operation of Ultra-High-Frequency Vacuum Tubes 



By F. B. LLEWELLYN 



Previous electronics analyses are extended by the introduction of more 

 general boundary conditions. The results are applied to the calculation of 

 the rectifying properties of diodes at very high frequencies and to the ampli- 

 fying properties of negative grid triodes at both low and high frequencies. 

 The effect of space charge on the various capacitances in triodes is discussed, 

 and formulas for the amplification factor and plate impedance are presented 

 in terms of the tube geometry. Finally, a discussion of the input impedance 

 of negative grid triodes is given together with a comparison of the theoretical 

 value with the results of measurements made by several well-known experi- 

 menters. 



IN the study of the functioning of vacuum tubes at ultra-high 

 frequencies it has been necessary to retrace the steps followed in 

 the early history of vacuum tube performance but with the difference 

 that a microscope for viewing the path at close range must be substi- 

 tuted for the telescope with which the original trail was mapped from 

 afar off. As a result of this microscopic survey, formulas have been 

 developed which are applicable to frequencies so high that the time 

 of flight of the electron across the tube may occupy several cycles of 

 the high-frequency oscillation. In addition to this result, several by- 

 products of the study are found to have a useful application in the low- 

 frequency field and to throw additional light on the multitudinous 

 activities of the electrons and their effect upon the external circuit. 



In this respect it is particularly interesting to see the way in which 

 the geometry of the vacuum tube enters into the determination of the 

 amplification factor of negative grid triodes and to compare the results 

 now obtained with the earlier results of such workers as Abraham, 

 King, Schottky, Lane and Van der Bijl. The effect of the negative 

 grid on the transit time of the electrons also yields low-frequency 

 relations in which certain new facts concerning the plate resistance are 

 brought out. 



Various papers ^' '• ^' ■*- ^ published within the last few years have 

 dealt with the general problem of vacuum tubes in which the electron 

 transit time is of importance and have derived results which are useful 

 in several practical applications. However, in none of these have the 

 initial relations been general enough to allow more than a very rough 

 application to be made to the most widely used tube of all — the 

 negative grid triode. A paper ^ by the present writer contains certain 

 general conclusions concerning the negative grid tube at very high 



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