664 BELL SYSTEM TECHNICAL JOURNAL 



Ferris' paper so that it is not evident whether the exponent is greater 

 than 2. The loss did, however, increase with transconductance and 

 was checked by the computations in a satisfactory manner, which 

 would imply either that the exponents were actually greater than 2 in 

 Mr. Ferris' tubes, or that their cylindrical shape caused a decrease in 

 the effect of the transconductance on the transit angle. 



The equations in general indicate that the shunting resistance 

 between cathode and grid is proportional to the square of the wave- 

 length. This is in accord with the theory and experiments of Thomp- 

 son and Ferris,^' ^^ and with the experiments of J. G. Chaffee * on 

 tubes biased as class A amplifiers. However, when the tubes were 

 biased as detectors, Chaffee ^' ^ found that the resistance varied more 

 nearly as the first power of the wave-length. There are several factors 

 which may contribute to this difference. With detector bias near cut- 

 off the transit angles are large so that more terms of the fundamental 

 equations may be needed. In Chaffee's work these were computed to 

 be of the order of two or three radians which was scarcely enough to 

 cause the entire effect observed by him. Another cause is thought to 

 be an actual reversal in the direction of motion of electrons caused by 

 the alternating potential operating in the vicinity of cut-off. Further 

 study both of experimental and theoretical nature is required, however, 

 before the point can be considered to be satisfactorily explained. 



Conclusion 



In general, the analysis presented in the foregoing pages is capable 

 of serving as a guide to indicate the kind of results to be expected in 

 the operation of vacuum tubes at ultra-high frequencies. In those 

 cases where the physical structure of the tube complies with the con- 

 ditions laid down for the theoretical treatment, a quantitative agree- 

 ment can be anticipated. The importance of departures of the 

 physical structure from this ideal can be evaluated in many instances 

 by a careful comparison of the actual with the ideal structure. 



Much yet remains to be done in the way of computing and tabulating 

 the various factors involved in the equations and of investigating the 

 effects of such things as initial electron velocities from a hot cathode, 

 large size grid wires, coarse mesh grids, and cylindrical structures. 



References 



1. W. E. Benham, "Theory of the Internal Action of Thermionic Systems at 



Moderately High Frequencies." Phil. Mag., p. 641, March 1928. Part II, 

 Phil. Mag. Supp., Vol. 11, p. 4.S7, February 1931. 



2. F. H. Llewellyn, "Vacuum Tube Electronics at Ultra-High Frequencies." Proc. 



I.R.E., Vol. 21, November 1933; also B.S.T.J., Vol. XIII, January 1934. 



