OSCILLATION GENERATOR 311 start until the plate voltage is raised to a higher value than that necessary when using the grid leak resistance instead of a battery. 0.8 0.7 o. O.I ioo eoo 300 400 500 Plate Voltage FIG. 182 100 ZOO 300 400 500' Plate Volts FIG. 183. If the plate voltage be further increased, the oscillation current increases almost linearly as indicated in Fig. 183. But if the plate 312 THERMIONIC VACUUM TUBE voltage be again reduced, the oscillations will persist until this voltage reaches a value which is quite appreciably lower than that necessary to start the oscillations. The output power as a function of the plate battery voltage can be represented by a curve like that shown in Fig. 184, which shows a rather rapid increase as the plate voltage is raised. To obtain increase in output power by increasing the plate voltage, it is, of course, necessary to insure that the filament current is 100 ZOO 300 400 500 Plate Volts FIG. 184. high enough to prevent the space current from becoming sat- urated. Also, the power delivered to the oscillation circuit depends on the resistance of this circuit and the resistance of the tube. The latter depends on the d-c. plate potential so that in general an increase in the plate battery voltage would necessitate a read- justment of the capacity and inductance in the oscillation circuit to give the maximum output power. 96. Range of Frequency Obtainable with the Vacuum Tube Oscillator. Circuits for Extreme Frequencies. The vacuum tube has been used to give oscillations having a frequency ranging VACUUM TUBE AS AN OSCILLATION GENERATOR 313 from a fraction of a cycle per second to many millions of cycles per second. For low frequencies, the frequency is determined almost entirely by the inductance and capacity in the oscillation circuit, and the only limitation to this end of the scale is the size cf the inductances and capacities. For very high frequencies, the fre- quency of the oscillation is determined mainly by the electrostatic capacity between the electrodes of the tube and by the inductances and capacities of the wires connecting the electrodes. The upper limit to the frequency obtainable depends mainly on the intra- electrode capacities. FIG. 185 When very low frequencies are desired, it is best to use a Hart- ley circuit, in which the two coils LI and Z/2 of Fig. 159 take a form of an iron core transformer such as is shown in Fig. 185. By means of such a circuit it has been possible to obtain frequencies as small as a fraction of a cycle per second. When it is desired to obtain exceptionally high frequencies, the inductances in the oscillation circuit can be reduced to the utmost extent, until they take the form of short straight wires connecting the electrodes. The capacity between grid and plate forms the capacity of the oscillation circuit. A circuit which has been used, for example, by W. C. White, 1 to obtain a fre- 1 General Electric Review, Vol. 19, 771, 1916? 314 THERMIONIC VACUUM TUBE quency of fifty million cycles per second is shown in Fig. 186. The grid inductance is furnished by the connecting wire GAP and the plate inductance by the connecting wire PDB. The plate current is supplied by the battery Ej, through the choke coil LI. Ci represents a by-pass for the high frequency and is so large that it does not affect the oscillation frequency. W represents a long pair of parallel wires connected to the system through the small capacities 2 and 3. By suitably adjusting the bridge H, stand- FIG. 186. ing waves can be obtained. In White's experiments these waves were about 6 meters long. This circuit represents a very simple means of demonstrating standing waves. The vacuum tube is much superior to the induction coil frequently used in laboratories for this demonstration experiment. By using tubes that are specially designed to have low electrostatic capacities between its electrodes, it is possible to obtain waves of a few feet in length. . CHAPTER IX MODULATION AND DETECTION OF CURRENTS WITH THE VACUUM TUBE 97. Elementary Theory of Modulation and Detection. In the applications of the vacuum tube considered so far, it is desirable that the characteristic of the plate circuit be as straight as possible. For example, when using the device as an amplifier, it was explained in Chapter VII that the external impedance in the plate circuit is usually made so large that the current voltage characteristic of the plate circuit is sufficiently straightened out to enable us to neglect quantities of higher order than the first. When using the tube as an oscillation generator, it is also desirable to have a linear characteristic because the curvature introduces harmonics which result in a waste of power. In the following we shall consider those applications of the vacuum tube which depend directly on the curvature of the characteristic. The two most important of these applications are the use of the tube to modulate high frequency currents for purposes of signaling and the detection of high frequency currents. When considering the second order quantities that enter into the characteristic of the device, it is generally not possible to express the characteristic by a simple equation, but we can still apply the equation derived in Section 22, Chapter III, which holds generally for three electrode devices. Neglecting the small quantity we can write this equation in the form In general the function / is not linear and, therefore, if a sinusoidal voltage be impressed upon the input of the tube, the output wave will be distorted in the manner explained in Section 57. For such a condition we can express the varying current in the output 315 316 THERMIONIC VACUUM TUBE as a function of the sinusoidal voltage impressed upon the input by a simple power series, (2) where J represents the varying current and will in general have the form of a lopsided wave, and will, therefore, comprise currents of different frequencies and a direct-current component. This series, it has been found, usually converges so rapidly that we can neglect all quantities of higher order than the second. Experi- mental proof of this will be given later on. The first term of equation (2) represents a current having the same frequency as that of the input voltage e. The second term is the one which gives rise to modulation and detection effects. To evaluate the coefficients a\ and 02, we can proceed in the manner given by J. R. Carson. 1 Carson has considered two cases, namely, when the output circuit contains a pure non- inductive resistance and secondly when the output circuit contains a general impedance. In order to derive an expression for the coefficient 0,2 in terms of the parameters of the tube, we khall discuss only the first case, namely, in which the plate circuit contains only a pure resistance. The quantities to be considered in the circuit can be expressed as follows: E =E c +e (3) where I&, E b and E c represent the d-c. values of plate current and potential, and grid potential, and I p , E F and E are the quantities that obtain as a result of the variations J, v and e superimposed on the d-c. values. Substitution of equation (3) into (2) gives: ...... (4) where PI, P 2 , etc., are given by P -L -n\(3EJ Ep = Eb - ' ..... (5) 1 J. R. CARSON, Proceedings I.R.E., Vol. 7, p. 187, 1919. DETECTION OF CURRENTS WITH THE VACUUM TUBE 317 The physical significance of the differential parameters P n become apparent when they are evaluated with the help of the character- istic equation (1). Thus, P = 2r 2 (6) where r p is the plate resistance of the tube and r' P is the variation in the plate resistance due to the curvature. These equations now enable us to evaluate the coefficients ai and 0,2 of equation (2). To do this it should be noted that the variation v in plate voltage is equal and opposite to the voltage drop established in the external resistance TQ due to the varying current / in the output. Hence, substituting v= roJ into equation (4), we get: This equation now gives the varying current / in terms of the input voltage e and the parameters of the tube and circuit. To express J as an explicit function of the input, we can substitute the series for J given by equation (2) into equation (7) and equate coefficients of like powers of e. When this is done the expression for the varying current J becomes, UP 1 /|2 r ' r P*> T fj,e i v r p r p e If the characteristic is linear, the plate resistance r p is constant and, therefore, its derivative r' p is zero. This makes the second term of the above equation zero. Hence, replacing the varying values J and e by the R.M.S. values i p ^nd e ffj equation (8) reduces to equation (22) given in Chapter VII. The second term of equation (8) represents the property of the tube that enables it to act as a modulator and detector. The value of the coefficient given by the second term in equation (8) will be helpful in the interpretation of the equations that follow. For the present we shall use equation (8) in the simple form . (9) 318 THERMIONIC VACUUM TUBE to explain how the second term is instrumental in producing mod- ulation and detection. 98. Modulation. Suppose that a tube be inserted in a cir- cuit such as that shown in Fig. 187. Let high frequency currents be impressed at H. F. and low frequency currents, lying within the audible range, at L. F. The total input voltage on the tube is then, =i sin pt+e 2 sin qt, ..... (10) where - and represent the high and the low frequencies ZTT 2iir respectively. In order to obtain the output current, we have to substitute this expression for e in equation (9). When using the mm \ L.F. FIG. 187. tube as a modulator, we are interested only in currents having frequencies lying within the range ^ - . Hence, substituting (10) into (9), evaluating and dropping all terms having frequencies lying outside of this range, we obtain, J = a\e\ sin pt-\-2a,2eie2 sin pt sin qt. . . . (11) This expression represents a wave of varying amplitude as shown in Fig. 188, the amplitude of the high frequency carrier 1 wave 1 The word " carrier " is here used as a general term to indicate the high . frequency wave, which is modulated by the signaling wave. It has also a more specific meaning in which it refers to the transmission of high fre- quency currents over wires. DETECTION OF CURRENTS WITH THE VACUUM TUBE 319 varying in accordance with the audio frequency wave impressed on the input of the tube. We can, for purposes of explanation, write equation (11) in the form, J = Asmpt(l+Bsmqt). .... (12) FIG. 188. b A FIG. 189. The way in which a wave of the type shown in Fig. 188 is pro- duced by the vacuum tube, becomes apparent when we consider the characteristic. For example, Fig. 189 shows the plate cur- rent grid potential characteristic. Suppose a constant potential 320 THERMIONIC VACUUM TUBE EC be applied to the grid so that the normal plate current is rep- resented by the ordinate AO. Now let a high frequency voltage of amplitude Oa be superimposed on this constant grid potential. The output of current wave will then have the amplitude given by ab. If the grid potential be increased to the value BC and a high frequency voltage of the same amplitude as before be impressed on the input, the output current wave will have an amplitude a"b", and this is smaller than before. If, on the other hand, the grid potential be reduced to the value DC, the amplitude of the FIG. 190. output current wave for the same amplitude of input becomes greater and is represented by a'b'. If now, we impress on the input not only a high frequency voltage of constant amplitude Oa, but also at the same time a low frequency having an amplitude equal to say AB, then the amplitude of the output current wave will alternately increase and decrease at a frequency equal to that of the low frequency wave impressed on the input and the result is an output current wave of the shape shown in Fig. 188. Fig. 190 represents the input and output waves. The input wave is a high frequency of constant amplitude superimposed on a low fre- DETECTION OF CURRENTS WITH THE VACUUM TUBE 321 quency, while the output wave is a high frequency of varying amplitude superimposed on a low frequency. If the output circuit (Fig. 187) be tuned to the high frequency, the low frequency cur- rent variations are filtered out, thus resulting in the wave shown in Fig. 188. If the low frequency voltage impressed on the input circuit has such a value that the maximum negative potential of the grid becomes equal to CF (Fig. 189), the current is reduced to zero and the modulated output wave then takes the form shown in Fig. 191. The wave can then be said to be completely modulated. When this happens the coefficient B in equation (12) is unity and the maximum amplitude of the high frequency wave when the grid has its minimum negative potential is then 2 A . In some measure- ments it is very important to insure that the wave is completely FIG. 191. modulated as will become evident later on when we come to con- sider measurements on the detecting efficiency of tubes. The second term in equation (11) gives a measure of the extent to which a wave is modulated. The coefficient 2 is given by equation (8), namely, (13) The amplitude of the modulated wave is, therefore, proportional to 162 (14) It is, therefore, proportional to the product of the amplitudes of the audio and the radio input voltages and to the curvature r' p of the characteristic. The modulated output power is also pro- portional to -. -~- -rg, and this is a maximum when ro is equal to 322 THERMIONIC VACUUM TUBE $r p , a result which was stated by Carson. 