480 BELL SYSTEM TECHNICAL JOURNAL 



cross the gap so slowly that for them /3 would be very small and their effect 

 on the circuit would also be small (d) there might be considerable loading of 

 the resonator due to transit time effects in the gap. Of course, it is not 

 justifiable to apply the small signal theory in any event, since it was derived 

 on the assumption that /ST' is small compared with Fo . 



In Appendix IV there is presented a treatment by R. M. Ryder of these 

 Laboratories in which it is not assumed that /3r«Fo . This work does 

 not, however, take into account variation of /3 with electron speed or the 

 possibility of electrons being turned back at the gap. 



For drift angles of If cycles and greater, the results of Ryder's analysis 

 are almost indistinguishable from those given by the simple theory, as may 

 be seen by examining Figs. 128-135 of the Appendix. His curves approach 

 the curv-es given by the simple theory for large values of n. 



For small values of n, and particularly for f cycles drift, Ryder's work 

 shows that optimum power is obtained with a drift angle somewhat different 

 from n + f cycles. Also, Fig. 131 shows that the phase of the electronic 

 admittance actually varies somewhat with amplitude, and Fig. 130 shows 

 that its magnitude does not actually pass through zero as the amplitude is 

 increased. 



The reader is also referred to a paper by A. E. Harrison. 



The reader may feel at this point somewhat uneasy about application of 

 the theory to practice. In most practical reflex oscillators, however, the 

 value of w is 2 or greater, so that the theory should apply fairly well. There 

 are, however, so many accidental variables in practical tubes that it is well 

 to reiterate that the theory serves primarily as a guide, and one should not 

 expect quantitative agreement between experiment and theory. This will 

 be apparent in later sections, where in a few instances the writers have made 

 quantitative calculations. 



V. Special Drift Fields 

 In the foregoing sections a theory for a reflex oscillator has been developed 

 on the assumption that the repeller field is a uniform retarding electrostatic 

 field. Such a situation rarely occurs in practice, partly because of the diffi- 

 culty of achieving such a field and partly because such a field may not return 

 the electron stream in the manner desired. In an effort to get some in- 

 formation concerning actual drift fields, we may extend the simple theory 

 already presented to include such fields by redefining X as 



X = ^VFe/2Vo. (5.1) 



Here the factor F is included. As defined in Section /// this is the factor 

 which relates the effectiveness of a given drift field in bunching a velocity 



^ A. E. Harrison, "Graphical Methods for Analysis of Vrlocitv Modulation Bunching." 

 Proc. I.R.E., 33.1, pp. 20-32, June 1945, 



