Vacuum Tube Electronics at Ultra-high Frequencies * 



By F. B. LLEWELLYN 



Vacuum tube electronics are analyzed when the time of flight of the 

 electrons is taken into account. The analysis starts with a known current, 

 which in general consists of direct-current value plus a number of alter- 

 nating-current components. The velocities of the electrons are associated 

 with corresponding current components, and from these velocities the 

 potential differences are computed, so that the final result may be expressed 

 in the form of an impedance. 



Applications of the general analysis are made to diodes, triodes with 

 negative grid, and to triodes with positive grid and either negative or posi- 

 tive plate which constitute the Barkhausen type of ultra-high-frequency 

 oscillator. A wave-length range extending from infinity down to only a 

 few centimeters is considered, and it is shown that even in the low-frequency 

 range certain slight modifications should be made in our usual analysis of 

 the negative grid triode. 



Oscillation conditions for positive grid triodes are indicated, and a brief 

 discussion of the general assumptions made in the theory is appended. 



I. Foreword 



THE art of producing, detecting, and modulating ultra-high-fre- 

 quency electric oscillations has reached the same state of develop- 

 ment which was attained in early work on lower frequency oscillations 

 when experiment had outstripped theory. The experimenters were 

 able to produce oscillations by using vacuum tubes, but were not 

 able to explain why. They were able to make improvements by the 

 long and tedious process of cut and try, but did not have the powerful 

 tools of theoretical analysis at their command. In particular, the 

 advantage of the theoretical attack may be illustrated by the rapid 

 advance in technique which followed the theoretical concept of the 

 internal cathode-plate impedance of three-element vacuum tubes. 

 The work of van der Bijl and Nichols showed that for purposes of 

 circuit analysis this path could be replaced by a fictitious generator 

 of voltage, fiCg, having an internal impedance whose magnitude is 

 given by the reciprocal of the slope of the static Vp — Ip characteristic. 

 Development of commercially reliable vacuum tube circuits began 

 forthwith. In a similar, yet less complicated manner, the internal 

 network of two-element tubes may be replaced by an equivalent 

 resistance when relatively low frequencies only are considered. 



In these concepts where the vacuum tube is replaced by its equiva- 



* Presented in brief summary before U. R. S. I., Washington, D. C, April, 1932. 

 Proc. I. R. E., Vol. 21, No. 11, November, 1933. 



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