1 If we put ro = nr p expression (14) may be written: which shows that the value of the device as a modulator depends on the ratio of n to r p . This quantity which is the mutual con- ductance of the tube has also been found to be a measure of the figure of merit of the tube as amplifier and as oscillation generator. 99. Modulation Systems. The results derived above can be interpreted by stating that a device will operate as a modulator if it has a varying resistance characteristic; the resistance to the radio frequency currents is varied in accordance with audio fre- quency currents. There are, therefore, two main systems whereby modulated currents can be transmitted over a line or from an antenna. The first is exemplified in Fig. 187. Radio frequency and audio frequency voltages are impressed on the grid and the resulting modulated current in the output of the tube is trans- mitted over a line or antenna of constant impedance. The antenna must then be tuned to a frequency range 75, where - ir is the carrier or radio frequency and ~ the audio frequency. ir In telephony ^- covers a range of from about 100 to 2000 or 3000 2ir cycles per second. The antenna must; therefore, be tuned so that it has approximately the same impedance for frequencies covering a range of about 2000 cycles. This is also a condition for ordinary wire telephony which requires that the telephone line should be capable of transmitting this whole range of frequencies with about equal facility. The only difference is that in ordinary wire telephony the frequencies cover a range up to about 2000, whereas in carrier or radio telephony the frequencies cover the same range but their actual values are in the neighborhood of the carrier frequency. The other system consists in impressing a high frequency directly on the antenna or line and then varying the resistance of the antenna in accordance with audio frequency. Such a system is shown schematically in Fig. 192, which shows the modu- : Loc. cit. DETECTION OF CURRENTS WITH THE VACUUM TUBE 323 lator M in shunt with the antenna inductance, that is, the antenna inductance is shunted by the plate resistance of the modulator tube. The amount of current in the antenna, which is supplied by the high frequency oscillation generator, will, therefore, depend on the resistance of the tube M. This resistance is varied in accordance with the speech voltages impressed on its input in the manner explained with reference to Fig. 189. A modification given by R. A. Heising l is shown in Fig. 193. The oscillation circuit shown here is the same as that given in Fig. 179, the capacity of the antenna forming the capacity 2 of Fig. FIG. 192. 179. The oscillator and modulator are both supplied by a battery- through a low frequency choke coil which insures that they are both supplied with constant direct current. The speech or audio frequency voltage is impressed on the grid of the modulator by means of the transmitter through the transformer as indicated. Between the plates of the modulator and oscillator is a high fre- quency choke. If the telephone transmitter is not actuated, the oscillator tube supplies high frequency currents of constant ampli- tude to the antenna. If now an audio frequency voltage be impressed on the grid of the modulator, audio frequency currents are established in the output circuit of this tube and consequently 1 See CRAFT and COLPITTS, Proceedings, A.I.E.E., Vol. 38, p. 360, 1919. 324 THERMIONIC VACUUM TUBE the potential of the plate of the oscillator varies in accordance with the low frequency, thus producing low frequency variations in the amplitude of the high frequency oscillations obtained from the oscillator and impressed on the antenna. The coupling is adjusted by sliding the contact Q as explained in connection with Fig. 179 in Chapter VIII. A number of modulating and transmitting circuits have been suggested. The circuit shown in Fig. 194 J is another illustration of the application of the principles given in the foregoing. This circuit is so arranged that the high frequency is impressed at H. F. in such a way that the grids of both tubes are in phase, The high Low Frequency Choke High Frequency Choke FIG. 193. frequency currents in the output coils, therefore, flow in opposite directions and the output in the secondary of the transformer To is zero. But if the audio frequency voltage is impressed as indi- cated at L. F., the grid of the one tube becomes positive wheYi the other becomes negative so that the resistance of the one tube is reduced while that of the other is increased. This causes an increase in the amplitude of the high frequency currents flowing through the one tube and a decrease in the amplitude of those flowing through the other tube. In this way, therefore, energy is radiated only during the time that the tube is actuated by the 1 British Patent 130219, 1918. DETECTION OF CURRENTS WITH THE VACUUM TUBE 325 speech voltage. What is transmitted then is only the waves given by the second term of equation (11). 100. Detection. The mechanism of detection is identical with that of modulation and is due to the same cause, namely, the curvature of the characteristic. In general, therefore, the equations derived above are applicable also to the problem of radio detection with the thermionic tube. The only difference is that in this case we are concerned with a different range of frequencies. While in the case of the modulator, the output is tuned to radio frequencies, in the detector the output is tuned to audio frequencies because the problem of detection involves FIG. 194. transforming high frequency into low frequency currents so that they can become audible. We can, therefore, use equation (9) to determine the low frequency output of a detector. In this case, however, we are not concerned with the first term at all. For example, if a radio frequency e sin pt be impressed upon the input of a detector, the output current is given by: = aie sn -- -r cos 2 pt. (16) The first term is simply an inaudible high frequency. It need, therefore, not be considered and we can write instead of equation (9) the equation for the instantaneous detecting current Id as la = ae 2 sin 2 pt } (17) 326 THERMIONIC VACUUM TUBE where a is written for 02. We shall refer to a as the detection coefficient. Its value in terms of the parameters of the circuit is given by equation (13). Equation (16) contains only high frequency components and a d-c. component. The d-c. component of equation (16) makes possible the detection of high frequency incoming currents im- pressed on the input of the detector, if the output of the detector contains a d-c. current measuring instrument which is sensitive enough to indicate a change in the plate current given by the sec- ond term of equation (16). When a telephone receiver is used in the output continuous incoming waves of constant amplitude cannot be detected, because equation (16) does not contain an audio frequency term. The incoming waves must either be mod- ulated high frequency waves or if they are continuous waves 6f constant amplitude, the heterodyne method must be used to detect them (see Section 109). If a modulated high frequency wave such as that given by equation (12) be impressed on the detector, the instantaneous value of the detecting current is given by I d = a\A sin pt (l+B sin qt)] 2 . .. ' . . . (18) In evaluating this expression, all terms containing frequencies that lie outside the audible range can be neglected. This gives: I d = aA 2 Bsmqt-^-j cos 2 qt. .... . (19) Now q in equation (12) represents the low frequency component of the modulated wave. It is seen, therefore, that in view of the curvature of the characteristic cf the tube the output current contains a term of the same frequency as the audio frequency with which the carrier wave was modulated. It also contains a term having twice the audio frequency. This term is, however, usually so small as not to cause any appreciable distortion of the wave in the output of the detector. In deriving these expressions it is assumed that the grid does not take appreciable current. The circuit in which the detector can be used to comply with the above equations is shown in Fig. 195. The input circuit LC is tuned to the frequency of the incom- ing oscillations and the grid is kept negative with respect to the filament by means of the battery E g . The condenser Ci serves as DETECTION OF CURRENTS WITH THE VACUUM TUBE 327 a by-pass to the high frequency currents in the output circuit, the audio frequency component of the output passing through the telephone receiver. A receiving circuit that is commonly used and in which the battery E g is replaced by a condenser, will be discussed later on. (Section 103.) It will be apparent that the reason why equation (19) con- tains a term having the same frequency ~ that is used to modu- 2ir . late the wave at the transmitting station, is because the incoming wave, which is given by equation (12), contains both the terms A sin pt and AB sin pt sin qt. If the incoming wave were of the FIG. 195. form C sin pt sin qt, simple trigonometry will show that the only audio component of the current in the output of the detector is one which has double the modulating frequency, the audio detecting current being given by: (20) which on evaluating and dropping inaudible terms becomes: (21) It follows therefore that in order to obtain the modulating frequency ~, the waves impressed on the input of the detector 328 THERMIONIC VACUUM TUBE must be made to include a wave of the desired strength having the frequency -. 4TT 101. Root Mean Square Values of Detecting and Modulated Currents. The above equations give the instantaneous values of the currents or voltages considered. The R.M.S. values can readily be obtained. Thus, the R.M.S. value id of the detecting current, the instantaneous value of which is given by equation (19) is: (22) If we neglect the small double frequency quantity given by the second term in the parenthesis, id reduces to the common form The R.M.S. value of the modulated input voltage as given by equation (12) can be obtained by putting p = nq, since p is large compared with q. (^- covers frequencies ranging to 2000 or V 3000 cycles per second, while J- is generally of the order of sev- Zir eral hundred thousand cycles per second). The R.M.S. of the modulated wave which can be taken as the effective input volt- age e e on the grid of the detector, then becomes : (24) and involves B which is a measure of the extent to which the wave is modulated. If the wave is completely modulated B=l, as was explained in Section 93. In this case, remembering that the peak value of the high frequency is 2A we find that the ratio of the R.M.S. to the peak value is 7= instead of V2 as in un- Vz damped waves. 102. Relation between Detection Coefficient and the Operating Plate and Grid Voltages. The detection coefficient a depends on the values of the d-c. plate and grid voltages so that in deter- mining the value of a tube as a detector, this relationship must be DETECTION OF CURRENTS WITH THE VACUUM TUBE 329 taken into account. If the detecting current id be measured as a function of the effective voltage E y = ( +E g +e} it will be found that as this voltage is increased by increasing either E p or E a , the detecting current at first increases, reaches a maximum, and then decreases. It is assumed that the grid is at all times negative with respect to the negative end of the filament. Now the detection coefficient a is given by the second derivative of the char- acteristic, and is a measure of the detecting current, that is, the audio frequency component in the output. The maximum of FIG. 196. detecting current such as shown in Fig. 196 is due to the potential drop in the filament due to the heating current. It can be ac- counted for if we take regard of the voltage drop in the filament in giving an expression for the current as a function of the plate or grid voltage. It was shown in Section 28 that if this be con- sidered, the characteristic of the tube can be expressed by means of two equations, one which holds for values of the applied plate potential less than the potential drop in the filament and the other for larger values of the plate potential. These two equations are given as equations (17) and (19) of Chapter IV. They were derived for the case of a simple valve containing only anode and 330 THERMIONIC VACUUM TUBE cathode. But we can, to a first approximation, apply the con- siderations given there to the three electrode device if we replace , /Fi V the plate potential by the expression E y = ( '+E a -\- e ) so that we can write the characteristic equations in the form orE y ^E f , ........ (25) (E y -E,) 5/ *}forE^E,. . . . (26) where E f is the voltage drop in the filament. These two equations can be represented by a continuous curve closely approximating a parabola. The detecting current, or the second derivative of equations (25) and (26) when plotted as a function of the effective voltage on the other hand, shows a distinct maximum, which occurs at a value of the effective voltage E y equal to the voltage drop in the filament. The simple rule, therefore, to obtain the best results when using the tube in the circuit shown in Fig. 195 is to make (27) Fig. 197 shows an experimental curve in which the detecting current is plotted as a function of the plate potential E p , the grid potential remaining constant. For n = l2, =0.5, #/=2.5 volts and E g = Q, the maximum according to equation (27) occurs at a plate potential of about 36 volts. The condition given by equation (27) states that the potential difference between a plane coincident with that of the grid and the positive end of the filament is zero. This condition holds gen- erally even when the grid is connected to the positive end of the filament instead of to the negative. If it is connected to the pos- itive end the condition for maximum detecting current is E y = Q. This has also been verified experimentally. The condition E y = when the grid is connected to the positive end of the filament does, of course, not mean that the space current is zero because since E y is positive when reckoned from all points on the filament other than the extreme positive end. When using the tube in the simple circuit shown in Fig. 195 it is necessary to make sure that electrons do not flow to the grid. This is usually secured by putting in the negative grid battery E g . DETECTION OF CURRENTS WITH THE VACUUM TUBE 331 In practice, especially when receiving weak signals, it is usually not necessary to insert this battery because the potential varia- tions impressed on the grid seldom exceed a small fraction of a volt, and, under these conditions, the current flowing to the grid is usually negligibly small. There is, however, a factor which must be considered, namely the contact potential difference between 140x10 r 120 100 60 40 40 Plate Voltage FIG. 197. the filament and the system constituting grid and plate. The quantity e in the characteristic equation gives a measure of this effect. If the filament, grid and plate are of the same material e will usually be practically zero, but if the filament is, for example, of a different material e may be either positive or negative, but it seldom exceeds the value of about 1 volt. If it is positive it means that the grid is intrinsically positive with respect to the filament and, therefore, to secure best operation it is necessary to insert 332 THERMIONIC VACUUM TUBE a grid battery to maintain the resultant potential of the grid negative with respect to the negative end of the filament. In the case of tubes containing oxide coated filaments, e is usually negative. In such a case, therefore, the grid battery can be dis- pensed with altogether. The quantity e will differ from zero whenever the electron affinity of the filament is different from that of the grid, the contact potential difference between the two being equal to the difference between their electron affinities expressed in volts (see Chapter III). 103. Detection with Blocking Condenser in Grid Circuit. The method of detection discussed above and which can be carried out in practice with a circuit like that shown in Fig. 195 is perhaps not used as commonly as another type of circuit which is shown FIG. 198. in Fig. 198. The difference between these two circuits is that Fig. 198 contains in the grid circuit a condenser C s shunted by a high resistance leak R s . The mechanism of detection with such a circuit is different from that in which the blocking con- denser is omitted. In the latter case the best results are obtained when the grid is maintained at a sufficiently high negative poten- tial to prevent any convection current from flowing between fila- ment and grid, the detection depending only on the curvature of the plate-current characteristic. When the blocking condenser is used the detection depends on the curvature of the grid-current characteristic, the potentials of the elements being so propor- tioned that convection current does flow from filament to grid. In order to explain how the tube detects with a condenser in the grid circuit, let us first indicate briefly how the tube operates DETECTION OF CURRENTS WITH THE VACUUM TUBE 333 without the blocking condenser. Fig. 199 shows the processes involved in this case. Modulated high frequency potential varia- tions are impressed on the grid. On account of the curvature of the characteristic the high frequency current variations in the plate circuit can be represented by a lopsided wave curve. This effect was explained in Section 57. Such a lopsided wave gives rise to Grid Po+eh-Hal PI are Current Audio Current in Telephone FIG. 199. the audio frequency component as shown in the bottom curve of Fig. 199. When the blocking condenser is used in the grid circuit the operation of the tube as a detector is as follows: Suppose the incoming oscillations are again high frequency currents modulated by a low frequency as shown by the uppermost curve of Fig. 200. Suppose for the present that the resistance R s is omitted. When the grid potential becomes positive with respect to that of the filament, electrons are attracted to the grid. During the next half cycle when the grid potential becomes negative the electrons 334 THERMIONIC VACUUM TUBE cannot escape from the grid because they are trapped on the insulated part of the circuit comprising the grid and the one plate of the condenser C s . During the next positive loop of the incoming wave the grid attracts more electrons, which are also trapped so that they cannot escape from the grid during the succeeding negative loop. In this way the grid builds up a negative potential and the high frequency potential variations on the grid vary around ^ Incoming Oscillations, Oriel Potential Plate Current Audio Current in Telephone FIG. 200. the mean value of grid potential which becomes more and more negative as the strength of the incoming oscillations incr^ses. This reduces the plate current, and if the condenser C s and the insulation of the part of the circuit comprising C s and the grid were perfect the plate current would be permanently reduced, and this would make the tube inoperative. To prevent this a high resistance leak R s is shunted across the condenser C S) its value being so proportioned that the electrons cannot leak off through this resistance to any appreciable extent in a time comparable DETECTION OF CURRENTS WITH THE VACUUM TUBE 335 with the period of the high frequency oscillations but do leak off in a time which is of the order of magnitude of the low frequency variations of the amplitude of the high frequency oscillations. The result is that the potential of the grid takes such values as represented by the second curve of Fig. 200. This causes the plate current wave to assume the shape shown in the diagram. The high frequency variations in the plate circuit pass through the condenser Ci (Fig. 198) inserted in the output circuit and the current in the telephone receiver takes the shape shown by the bottom curve of Fig. 200. 1 In order to secure the best results with this type of circuit it is necessary to operate on that part of the grid voltage, grid cur- rent characteristic which shows the greatest curvature, and simul- taneously adjust the plate potential to such a value that the operating point on the plate current, grid potential characteristic lies in the region where this characteristic is steepest. This usually requires that the grid be maintained at a positive potential with respect to the negative end of the filament. The simplest way to secure this is to connect the grid circuit to the positive end of the filament as shown in Fig. 198 instead of to the negative end as is commonly done in other circuits. This makes the filament negative with respect to the grid, the average potential difference between them being in the neighborhood of the value where the grid current characteristic has its greatest curvature. The best value for the capacity C s usually lies between about 150-500 micro-microfarads while the leak resistance R s should be of the order of two megohms. If the detecting current be measured as a function of the effective voltage E y ={+Eg-\-e} a curve is obtained like that shown in Fig. 201. When the blocking condenser is not used we have seen the relation between detecting current and effective voltage gives a maximum as shown in Fig. 197. 104. Method of Measuring the Detecting Current. The meas- urement of the detecting current under conditions approximating those met with in practice has always been a difficult matter because it involves the measurement of very small alternating currents. Their values under practical conditions range from about 10~ 6 ampere down to 10~ 8 ampere and sometimes less. This makes it 1 E. H. ARMSTRONG, El. World, Vol. 64, p. 1149, 1914. 336 THERMIONIC VACUUM TUBE entirely impossible to use hot wire instruments. The telephone receiver is a very sensitive device for indicating small alternating currents, but does not directly give a measure of the value of the currents in the receiver. The audibility method, which will be discussed later on, has been suggested to measure detecting cur- rents with a telephone receiver. It consists in shunting the tele- phone receiver with a variable resistance and adjusting this resistance until the current in the telephone receiver is just large enough to make it possible to discriminate between the dots and dashes of the incoming signals. The ratio of the total current in the receiver and shunt resistance, that is, the detecting current Plctt-e Vol-t-age FIG. 201. to the current in the receiver alone, measures what is known as the " audibility." This method is not very reliable, and its accuracy depends to a large extent on the conditions under which the measurements are made (see Section 108). The following method requires only that two notes of the same pitch be adjusted to equal intensities. 