Impedance Properties of Electron Streams 



By LISS C. PETERSON 



The input impedance of an idealized space charge grid tube is 

 investigated under general conditions of space charge between the 

 accelerating grid and the negatively biased control grid. It is 

 shown that under certain space charge conditions the input 

 capacitance and conductance both may be negative. These im- 

 pedance properties persist up to frequencies for which the transit 

 angle is quite large. Possibilities of designing electronic negative 

 capacitances are thus opened up. Experimental results are also 

 given; these give a broad confirmation of the theoretical deductions. 



PART I 

 Theory 



IN the early stages of vacuum tube history the theoretical work on 

 d-c. space charge treated mainly potential distributions associated 

 with fairly small initial velocities of the electrons. With the advent 

 of multi-electrode tubes this situation changed for it then became 

 necessary to consider also potential distributions occurring when elec- 

 trons are injected with large initial velocities. Idealizations were 

 introduced to the extent that consideration was given only to space 

 charge conditions which can exist between two parallel planes at 

 known potentials when electrons with normal velocities corresponding 

 to these potentials are injected into the region through one or both 

 planes.^ 



Some time ago it was discovered experimentally that space charge 

 may under certain conditions produce a negative capacitance. The 

 negative capacitances were found during a series of low-frequency 

 measurements of the control-grid-to-ground capacitance of an experi- 

 mental space-charge-grid tube. In the course of these measurements 

 it was found that with all the electrodes carefully by-passed to ground 

 for a-c. except the negatively polarized control grid, the input 

 capacitance as well as the input conductance was negative in certain 

 domains which depended upon the d-c. operating voltages. 



In order to arrive at an understanding of this fact, a-c. phenomena 

 must be considered under the general d-c. space charge conditions 



1 Plato, Kleen, Rothe, Zeitschrift f. Phys., 101, July 1936. C. E. Fay, A. L. 

 Samuel, W. Shockley, Bell Sys. Tech. Jour., January 1938. B. Salzberg, A. V. 

 Haeff, R.C.A. Review, January 1938. 



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