REFLEX OSCILLATORS 473 



Then the power output for dn is 



P = 2(/oFo/0„)X/i(X) - V^Ga/2. {3,.i) 



The efficiency, 77, is given by 

 P 2 



■n = 

 From (2.4) and (2.9) 



Hence we may write 

 V = 



P 



DC 



^^^'W-"^]- (^-^^ 



'i^ = ~ X'. (3.5) 



2/0 Fn ye 



^)lH«-ff]- 



(w + 3/4) 



(3.6) 



TT 



Let us write r] = ~ where N = (» + f). We may now make a generalized 

 examination of the effect of losses on the efficiency by examining the function 



H = (l/7r)[AVx(X) - iG,/ye)Xy2]. (3.7) 



Thus, the efficiency for 6 =0„ is inversely proportional to the number of 

 cycles drift and is propotional to a factor H which is a function of X and 

 of the ratio Gnlye , that is, the ratio of resonator loss conductance to small 

 signal electronic conductance.'* For w + f cycles drift, the small signal 

 electronic conductance is equal to the small signal electronic admittance. 



For a given value of Gn/ye there is an optimum value of X for which H 

 has a maximum Hm ■ ^^'e can obtain this by differentiating (3.7) with 

 respect to A^ and setting the derivative equal to zero, giving 



XJo(X) - (Gn/ye)X = 



(3.8) 

 Jo{X) = (G,/ye). 



If we put values from this into (3.7) we can obtain Hm as a function of 

 Gnhe ■ This is plotted in Fig. 7. The considerable loss of efficiency for 

 values of Gn/ye as low as .1 or .2 is noteworthy. It is also interesting to 

 note that for Gnlye equal to \, the fractional change in power is equal to 

 the fractional change in resonator resistance, and for Gs/ye greater than \, 

 the fractional power change is greater than the fractional change in resonator 

 resistance. This helps to explain the fall in power after turn-on in some 

 tubes, for an increase in temperature can increase resonator resistance 

 considerably. 



^ An electronic damping term discussed in Appendix VIII should be included in resona 

 tor losses. The electrical loss in grids is discussed briefly in Appendix IX. 