1 It is, comparatively speaking, very accurate, and does not depend nearly so much on the conditions under which the measurements are made. The principle of this method can be explained with reference to Fig. 202. The incoming high frequency oscillations are impressed on the grid in the usual way. In order to measure the small 1 H. J. VAN DER BIJL, Phys. Rev., Vol. 13, p. 311, 1919; Proc. Inst. Radio Engineers, Vol. 7, p. 603, 1919. DETECTION OF CURRENTS WITH THE VACUUM TUBE 337 detecting current in the output of the detector we use a generator 7, giving a note of the same pitch as that of the detecting current, and then attenuate the current from the generator by means of a receiver shunt S until the current i d has the same value as the detecting current delivered by the tube. W is a switch whereby the telephone receiver can be connected either to the output of the tube or to the output of the generator. The shunt and series resistances of the receiver shunt are adjusted until the tone heard in the receiver is of the same intensity for both positions of the switch W. The receiver shunt has been described in Section 72. FIG. 202. The shunt and series resistances are varied in definite steps by the simple operation of turning a dial, these steps being so propor- tioned that the impedance in the output of the generator U remains constant for all adjustments of the shunt. The current ii delivered by the generator into this impedance is so large that it can easily be measured with a hot wire instrument A such as a thermo-couple. It was shown in Section 72 that the relation between the current i\ and the branch current id flowing through the receiver is (28) where a is the constant of the receiver shunt and d expresses the current attenuation produced by the shunt in terms of length of 338 THERMIONIC VACUUM TUBE the cable or line having an attenuation constant equal to a per unit length. For the standard cable of reference commonly used in telephony a = 0.109 per mile, d being expressed in miles (see Section 72). Expressing the above equation in common logarithms we get log^=logn--, (29) where 2.303 = 21.13. ..... (30) Now ii is measured by means of the instrument A, and d is a known value depending on the adjustment of the receiver shunt in the manner explained in Section 72; hence, if the shunt be so adjusted that the tone in the receiver is of the same intensity for both positions of the switch W we can, from the above equation, obtain the detecting current id. The impedance of the telephone receiver should, of course, have such a value that the best operation is obtained. If neces- sary, we can, to secure this, insert a transformer between the tele- phone receiver and the output of the tube. Furthermore the detecting current depends on the value of the voltage variation impressed on the grid and upon the extent to which the incoming wave is modulated. The R.M.S. value of the voltage can be measured by means of a resistance r and an a-c. galvanometer G as shown, for example, in Fig. 208. When comparing tubes for their operation as detectors the input need not be measured, nor is it necessary to insure that the incoming wave is completely modulated as long as these quantities remain the same throughout the measurements. When measuring the detecting efficiency of the tube, however, it is necessary, as will be explained later on, to measure these quantities. This method of measuring the detecting current has been found to be very useful when studying the influence of the operating parameters such as the d-c. plate and grid potentials on the detect- ing current. 4 When making such measurements it is customary to express the detecting current simply in terms of the adjustment d of the receiver shunt instead of computing the actual value of the detecting current from equation (29). It will be noticed, how- ever, that d increases when the detecting current decreases. It DETECTION OF CURRENTS WITH THE VACUUM TUBE 339 is therefore advantageous to calibrate the receiver shunt in terms of D-d when D is an arbitrary constant. 105. Measurement of the Detection Coefficient. The method described above makes it possible to measure the detection coeffi- cient if the relation between the detecting current and the voltage impressed on the input is known. If the tube is used without a blocking condenser in the grid circuit the detecting current can be given by the equation (31) When the tube is used with a blocking condenser this relation also holds fairly accurately provided the input voltage is small, gen- erally not greater than about half a volt. If we put this value of id into equation (29) we get d = 2Klog 10 e g +C, ...... (32) where C = 1C (log u -log a) ...... (33) Hence if we measure the relation between the input voltage e g and the setting d of the receiver shunt we obtain a straight line from the intercept of which the detection coefficient a can be determined. The intercept C is obtained when e \. This gives c loga = logz'i--^ ....... (34) The detection coefficient can therefore be obtained to any desired degree of accuracy by taking a sufficiently large number of obser- vations of e g and d. The circuit whereby such measurements can conveniently be made is shown in Fig. 203. In this circuit the source of audio frequency current used to modulate the high frequency current also supplies the current with which the detecting current in an output of the detector is compared. U is the generator of the audio frequency currents. This can be a vacuum tube oscillator or a microphone generator such as that described in Section 72. (See Figs. 114 and 115.) Its output passes through a filter F, which transmits only frequencies of about 800 cycles. This current is sufficiently large to be measured with a thermo-couple A. but after passing through the receiver shunts S and S' it is atten- uated until the intensity of the tone heard in the receiver T is equal 340 THERMIONIC VACUUM TUBE to the detecting current coming from the detector tube D. B;- means of the switch W either the detecting current or the current from the generator U can be passed through the telephone receiver. If the switch is thrown to the left the current from U passes directly through the receiver after being attenuated by the receiver shunt. When W is thrown to the right the output of U is im- pressed on the input circuit of the modulator M . This low fre- FIG. 203. quency current is therefore used to modulate the high frequency current also impressed on the input of M and obtained from the vacuum tube oscillator 0. The output of the modulator is impressed on the detector D, the voltage between filament and grid of D being measured by means of the resistance r and thermo- galvanometer G. It follows then from the equations developed above that the audio frequency output of the detector is of the same pitch as the current supplied by the generator U, thus making the adjustment of the receiver shunt S for equal inten- DETECTION OF CURRENTS WITH THE VACUUM TUBE 341 sities of these two notes a comparatively simple matter. It is true that the output of the detector also contains a note of double frequency, as shown, for example, by equation (19), but this double frequency note is usually so weak as not to cause any trouble. The circuit shown in Fig. 203 requires that certain precautions be taken to obtain reliable results; for example, it is necessary to make sure that the output impedance of the generator U remains constant for both positions of the switch W. Thus, sup- posing that the impedance of the telephone receiver T is 20,000 'ohms, it is necessary to make the input impedance of the trans- former T 2 which is placed in the input circuit of the modulator M also 20,000 ohms. This transformer is usually wound to have a high output impedance in order to impress the highest input voltage on the grid of the tube to which it is connected for the lowest amount of power expended in the input. The transformer TI is inserted when the impedance of the generator U is different from that of the telephone receiver T. In order to adjust the current from U to the desired value the primary of transformer T\ is shunted with a resistance and the connection to the output of the generator is made by means of a sliding contact as indicated in the diagram. The receiver shunt S f has a fixed value, giving an attenuation equal to the maximum attenuation given by the varia- ble shunt S, and can be inserted when the detecting currents to be measured cover a greater range than can be taken care of by one receiver shunt. Receiver shunts are seldom made to cover a greater range of attenuation than 30 miles of standard cable ('4=26.3). \id / In making measurements of this kind it is necessary to insure that the modulated wave impressed on the input of the detector is completely modulated. The necessity for this can readily be seen by referring to equations (23) and (24), which give the R.MJ3. values of the detecting current and the modulated voltage on the input of the detector. From these equations it will be seen that for a constant modulated input voltage e g the detecting current depends on B and this, we have seen, is a measure of the extent to which the wave is modulated. This can also be seen by referring to Figs. 188 and 191. Two waves such as those shown in these figures may have the same heating effect as measured, for example, by means of a resistance and thermo-galvanometer, but they will 342 THERMIONIC VACUUM TUBE not produce the same detecting effect when they are impressed on the detector. In the limiting case in which the wave is not mod- ulated at all C6*=0) the R.M.S. of the input voltage will have a j^ finite value - , but the detecting current will be zero (equation V2 23). In order to insure that measurement of the detection co- efficient shall have any meaning the extent to which the wave impressed on the input of the detector is modulated must be kept constant, and the simplest way to do this is to completely modulate the wave, thus making B=l. This can readily be done in prac- tice in the following way: Referring to Fig. 204, which represents FIG. 204. the relation between plate current and grid potential, it is evident from the explanations given in Section 53 that the intercept OA which represents the negative grid potential necessary to reduce TjfT the -plate current to zero is . If we now apply a constant Tjl grid potential E g = p~ and make the peak value of the low fre- Zp quency input voltage equal to this quantity, then the amplitude of the high frequency oscillations is reduced to zero every time that the grid acquires its maximum negative- potential CA and then the wave will be completely modulated. The simplest way to secure this in practice is first to adjust the negative grid battery DETECTION OF CURRENTS WITH THE VACUUM TUBE 343 7F 7? in the input circuit of the modulator to a value +^; that is, to a value given by OD (Fig. 204), and then gradually increase the strength of the low frequency input voltage until a d-c. meter placed in the output of the modulator just indicates a current flow in the output of the modulator. The peak value of the -pi input potential is then equal to DA or -^-. The voltage of the high 10 80 TO 60 7 Slope =4?.? 50 -0.2 -0.4 -0.6 -0.8 -1.0 *ll -1.4 FIG. 205. frequency impressed on the modulator can also be measured in the same way and should in general be somewhat smaller than the low frequency voltage. Finally the grid battery in the input circuit of the modulator is adjusted to the value OC, before the measurements on the detecting current are undertaken. Fig. 205 shows some experimental results that were obtained with the circuit shown in Fig. 203. The ordinates indicate the setting of the receiver shunt for different values of the input volt- age e g , the logarithms of which are plotted as abscissae. Accord- 344 THERMIONIC VACUUM TUBE ing to equation (32) these points should lie on a straight line. Furthermore, if equation (31) holds the slope of this line should be 2K; that Is, 42.26, since K for the receiver shunt used is 21.13. The crosses and circles represent observations made by two dif- ferent observers on different days. The slope of the line drawn through them is 42.2. These measurements were made without a blocking condenser in the grid circuit and prove that in deriving the equations in the previous pages we were justified in assuming that the power series given by equation (2) converges so rapidly that we can neglect quantities of higher order than the second, and that therefore the detecting current is given by a simple equation (31). From the intercept C of this line (log e g = 0), and the value of the current i\ the detection coefficient can be obtained directly with the help of equation (34). In the case to which the experi- mental results given in Fig. 205 apply the current i\ as measured by a meter inserted in the 20,000 ohm line was 3.10X10" 3 ampere and the intercept for e ff =l is 40.8. From this we obtain for the detection coefficient a = 36.2X10~ 6 amp. (volts) 2 . 