VACUUM TUBE ELECTRONICS 61 



In the meantime, the production of ultra-high-frequency oscilla- 

 tions had been progressing in a somewhat different direction. The 

 discovery, about 1920, by Barkhausen that oscillations of less than 

 100 centimeters wave-length could be secured in a tube having a 

 symmetrical structure, when the grid was operated at a fairly high 

 positive potential, while the plate was approximately at the cathode 

 potential, started experiments on what was thought to be an altogether 

 different mode of oscillation. Workers by the score have extended 

 both the experimental technique and the theory of production of this 

 newer type of oscillation. However, one of the results which an 

 analysis of ultra-high-frequency electronics illustrates is that the elec- 

 tron type of oscillator is merely another example of the same kind of 

 oscillation which was produced in the old-time so-called regenerative 

 circuits. 



For the purpose of extending the theory of electronics within vac- 

 uum tubes to frequencies where the time of transit of the electrons 

 becomes comparable with the oscillation period, it is important at the 

 outset to select an idealized picture which is simple enough to allow 

 exact mathematical relations to be written. At the same time, the 

 picture must be capable of adaptation to practical circuits without 

 undue violence to the mathematics. An example of this kind of 

 adaptation is illustrated by the classical calculation of the amplification 

 factor fx, which was accomplished by consideration of the force of the 

 electrostatic field existing near the cathode in the absence of space 

 charge even though tubes were never operated under this condition. 

 In a like manner, such violations of the ideal must, of necessity, be 

 made in ultra-high-frequency analysis but their practical validity lies 

 in so choosing them that the quantitative error introduced is less than 

 the expected precision of measurement. It becomes, therefore, of the 

 utmost importance to state clearly the transitions which occur be- 

 tween results obtained for the idealized case to which the mathematics 

 is strictly applicable and the practical circuits where the assumptions 

 and approximations are made to conform with operating conditions. 



A start has already been made on the problem of developing such 

 a generally valid system of electronics. This was done by Benham ^ 

 who considers a special case comprising two parallel-plane electrodes, 

 one of which is an emitter and the other a collector, when conditions 

 at the emitter are restricted by the assumption that the electrons are 

 emitted with neither initial velocity nor acceleration. This work of 

 Benham's has the utmost importance in a general electronic theory 



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

 Moderately High Frequencies," Part I, Phil. Mag., p. 641; March (1928); Part II, 

 Phil. Mag., Vol. 11, p. 457; February (1931). 



