Electronic Admittances of Parallel-Plane Electron 

 Tubes at 4000 Megacycles 



By SLOAN D. ROBERTSON 



This paper reports the results of some measurements of the electronic admit- 

 tances of close-spaced parallel-plane diodes and "1553" triodes at a frefjuency 

 of 4060 megacycles. These results reveal that the diode admittance and the 

 input short-circuit admittance of the triode depart considerably from the values 

 predicted \>y single-velocity theory. The triode transadmittance, however, is 

 onl\- slightl\- lower in magnitude than the low-frequency value. 



THE high-frequency admittances of electron streams flowing between 

 parallel-plane electrodes have stimulated considerable theoretical 

 interest. Llewellyn^'--^'^ has given an analysis of the particular case in which 

 all electrons in any plane perpendicular to the direction of flow are assumed 

 to have identical velocities. In practice, this approximation gives a reason- 

 ably accurate expression for electron stream admittances if the electrode 

 spacing is relatively large, and if the frequency is not so high that the 

 actual spread in electron velocities represents an appreciable fraction of the 

 transit time. Others have treated various aspects of the general prob- 

 lgni4,5.6,7,8.9,io_ Theoretical consideration has also been given to the problem 

 of electron flow in which the electrons possess a MaxweUian velocity dis- 

 tribution"'^-'^'-^*. There has been, however, no complete analysis of the 

 microwave-frequency case which takes account of the MaxweUian velocities. 

 In order to orient the present work properly with previous work let us 

 consider briefly the parallel plane diode shown in Fig. 1, which shows three 

 representative potential distribution curves. If only a relatively few elec- 

 trons are available at the cathode, the potential distribution between elec- 

 trodes will be approximately equal to the space-charge-free distribution 

 indicated by curve a. If an ample supply of electrons is provided by the 

 cathode and if all electrons leave the cathode with zero velocity, then the 

 space charge is complete in accordance with Child's law, and the potential 

 distribution follows curve b. If, on the other hand, the cathode is capable 

 of supplying an ample supply of electrons, the electrons being emitted with 

 a MaxweUian velocity distribution, the potential distribution wUl be rep- 

 resented by a curve of the type shown by c. The cases shown by curves a 

 and b can be treated by the Llewellyn analysis. With wide spacings and at 

 lower frequencies the admittances obtained with distributions of the c 

 type may be approximated by the results obtained by analysis of distribu- 

 tions of the b type. With the very close spacings encountered in the Bell 



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