106. Detecting Efficiency. The detection coefficient a gives a measure of the audible component of the current in the output of the detector and depends on the impedance of the telephone receiver. It is therefore not suitable for expressing the figure of merit of the tube as a detector. The impedance of the tele- phone receiver should be chosen to give maximum response. The audio frequency output power is the quantity which gives a better indication of the behavior of the tube, and is given by the product of the square of the detecting current and the resistance of the telephone receiver. The power developed in the receiver depends, of course, also on the power developed in the input circuit, that is, on the strength of the incoming oscillations, the figure of merit of the tube as a detector being given by the ratio of audio frequency output power to radio frequency input power. This is a difficult quantity to measure. It was shown, for example, in Section 71 that the power expended in the grid circuit depends on the con- stants of the output circuit. The reaction of the output on the input circuit through the electrostatic capacities between the electrodes of the tube causes the tube to behave as if it had an effective input impedance. If the output circuit contains only a pure resistance, the resistance component of this effective DETECTION OF CURRENTS WITH THE VACUUM TUBE 345 impedance between filament and grid has a positive value, which, however, is usually small compared with the reactance component. If, on the other hand, the external circuit contains an inductive impedance, the grid resistance may be negative, thus giving rise to a generation of power in the input. At very high fre- quencies, it was shown in Section 71, the resistance component of the input impedance is practically zero, but the input voltage may be considerably reduced on account of the input circuit being shunted by the capacity between filament and grid. When the tube is used with a blocking condenser in the grid circuit there is a convection current between filament and grid, thus giving rise to an input resistance which must be added to that caused by the inter-electrode capacities. If, on the other hand, the tube is used without a blocking condenser in the input circuit, in which case the grid should be kept negative with respect to the filament, the input resistance is due entirely to the reaction of the output cir- cuit to the input through the capacities of the tube, and can be made as small as we please by properly adjusting the constants of the circuit. Most of the input power is then dissipated in the input coil and condenser. The input power can therefore be dissipated at the grid, in the external input circuit and in a fic- titious input resistance occasioned by the reaction of the output circuit on the input. The relative amounts of power dissipated in these parts depends on the adjustments of the circuit. It is for this reason usually better to express the figure of merit of the device as a detector in terms of the audio frequency output power for a given high frequency voltage impressed on the input because there is a definite relation between these quantities. The equa- tions developed in the previous sections express the quantities considered in terms of the input voltage, and therefore hold what- ever may be the effect of the circuit and the inter-electrode capacities on the input power. Expressing the detecting effi- ciency 6 in terms of the relation of output audio frequency power to input radio frequency voltage we have: (35) where ro is the resistance in the output of the detector and a is the detection coefficient. The curve shown in Fig. 205 was obtained with a circuit in which the telephone receiver used had an im- 346 THERMIONIC VACUUM TUBE pedance of 20,000 ohms and a resistance of 6400 ohms at about 800 cycles per second. The detecting efficiency of the tube on which these measurements were made is therefore 8.1X10" 6 watt (volt) 4 . The smallest amount of power dissipated in this receiver which could still give a signal that is barely audible is about 3 X 10~ 12 watt. The high frequency input voltage necessary to give the least audible signal with this particular tube and tele- phone receiver is therefore about 0.025 volt. These measurements were made on a Western Electric type VT1 tube (Fig. 127). This tube operates on a plate voltage of about 20 volts. The power consumed in heating its filament ranges from 2.2 to 3.5 watts. On account of the small amount of power involved when using the tube as a detector it is desirable to make the filament as small as possible in order to reduce the power expended in heating it. The limitation to the decrease in the size of the filament is due mostly to mechanical difficulties, but smaller types of tubes have been developed, of which the one shown in Fig. 131 (page 244) is a sample. This tube only requires a small fraction of a watt to heat its filament, the filament operating on a voltage ranging from 1.0 to 1.5 volts so that it can be used with a dry cell. The detecting efficiency of this little tube was found to be about 4.3 X 10" 6 watts/ (volts) 4 . A ratio of two in the output power corresponds to a difference of about three standard cable miles, which is not a big difference. A difference of one standard cable mile is hardly noticeable unless comparison be made directly. 107. Comparison of Detectors. The circuit shown in Fig. 203 is not always suitable for use where a large number of tubes are to be tested, because it requires accurate calibration and careful adjustment of the operating parameters such as the radio fre- quency voltage impressed on the input of the detector, the audio frequency current delivered by the generator C7, etc. The con- stancy with which vacuum tubes can be made, however, makes it possible to test tubes by comparison methods that are simple to operate. The tubes to be tested can then be compared with a standard tube that was carefully calibrated by means of such a circuit as shown in Fig. 203. If a tube is well evacuated it will retain constant operation over a considerable length of time. The writer has, for example, used a " standard " Western Electric tube whose detecting efficiencj' did not change to any noticeable DETECTION OF CURRENTS WITH THE VACUUM TUBE 347 extent in the course of about a year, during which time it was in frequent use. A simple circuit whereby detectors can be compared is shown in Fig. 206. The input voltage can be adjusted to the desired value by adjusting the resistance r and need not be known accurately, it being sufficient to know that it lies within the range of voltages used in practice. By means of the switch W either one of the detectors can be inserted in the circuit and the receiver shunt S adjusted until the note in the receiver T has the same intensity for both positions of the switch W. The key K serves to throw FIG. 206. the shunt into or out of the circuit according as W connects the tube of higher or lower efficiency. The capacity C is a radio fre- quency leak and the output circuit is connected across the choke coil, which insures that the d-c. potential on the plate remains constant for all adjustments of the resistances of the receiver shunt S. If id and i'a be the detecting currents obtained from the tubes I and II, and a and a', their detection coefficients, then since the input voltage is the same for both, we have d d' (36) where d and d' are the adjustments of the shunt in units depending on the units of K. The detecting efficiency of the tube under test 348 THERMIONIC VACUUM TUBE is then given by (37) Fig. 207 shows the complete circuit as it can be used for com- paring detectors in practice. This circuit contains an amplifier tube connected to the output of the detectors. When the detector is to be used in practice with an amplifier such a circuit is desirable to insure that the detector is tested under conditions approximating as closely as possible to practical conditions. If the detector is not to be used with an amplifier the receiver shunt and telephone FIG. 207. receiver can be connected directly to the output of the detector as shown in Fig. 206. To obtain a modulated high frequency test wave would ordinarily require a radio frequency oscillator, an audio frequency oscillator and a modulator, but in comparing detectors it is not necessary that the wave be completely modu- lated, and under such conditions a modulated high frequency wave can be obtained very easily by means of a vacuum tube oscillator and a microphone generator such as the one described in Section 72. In Fig. 207 U is the microphone generator, the carbon button of which is inserted directly in the oscillation circuit C\L\. When this generator is in operation the resistance of the carbon button varies periodically at an audio frequency, thus causing audio DETECTION OF CURRENTS WITH THE VACUUM TUBE 349 frequency variations in the amplitude of the radio frequency oscillations produced by the oscillator tube. Modulation pro- duced in this way is not complete, but in this case complete modu- lation is not necessary because the input is the same for both tubes. The condenser 2 in the output of the detector serves as a high frequency leak and the resistance r is inserted to prevent the grid from acquiring a negative charge. Its value is in the neigh- borhood of 2 megohms. 108. Audibility Method of Measuring the Detecting Current. The audibility or " shunted telephone " method has been fre- quently applied to the measurement of the strength of received signals in long distance radio communication, and has also been used to obtain an idea of the sensitiveness of detectors. In this method the telephone receiver is shunted by means of a resist- ance r s which is adjusted until the signal heard in the receiver is just barely audible. If id is the detecting current and io the least audible current in the receiver, then the "audibility" is given by (38) where ZQ is the impedance of the receiver. In using a method like this it must, of course, be remembered that ZQ cannot be replaced simply by the resistance of the receiver as is sometimes done, but the reactance and the motional impedance of the receiver must be taken into consideration. This method is open to other serious objections. In the first place, it is liable to considerable error because the measurement of least audible signals is made difficult by the influence of extraneous noises such as room noises and static. The least audible current depends furthermore to an appreciable extent upon the condition of the observer, so that the current necessary to give the least audible signals will vary from time to time even with the same observer. These disadvantages make the method unreliable for purposes of de- termining the detecting efficiency of a tube with any degree of accu- racy. Secondly, the way in which the audibility method is ordina- rily used, does not make provision for the Change in the effective impedance of the output circuit to the detecting current when the shunt resistance r s is varied. This would give misleading results, since the detecting current depends upon the relative values of the 350 THERMIONIC VACUUM TUBE internal output impedance of the tube and the external impedance in the output circuit. It is therefore necessary in all measure- ments of this kind to adjust these impedances properly and keep them constant throughout the measurements. If the audibility method is to be used the " audibility box " should be so designed that any variation in the shunt resistance is accompanied by an addition or subtraction of an equivalent resistance so as to keep the total impedance of the circuit constant. This can be done with the scheme that will now be described. This scheme was used by the writer 1 to determine to what extent the audibility method may give reliable results if precautions are taken to elim- inate sources of error other than those which depend only on the psychological and physiological influences on the observer. The fact that the current necessary to give the least audible signal has different values for different observers and is therefore incapa- ble of objective determination does not of itself rule out the audible method for the measurement of signal strength, since the detector set could first be calibrated by determining the audibility for known input signals and then used by the same observer to make the final measurements. Hence assuming that extraneous noises could effectively be cut out, the possibility of adapting this method to such measurements would depend upon the extent to which the observer's conception of least audible signal remains constant during the time that elapses between his calibration of the set and the making of the final measurements. It is hardly necessary to say that the whole set must remain unchanged, especially the tube and the telephone receiver. The circuit whereby the least audible signal can be studied under constant circuit conditions is shown in Fig. 208. To cut down the current in the telephone receiver a receiver shunt is used such as that described in Section 72. This shunt contains a series and shunt resistance, both of which are variable, instead of simply a shunt resistance. The receiver shunt is so calibrated that the series and shunt resistances are changed simultaneously in such a way that the total impedance to the detecting current in the output circuit of the tube remains constant. A choke coil L by-passes the direct current in the plate circuit and insures that the d-c. potential of the plate remains constant for all adjustments of the receiver shunt. This is necessary because the shunt is so 1 H. J. VAN DER BIJL, Proc. I.R.E., Vol. 7, p. 624, 1919. DETECTION OF CURRENTS WITH THE VACUUM TUBE 351 designed