96 BELL SYSTEM TECHNICAL JOURNAL 



curve A in Fig. 16 could be attained practically, it would be possible to 

 secure oscillations even at low frequencies by connecting an inductance 

 between the plate and cathode terminals. Curve B shows a low-fre- 

 quency limit of a little less than f tt for the grid-plate transit angle. 



One of the more important observations to be drawn from the 

 curves of Figs. 11, 14, 15, and 16 is that if the inductance between plate 

 and cathode is obtained by means of a tuned antiresonant circuit, then 

 the circuit must be tuned to a frequency somewhat higher than the 

 oscillation frequency. This is in order that it may effectively present 

 an inductive impedance to the oscillating tube, so that the extended 

 curves in the figures may encircle the origin in a clockwise direction. 



Another conclusion is that there are so many different permutations 

 and combinations of the operating conditions that it is small wonder 

 that there have been a great many different "theories" and empirical 

 frequency formulas advocated. For instance, operation under condi- 

 tions giving din R — X diagram which shows negative resistance over 

 a small frequency range, only, such as A in Fig. 11, or B in Fig. 15, 

 would give oscillations whose frequency would be much more nearly 

 independent of the tuning of the external circuit than would conditions 

 which resulted in a negative resistance over a wide frequency range, 

 as at A in Fig. 16. In this latter case the external circuit exerts a large 

 influence upon the frequency. 



The data from which Figs. 11 to 16 were plotted are given in the 

 appended tables. The final step in the calculation of these data was a 

 multiplication by 12 which was performed on a slide rule. For all 

 previous steps seven-place tables were employed because of the fre- 

 quent occurrence of differences of numbers of comparable magnitude. 



The effect on the frequency of a change in the operating voltages 

 can be deduced inferentially from the curves. Thus, in general, the 

 formulas for the transit angle have the form, 



Kx 



\\Vo 



where x is the grid-origin distance, 

 X is the wave-length, 

 V[) is the grid potential, 

 i^ is a constant which depends on the mode of operation. 



When the plate potential is changed by a relatively large amount 

 the operation undergoes a transition from a limiting mode illustrated 

 by one of the figures to another limiting mode shown on some other 

 one of the figures. 



On the other hand, a change in grid potential will act to change the 



