REFLEX OSCILLATORS 513 



A. Fixed Element Loads 



In this discussion it will be assumed initially that M, the phase angle of 

 — Ye , is not affected by frequency. The results will be extended later to 

 account for the variation of A0 with frequency. A further simplification is 

 the use of the equivalent circuit of Fig. 118, Appendix I. Initially, the 

 output circuit loss, R, will be taken as zero, so the admittance at the gap 

 will be 



Yc = Gr^ 2jM^oi/oi + Yl/N\ (9.1)8 



Here, Gr is the resonator loss conductance, M is the resonator characteristic 

 admittance, and Fj, is the load admittance. 



We will now simplify this further by letting Gk = 



F. = 2iMAco/co + Yl/N\ (9.2) 



From Fig. 12 we see 



GJN^ = yA2Ji(X)/X] cos Ad (9.3) 



B, ^ 2MAC. ^ _y^i2MX)/X] sin Ad . (9.4) 



Now it is convenient to define quantities expressing power, conductance and 

 susceptance in dimensionless form. 



p = X^G^/2.Smye (9.5) 



Gi = GjWye (9.6) 



^1 = Bz./7V2y«. (9.7) 



The power P produced by the electron stream and dissipated in G^, is related 

 to p 



e-^>- 



P = (^-^7 P- (9.8) 



In terms of p and Gi , (9.3) can be written 



p = (l/1.25)(2.5/>/Gi)~Vi[(2.5/^/Gi)1 cos A0. (9.9) 



By dividing (9.4) by (9.3), we obtain 



Aco/coo = (-Gi/2A'W) tan A^ - BlI2X'^M (9.10) 



- (2M/ye)Aco/a'o = Gi tan AQ -^B,. (9.11) 



* To avoid confusion on the reader's part, it is perhaps well to note that we are, for the 

 sake of generality, changing nomenclature. Hitherto we have used F/, to denote the 

 load at the oscillator. Actually our load as the appendix shows is usually coupled by 

 some transformer whose ecjuivalent transformation ratio is 1/A'^, so that the admittance 

 at the gap will be YiJN^. 