that for all its adjustments the impedance of the output circuit remains constant, but the resistance does not remain con- stant, and therefore if the choke coil and capacity were omitted, thus making it necessary for the d-c. plate current to pass through the shunt, the potential of the plate would be different for dif- ferent adjustments of the receiver shunt. It is very important to keep the relation between the impedances constant because the detecting current depends very markedly on the value of the external impedance in the plate circuit. The wave impressed on the input of the detector can be a spark signal wave or a modulated wave which is interrupted. For test purposes such a wave can easily be obtained with an arrangement such as that shown in Fig. 207, where the oscillator tube and the microphone generator U together form a simple system for pro- FIG. 208. ducing modulated waves. The output of this oscillator system can then be passed through an omnigraph to produce the signals. The R.M.S. of the input can, as before, be measured by means of a resistance r and galvanometer G (Fig. 208). The use of the receiver shunt makes it possible to express the audibility in a simple way. If u be the detecting current and io the least audible current in the receiver the audibility 4- can be *o expressed in miles of standard cable by making use of the equa- tions developed in Sections 104 and 105. Thus, taking the case in which the detecting current is proportional to the square of the input voltage, we obtain d = 2Kloge g +K(\oga-\ogio), .... (39) which thus gives a linear relation between the logarithm of the input voltage and the audibility when expressed in terms of miles 352 THERMIONIC VACUUM TUBE d instead of current ratio, the relation between d and the cur- rent ratio being given by equation (28). The intercept of this line, obtained by putting e g = 0, is K (log a -log to), (40) and gives a measure of the audibility efficiency of the tube ex- pressed in miles/ (volt) 2 . The simple linear relation (39) makes it possible to obtain the audible efficiency as an average of a large number of observa- 19 / Audibility in Miles of Standard Cable IO o e> o o S S / S/ / y '0 Slop e=4l -!..._ * i i i i FIG. 220. the increase in current during the positive half wave is greater than the decrease during the negative half wave. When the characteristic tails off and accuracy is desired, it may be necessary to apply a correction. Fig. 221 shows the relation between the true voltage and the voltage measured by the tube which did not show a sharp intercept on the grid voltage axis. 115. High Tension Voltmeter. The three-electrode tube makes it possible to measure extremely high voltages with comparative ease, by an arrangement that has been suggested to me by Dr. E. R. Stoekle. In this case the high voltage to be measured is 370 THERMIONIC VACUUM TUBE applied between filament and plate. By means D a battery and potentiometer the grid is adjusted until the current in the plate 1.0 1.6 14 , / / / / / 1 0.4 / / , ' 0.4 0.8 \.Z 1.6 Z.O IA True Voltage FiG. 221. circuit is reduced to zero. Since the current through the tube is given by it follows that the voltage to be measured is E g when the current is just reduced to zero. By using a tube which has a large value of MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 371 /z the necessary grid battery voltage need not be large. Thus, if ju = 1000, a grid battery of 50 volts is sufficient to measure 50,000 volts. Such a tube should be designed with long side tubes as shown in Fig. 222, to prevent arcing across the glass. 116. The Audion Voltage and Current Regulator. The follow- ing circuit arrangements, for which I am indebted to Dr. P. I. Wold, indicate how the tube can be used to control the output of a generator or other source. The generator S supplies power to Line Line FIG. 223. the line as shown in Fig. 223. To prevent voltage fluctuations the vacuum tube is connected in series with the field winding of the generator. The grid of the tube is connected to a con- venient point on the resistance R in parallel with the field winding. Suppose, now, that the voltage of the generator tends to increase. 372 THERMIONIC VACUUM TUBE This increases the flow of current through the resistance R, which makes the grid more negative than before, thus increasing the resistance of the tube and, therefore, decreasing the current through the tube and field winding, because the tube and field FIG. 224. winding are in series. By this means, any tendency for the voltage to increase is counteracted. The same thing, of course, holds when the voltage tends to drop. Fig. 224 shows an adaptation of this method of control for keeping the current output of the generator constant. It will be FIG. 225. seen that if the current through the resistance R tends to increase, the grid tends to become more negative with respect to the fila- ment, thus increasing the resistance of the tube and decreasing the current through the field winding. Fig. 225 shows a circuit arrangement in which the tube and field winding are connected in parallel. The high resistance R to which the grid is connected is also in parallel with the field winding. In this case, when the output voltage of the generator MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 373 tends to increase, the grid tends to become less negative with respect tc the filament, on account of the increased voltage drop established in the resistance R. This tends to reduce the resistance of the tube, thereby decreasing the current through the field wind- ing, which is in parallel with the tube. 117. Power-limiting Devices. It has been pointed out in Chapter VI that the thermionic valve acts not only as a rectifier but also as a power-limiting device, because, while it blocks current in one direction, the current in the other direction cannot exceed the saturation value. This is, therefore, the maximum current that can be transmitted through the tube. J&O.Z o. Grid Potential FIG. 226. The three-electrode tube can be very well adapted for the pur- pose of limiting the output power. If, for example, the grid becomes sufficiently negative, the plate current is reduced to zero. If, on the other hand, the grid becomes sufficiently positive the plate current reaches a saturation value. It will be evident from the explanations given in Chapter VII, that this saturation value may be due to two causes: Firstly, the strength of the field in the space between filament and grid may become sufficiently great to pull the electrons away from the filament as fast as they are emitted. This gives rise to the ordinary saturation current. If the cathode has a smooth and pure surface, the knee of the curve, where it bends over to the saturation current, is fairly well defined. In cases of filaments having rough surfaces, on the other hand, the saturation current is approached gradually and the curve does not become quite parallel to the voltage axis. Under such conditions 374 THERMIONIC VACUUM TUBE the device is not very suitable for power-limiting purposes, but but use can be made of a second factor which limits the current. If the external circuit contains a resistance, the potential of the plate decreases as the potential of the grid increases, on account of the voltage drop established in the external resistance in the plate circuit. A condition can then be reached where the positive potential of the grid becomes comparable with that of the plate, and in that case a large proportion of the electrons will be attracted to the grid, thus limiting the flow of electrons to the plate. This factor results in a very good curve, a sample of which is shown in Fig. 226. In obtaining this curve the voltages were so adjusted FIG. 227. that the saturation value was obtained at a positive grid potential equal to the negative grid potential that just sufficed to reduce the current to zero, thus resulting in a curve which is nearly sym- metrical with respect to the axis of zero grid potential. Instead of using a single tube we can make use of the push- pull arrangement which was described in Chapter VII. This gives a good circuit for power-limiting purposes. The arrange- ment is shown in Fig. 227. The input voltage was measured by means of a thermo-couple, G and the output current was measured with the a-c. ammeter A. The result obtained is shown in Fig. 228. For low input voltages the alternating current in the output increased practically linearly with the voltage, but became lim- ited to a value of about 3.6 milliamperes, beyond which it did not increase, although the input voltage was increased to 10 volts, as shown by the curve. The current was actually measured for input voltages up to 42 volts. At the higher voltages the current showed a tendency to decrease. MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 375 118. .The lonization Manometer. It was shown in Section 36 that if the gas pressure in a tube is so low that the mean free path of the electrons in the gas is large compared with the distance between the electrodes, the pressure is proportional to the number of positive ions formed by collision of the electrons with the resid- ual gas molecules. This is expressed in equation (6), Chapter V, and was verified by 0. E. Buckley, 1 and used by him for the con- struction of an ionization manometer. 40Fo 3.2 0.5 4 5 A.C.1nput-Volt5 FIG. 228. This device consists of throe electrodes connected in a circuit as shown in Fig. 229. The grid is maintained at a positive poten- tial with respect to the filament, and the plate is kept negative with respect to the negative end of the filament. The electrons emitted from the filament are attracted toward the grid, some going to the grid and some passing through the openings in the grid. Between the grid and the, plate, however, is a retarding field, and, since the plate is negative with respect to the filament none of the electrons that are emitted from the filament can reach the plate; they attain their maximum speed in the neighborhood of the grid. Those that pass through the grid are retarded and finally return to the grid before they have a chance of reaching the plate. It is usually sufficient if the plate is maintained at a poten- National Academy of Science, Vol. 2, p. 683, 1916. See also DUSHMAN and FOUND for calibration of this gauge for various gases, Phys. Rev., Febr., 1920, p. 133. 376 THERMIONIC VACUUM TUBE tial of about 10 volts negative with respect to the negative end of the filament. Now, if there are gas molecules in the space, positive ions will be formed by collision, if the electrons move with a suf- ficiently high speed. The positive ions that are formed between filament and grid go to the filament, but those that are formed between grid and plate are attracted to the negative plate, thus giving a current through the galvanometer G; and this current is a measure of the number of positive ions formed. The total number of electrons flowing to the grid can be measured with the ammeter A, and must be kept constant. It is, therefore, desirable to work on the saturation part of the curve. The grid battery E c FIG. 229. should be about 200 volts, but depends, of course, on the con- struction of the device. This type of gauge has the disadvantage that gases affect the emission of electrons from the filament; that is, the saturation current is dependent on the amount and kind of gas coming in contact with the surface of the filament. The electron emission from oxide-coated filaments is not as susceptible to the influence of gas as the emission from some metallic filaments, such as tungsten, and can therefore be used to advantage in ionization manometers. If the filament is operated at a high temperature, the effect of gas on the emission becomes less. (See Chapter V.) Other means can be used for keeping the grid current constant. The grid cir- MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 377 cuit can, for example, be connected to a regulating scheme, similar to those described in Section 116. The ionization gauge is very convenient for measuring quick changes in pressure because the positive current indicated by the galvanometer G is a direct measure of the amount of gas present in the device. On the other hand, the manometer must be calibrated separately for each kind of gas that may be encoun- tered, since the amount of ionization produced depends on the size of the gas molecules. The proportionality between the gas pressure and the positive current, as shown by equation 6, Chapter V., holds, in gauges of the most commonly used types, for pressures below about 1 micron. The manometer can, therefore, be calibrated against a McLeod gauge for pressures of about 1 micron, or somewhat less, where the McLeod gauge gives reliable readings. This, then gives the manometer constant K in the equation. (1) where I P is the positive current registered by the galvanometer G, I n the electron current to the grid, and P the pressure of the gas. This equation can then be used to measure pressures down to very low values where the McLeod gauge is quite unreliable. 119. Heterodyne Method of Generating Currents of Very Low Frequency with the Vacuum Tube. In Section 96 a circuit was shown for the production of low frequency currents with the vac- uum tube. The frequency is determined by the constants of the oscillation circuit; hence, a very low frequency requires the use of large inductances and capacities. If it is necessary to avoid the use of such large coils and condensers, use can be made of a scheme which was suggested to me by Dr. P. I. Wold. This system consists of using two vacuum tube generators to give fre- quencies differing by an amount equal to the frequency that it is desired to obtain. The output currents from these tubes are both impressed on the input of another tube, which operates as a modulator. The output of the modulator contains, among others, a frequency equal to the difference between the frequencies impressed on its input. (See Section 109.) Thus, if the two gene- rators give frequencies of, say, 99 and 100 cycles per second, then the output of the modulator will contain a current having a fre- 378 THERMIONIC VACUUM TUBE quency of one cycle per second. In the output of the modulator can be inserted a filter to by -pass all frequencies higher than the one desired. This method, of course, requires that the frequencies of the two generators be maintained constant to a high degree, since a small change in either of them will cause a relatively large change in the low frequency obtained in the output of the modu- lator. 120. The Thermionic Valve as a High- Tension Switch. On very high voltage power transmission lines, it is necessary to use especially designed switches for making and breaking the circuit. To prevent the arcing that ordinarily would take place when breaking a high voltage circuit, the thermionic valve could be used hi the manner suggested by Mr. J. R. Carson. The valve is inserted directly in the line and will transmit current in one direction when the filament is hot. When it is necessary to stop the flow of current, we can, instead of directly breaking the cir- cuit, simply cut out the filament current of the valve. The cur- rent flowing through the valve then dies down smoothly in a period which is short enough for ordinary work, but still large enough to prevent arcing. For the transmission of current in both directions, we can, of course, insert two valves, one to transmit current in one direction and the other in the opposite direction. 121. Devices Employing Secondary Electron Emission. The emission of electrons from cold electrodes under the impact of electrons (a phenomenon which is known as secondary electron emission or delta rays) results in a falling characteristic, as shown by the portion ABC of Fig. 16, page 48. The manner in which this characteristic is obtained is explained in Section 23. A. W. Hull 1 has made use of this phenomenon in the construction of a negative resistance amplifier and oscillator and has called the device a Dynatron. In the circuit shown in Fig. 15, the electrons coming from the filament impinge on the grid and so emit secondary electrons from it. These are drawn to the plate by the positive potential on the plate supplied by the battery E. When the number of secondary electrons emitted from the grid becomes large enough in proportion to the number of electrons striking it, the electron current flowing into the grid decreases as the potential of the grid is increased. There is another way in which the tube can be used to give a 1 Proc. I.R.E., Vol. 6, p. 5-35, 1918. MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 379 negative resistance. In this case the grid is maintained at a posi- tive potential with respect to the plate. The electrons passing through the grid and striking the plate cause the emission of secondary electrons from the plate and these are then drawn over to the positive grid. The circuit arrangement for this case is shown in Fig. 230. If TO is a resistance placed in the plate circuit, then a potential E p on the plate is given by 77T 77F 7" /O\ where I p is the current in the plate circuit, and E the voltage impressed on the plate circuit. Taking the point B of Fig. 16 as FIG. 230. the origin of coordinates, the sloping part ABC of the character- istic can be represented by the equation /=- (3) where r p is the plate resistance of the tube. Substituting equation (2) into this equation we obtain, (4) Differentiating I p with respect to E b , and multiplying by 7*0, we get: -^_ (5) r -r p 380 THERMIONIC VACUUM TUBE that is, a potential variation applied to the plate gives a voltage variation in the resistance ro which can be made very large by making ro nearly equal to r p . The device thus operates as an amplifier. Instead of using only the negative resistance characteristic of the device, connected in the manner explained above, Hull also made use of the normal amplifying property of the tube by insert- ing a second grid. This device he called a " Pliodynatron." By this means he has been able to obtain a voltage amplification of 1000 fold. To obtain such a high voltage amplification, however, it is necessary to make r p and ro nearly equal. When this is done the device becomes unstable and needs careful adjustment and constant attention. It was, however, found possible to obtain a voltage amplification of 100 fold without trouble. It is doubtful if a device of this kind is as good as the audion, because by properly designing the audion it is easy to obtain a voltage amplification of several hundred fold, and since the audion does not possess a falling characteristic, its operation is stable no matter how high the amplification constant be made. In cases where it may be necessary to use a negative resistance device, however, the dyna- tron will be found to be of value and better than an arc, which also shows a negative resistance characteristic. The dy natron, for example, does not depend for its operation on the ionization of gas or vapor and is therefore more reliable. The dynatron can be used also to produce sustained oscilla- tions if it be connected in a circuit of the type commonly used in connection with arcs. Fig. 231, for example, shows a circuit which makes possible the production of sustained oscillations with the dynatron. It was shown in Chapter VIII that the total resistance in the output circuit will be zero if the effective resistance of the oscillation circuit L ; C, r, namely ro=^-, is equal Or to the negative resistance of the tube. Hence, by adjusting the capacity C and the inductance L so that r becomes equal to the negative plate resistance of the tube, the total resistance of the output circuit is zero, and the device will produce sustained oscil- lations. 122. Tubes Containing More than One Grid. Various investi- gators have suggested using two grids instead of one for special purposes. Thus, R. A. Heising, for example, used a double grid MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 381 tube as a modulator, in which the radio frequency is impressed between the filament and one grid, and the audio frequency between the filament and the other grid. FIG. 231. There are various circuits in which the tubes with double grids can be used. In one type of circuit, for example, the grid nearest to the anode is used as an auxiliary anode, while the grid nearest to the cathode operates as a controlling electrode. In this case, FIG. 232. we can obtain the expression for the effective voltage as follows: Referring to Fig. 232, let us first regard grid Gi as a cathode. Let the amplification constant of the system so formed be 1*2 = ,* 72 then the effective voltage between Gi and G ? 2 is (6) where E' P is the potential on the plate, and E C 2 the potential on the grid Gi. This expression can be regarded as the effective anode potential for the system: F (cathode), G\ (controlling elec- 382 THERMIONIC VACUUM TUBE trode) and (^^(anode) . Hence, the effective voltage between F and G\ is . . .~v V . . (7) where E g \ is the potential on the grid Gi. Substituting the value of Ez given by equation (6), we get the effective voltage between ...... (8) and the current is /2=/2(7i72#'p+7i#*2+^i). '&&* . (9) In the case of a tube containing only one grid the corresponding expression for the current is Ii=fi(-YE P +E a ), . . . VY . . . (10) where 7 is the reciprocal of the amplification constant ju. If we make the potential of the plate in the case- of the double grid tube equal to n times that of the grid G%, we can write equa- tion (9): /2=/2 [^7172 + ^)^ + ^1 J. (11) This expression can be compared with that which holds for a single grid tube. Suppose that the amplification constant of the single grid tube is such that 7 = 7172. Then we find that the ratio of the negative potentials on the controlling grid, that are necessary to reduce the current to zero in the two cases, is Thus, suppose the potential of the plate is the same in both cases, and let n 2, and 72 = 0.!. Then the intercept of the character- istic on the axis of controlling grid voltage, in the case of the two grids, is about six times as large as in the case of the tube containing only one grid. Other comparisons can be made if the form of the characteristic of the double grid tube is known. In operating a double grid tube in the manner described above, the grid G% is usually sufficiently positive to draw an appreciable 1 See also BARKHAUSEN, Jahrb. d. drahtlosen Tel. u. Tel, Vol. 14, p. 43, 1919. MISCELLANEOUS APPLICATIONS OF THERMIONIC TUBES 383 number of electrons to it, and this decreases the current to the plate. In general, such tubes are not as good as audions when used for ordinary purposes. Circuits can, of course, be easily devised which enable one to make use of variations in the current flowing to the second grid, as well as that flowing to the plate or anode. Another way in which double grid tubes can be used is to use the grid nearest to the anode as the controlling electrode, and apply a positive potential to the grid nearest to the cathode, as has, for example, been done by Langmuir. This grid should then preferably be placed close to the cathode, and the potential applied to it should be high enough to pull the electrons away from the filament as fast as they are emitted from it, thus giving the condition for the saturation current. In this case the space charge between the filament and the first grid is small. If the second grid is kept negative with respect to the first grid, the electrons passing through the first grid will be slowed down in approaching the second grid, thus increasing the space charge between the two grids, but the electrons in the space are now spread throughout a greater volume, instead of being con- centrated around the filament, and hence, potential variations applied to the second grid can be expected to produce relatively large changes in current flowing to the anode. Here, again, the first grids robs the plate of current, but the circuit could be so arranged that use is made of the variation in both currents, namely, that flowing to the plate and that to the first grid. In using such devices, where electrons impinge on a conductor which does not have the highest positive potential in the system, the effect of secondary electron emission must be taken into con- sideration, because if the electrons impinge with sufficient violence on a conductor, secondary electrons are emitted from it, and if there is another conductor, which is positive with respect to the first, the secondary electrons will be drawn over to this positive conductor. If the velocity with which the electrons impinge on the first conductor is large enough, so many secondary electrons can be emitted that electrons will flow out of this conductor instead of into it, thus reversing the direction of the current. INDEX Abraham, 2, 8, 227 Admittance, mutual, 187 of plate circuit, 280 Aeroplane, radio transmitter, 240 radio receiver, 240 Amplification: circuits, 249 et seq. distortionless, 260 equations, 180 et seq. verification of, 189 expressed on logarithmic scale, 218 expressed in miles of standard cable, 218 as function of operating parame- ters, 224 measurement of, 215 power, 185 voltage, 181, 213 Amplification constant, 160 calculation of, 227 equation for, 231 for cylindrical structures, 234 measurement of, 203, 215 methods of measuring, 193 Amplifier, circuit with single source of voltage, 262 multi-stage, 252 push-pull, 261 telephone, 262 types of, 236, 249 et seq. voltage, 252 unilateral, 262 Amplitude of oscillations in three- electrode tube, 279 Amplitude factor, 125 values of, 128 Anode : power dissipated at, 75, 303 effects of temperature of, 76 Anode potential: effect of, on power from oscillator, 312 effect of, on oscillation current, 311 effect of, on amplification, 226 Anode temperature: effects of, in vacuum tubes, 76 Appleton, E. V., 202 Applications: miscellaneous, of thermionic tubes, 367 Arc discharge: difference between gas-free and, 107 Armstrong, E. H., 290, 335 Arnold, H. D., 81, 170, 188, 253, 255 Artificial line, 216 Attenuation constant, 217 of standard cable, 218 Audibility : expressed in miles of cable, 351 Audibility method of measuring de- tecting current, 336, 349 Audion, 145 von Baeyer, 42 Ballantine, S., 199, 285 Barkhausen, 155, 382 Blue glow, 21 Bohr, 18 Boltzmann, 25 Bridge: use of audion in, 213 385 386 INDEX Bright spots of coated cathodes, 85 Buckley, O. E., 375 Campbell, G. A., 139 Capacity: input, 208, 212 electrode, see electrode, 205 Carbon button generator, 223 Carrier wave, 318 Carson, J. R., 261, 316, 378 Cathode: equipotential, 55 efficiency, 76 Characteristic: for concentric cylinders, 59 effect of curvature of, on operation of tube, 73 dynamic, 295 effect of resistance on, 170 grid current, 186 lumped, 160 of inductive plate circuit, 174 of non-inductive plate circuit, 169 grid current-grid potential, 153 plate current-grid potential, 160 plate current-plate potential, 150 plate resistance, 196 static and dynamic, 170 et seq. verification for thermionic ampli- fier, 158 of thermionic valve, 50 for parallel plates, 54 influence of initial velocities on, 61 straightened by resistance, 128 Child, C. D., 55, 58 Coated filament, 81 operating temperature of, 81 See also Wehnelt cathode. Collision, elastic, 20 ionization by, 21 Colpitts, E. H., 261, 294, 306 Colpitts' oscillator circuit, 282 Comparison of detectors, 346 Complex circuits, 290 Conductance: mutual, 166, 189, 269 measurement of mutual, 199, 203 reflex mutual, 166 Conductance Continued relation between mutual, of tube and circuit, 279 Contact potential difference, 26 measurement of, 28 Convergence frequency, 21 Corpuscle, 1 Coupled circuits, 290 Coupling: method of adjusting, 306 Current limitation : by space charge, 52 by voltage drop in filament, 64, 69 by thermionic emission, 70 Curvature of characteristic: effect of, on operation of tube, 73 Davisson, C. J., 80, 82 Debije, P., 26 Delta rays, 47 Dember, H., 47 Detecting current, 169, 325 method of measuring, 335 r.m.s. value of, 328 as function of anode potential with- out grid condenser, 331 with grid condenser, 359 Detecting efficiency, 34.4 Detection : double, 365 with blacking condenser in grid circuit, 332 theory of, 315 Detection coefficient, 326 measurement of, 339 as function of plate and grid poten- tials, 328 Detectors, comparison of, 346 Dislodged electrons, current carried by, 57 Dislodgment of electrons: means of, 17, 30 from curved surfaces, 35 Distortion : due to harmonics, 168 reduced by external resistance, 169 Distortionless amplification, 178 Dushman, 77, 84, 122, 129, 375 INDEX 387 Dynatron, 378, 380 Eccles, 155 Edison effect, 30 Efficiency : of cathode, 76 et seq. thermionic, 77 for tungsten, 77 for coated filament, 80 detecting, 344 of thermionic oscillator, 298 rectification, 123 et seq. Einstein, 20, 41 Electrode capacities, 178, 205 Electron : accelerated, 13 current, 57 dislodgment of, 14 effect of electric field on motion of, 9 effect of magnetic field on motion of, 10 electromagnetic mass of, 7 field of moving, 5 field of "stationary," 4 free, 23 longitudinal mass of, 8 mass of, 2, 6, 8 size of, 2, 8 transverse mass of, 8 Electrons : free, 16 dislodgment of, 17, 30, 35 in equilibrium, 25 occurrence of, 16 Electron affinity, 24 effect of surface condition of cath- ode on, 34 effect of, on saturation current, 79 relation between Richardson's con- stant b and, 33 values of, 29 Electron evaporation constant, 24 Electrostatic voltmeter: vacuum tube as, 367 Elster and Geitel, 30 Emissivity, thermal, 75 Epstein, P. S., 63 Equipotential cathode, 55 Everitt, H. W., 200, 203 Falling characteristic, 170 Faraday, 2 Feed-back : Amplifier, 257 receiving circuit, 360 Filament current: effect of, on amplification, 225 on oscillation, 308 Filament voltage drop: effect on characteristic, 64, 69 effect on detecting current, 329 Filter, 138, 216, 265, see also Wave Filter Fleming, 30, 111, 125 de Forest, 42, 145 Form factor, 125 values of, 128 Found, C. G., 375 Franck and Hertz, 20 Free electrons, 23 Frequency : effect of, in reducing rectification, 134 heterodyne method of generating low, 377 obtainable with thermionic oscilla- lator, 312 of oscillations in three-electrode tube, 274 Fry, T. C., 63, 138 Gas: effect of, on discharge, 86 effect of, on electron emission, 98 surface effect of, 86, 98 volume effect of, 86 Gauge, ionization, 91, 375 Gherardi, B., 262 Graetz, 130 Grainacher, H., 141 Grid: action of, 146 effect of dimensions of, 228 screening effect of, 229 388 INDEX Grid current characteristic, 153 in oscillator, 295 Grid leak resistance, 309 Grid potential, means of maintaining, 250 Grids, tubes containing two, 380 Hallwacks, 38 Harmonics, 168, 177, 282 Hartley, 257, 282, 287, 293, 313 oscillator circuit, 282, 313 Hazeltine, L. A., 165, 269, 280, 283 Heising, 280, 283, 308, 310, 323, 367, 380 Hertz, H., 38 Hertz and Franck, 20 Heterodyne: method of generating low frequen- cy, 377 reception, 353 et seq. High tension voltmeter: vacuum tube as, 369 Homodyne, reception, 358 Hull, A. W., 49, 132, 378, 380 Impact, elastic, 20 Impedance, input, 206, 212 Infra-saturation part of characteris- tic, 71 Initial velocities : of photo-electrons, 38 influence of on tube characteristic, 61 Input capacity, impedance, power, etc., see corresponding nouns. Ion: negative, 19 positive, 18 lonization, 16 by collision, 21 directive effect on flow of gas, 101 effect on infra-saturation, 93 effect on operation of oscillator, 101 effects of, 91 gauge, 91, 375 heating of cathode by, 92 at high pressure, 106 at low pressures, 90 lonization, manometer, 375 proportional to low pressure, 91 voltage, 21, 22 Jewett, F. B., 262 Johnson, J. B., 213 King, R. W., 227, 234, 235 Langmuir, I., 55, 59, 75, 101, 154, 245, 383 Latour, M., 153, 187 von Laue, 227 Lenard, 42, 53 Life of a vacuum tube, 84 Lilienfeld, 53 Limitation of current, 52 by space charge, 52 by voltage drop in filament, 64, 69 by thermionic emission, 70 Limiting, power device, 373 Lorentz, 2, 8 n, see Amplification Constant. Manometer, inozation, 375 Marconi, 112 Maxwell, 227, 232 Mean free path of electrons in gases, 88 et seq. Meissner, 290 Microphone generator, 223, 339 for obtaining modulated waves, 348 Miles of standard cable: amplification expressed in, 218 audibility expressed in, 351 relation between amplification and, 219 Miller, J. M., 194, 197, 205, 209, 290 Millikan, R. A., 13, 41 Modulated current, r.m.s. value of, 328 Modulated wave: equation for, 319 completely, 321 method of obtaining completely, 342 .- Modulation : double, 365 INDEX 389 Modulation Continued systems of, 322 theory of, 315 Morecroft. J. H., 303 Multiplex telegraphy and telephony, 364 Multi-stage amplifier, 184, 252 design of, 256 with inductive connection, 252 with inter-tube transformers, 253 with non-inductive connection, 253 phase relations in, 260 Music, transmission of, 254 Mutual admittance, see Admittance. Mutual conductance, see Conduct- ance. Negative carriers, 71, 96 Negative resistance, 48, 108, 379, see also Resistance, 271 Nichols, 205, 215 Occluded gases, effects of, 102 Operating parameters, influence of: on amplification, 224 on oscillation, 307 Optimum voltage for rectification, 117 et seq. Oscillation: amplitude of, in vacuum tube, 279 conditions for, 267 in two-electrode tube, 269 in three-electrode tube, 271 Oscillation current as function of filament current, 309 of anode potential, 311 equations of vacuum tube, 267 generator, 266 et seq. Oscillations in amplifier circuits, 258 Oscillator: tuned grid circuit, 284 with grid leak resistance, 309 with grid battery, 310 practical, circuits, 292 for extreme frequencies, 312 Oscillograms : of current in valve rectifier, 129 of oscillator output, 302, 305 Parasitic circuits, 285 Peltier effect, 27 Phase relations: in amplifier, 174 in multi-stage amplifier, 260 in oscillator, 280 Photo-electric : effect, 38 equation, 41 long wave-length limit, 42 Photo-electrons, maximum velocity of, 38 Planck, 18, 20 Plate impedance, 160 Plate resistance, see also Resist- ance. characteristic, 196 Plate current, 177 Pliodynatron, 380 Poisson, 15, 52, 56 Positive electron, 2 Potential distribution: in audion, 147, 148 for finite initial velocities, 62 for zero initial velocity, 56 Power: effect of anode potential on, from oscillator, 312 in input circuit, 211 in output circuit of amplifier, 192 in output circuit of detector, 328 in output circuit of oscillator, 296 Power amplification, 185 Power-limiting devices, 373 Pure electron discharge, 22 Push-pull amplifier, 261 Radiation: from atoms, 19 due to accelerated electron, 13 Radiation constant, 75 Radio transmitting and receiving systems, 361 et seq. Reactance, input, 208 Receiver shunt, 216 computation of, 222 390 INDEX Receiver shunt for measuring ampli- fication, 218 for measuring audibility, 350 for measuring detecting current, 337 theory of, 221 Receiving systems, radio, 361 Recombination of ions, 96 Rectification : conditions for, 109 efficiency, 123 et seq. Regeneration, 287 Regulator : audion as current and voltage, 371 valve as voltage, 142 Repeater: Western Electric type, 239 circuit, 263 Resistance: computation of plate, 234 input, 208, 209, 212 measurement of plate, 195 negative, 271, 379 plate, 268 Richards, W. L., 262 Richardson, O. W., 24, 26, 31, 32, 53, 83 Saturation current, 50, 77 from contaminated tungsten, 37 effect of surface condition on, 37 from oxide-coated cathodes, 37 Schelleng, J. C., 303 Schottky, 55, 155, 227 von Schweidler, 53 Secondary electron emission, 47, 383 devices employing, 378 Singing: in amplifiers, 209, 259 in repeater circuits, 263 Soddy, 53 Space charge, 15, 55 current limitation by, 52 due to positive and negative car- riers, 52 relation between potential distribu- tion and, 15 Space current, 6, 57 control of, by third electrode, 42 as function of plate and grid poten- tials, 46 Standard cable: constants of, 218 Stefan-Boltzmann radiation law, 75 Stevenson, G. H., 198 Stoller, H. M., 142 Stoletow, 53 Stoney, G. J., 1 Strayfield, 146, 229 verification of, relation, 157 Structural parameters of tube, 226 Surface condition of cathode: effect of, on electron affinity, 34 on saturation current, 37 on characteristic, 70 force on electrons, 23, 24 Switch, valve as high tension, 378 Telegraphy, multiplex, 364 Telephone amplifier, 262 Telephony, multiplex, 364 Temperature : effects of anode, on operation of tube, 76 safe cathode, 85 saturation, 54, 308 Thermionic amplifier: types of, 236 et seq. Thermionic valve, 50 characteristics of, 51 as current limiting device, 124 as high power rectifier, 115 as high tension switch, 378 minimum resistance of, 126 types of, 120 voltage drop in, 115 Thermionic efficiency, 77 of coated cathode, 80 effects of electron affinity on, 78 of tungsten, 77 Third electrode for controlling space current, 42, 146 Thomson, J. J., 1, 5, 55 Three-halves power equation: for parallel plates, 58 INDEX 391 Three-halves power equation Con. for concentric cylinders, 60 Transformer, input and output, 250 Transmitting systems, radio, 361 Two-way, one-repeater circuit, 264 Two-way, two-repeater circuit, 263 Vacuum, by vaporization of calcium, 53 Vacuum test for tubes, 105 Vacuum tubes: types of, 120 et seq., 236 et seq. Vallauri, 154 Valve detector, 111 with anode battery, 112 See also Thermionic Valve. Voltage amplification, 181, 213, see Amplification. Voltage drop in filament, see Fila- ment, Voltmeter : vacuum tube as electrostatic, 367 Wave filter, 138, see also Filter. Wave shape: of current in output of audion, 166 of current in valve, 116 of modulated current, 320 Wehnelt cathode, 25, see also Coated Filament. White, W. C., 313 Wilson, H. A., 99 Wilson, R. H., 251, 355, 368 Wilson, W., 64 Wold, P. I., 371, 377 X-radiation: characteristic, 47 general, 47 soft, 47 MAY BE Overdues subject to replocement^harges^ RUE AS STAMPEDBblOW~ 'UNIVERSITY OF CALIFORNIA, BERKLEY FORM NO. DD1 1 , 80m, 8/80 BERKELEY, CA 94720 THE UNIVERSITY OF CALIFORNIA LIBRARY