-188 BELL SYSTEM TECHNICAL JOIRNAL 



It is of interest to ha\'e the value of Aw wo at half the i)o\ver for Aw = 0. 

 At half power, X = A'o/\/2, so 



(Ac., o;o)i = (:ye/2M)((2/i(Xo/V2)/(Xo/\/2))- - {IJ ,{X ,) / X ,y)\ (7.10) 



For given values of modulation coefficient and Fn , X is a function of the 

 r-f gap voltage V and also of drift angle and hence of A0, or repeller voltage 

 (see Appendix IV). For the fairly large values of d typical of most reflex 

 oscillators, we can neglect the change in A^ due directly to changes in M, 

 and consider X as a direct measure of the r-J gap voltage V, Likewise 

 Ve is a function of drift time whose variation with A0 can and will be dis- 

 regarded. Hence from (7.9) we can plot (X/A'o)- vs. Aw/coo and regard this 

 as a representation of normalized power vs. frequency. 



Let us consider now what (7.3) and (7.9) mean in connection with a given 

 reflex oscillator. Suppose we change the load. This will change Q in 

 (7.3) and A'o in (7.9). From the relationship previously obtained for the 

 condition for maximum power output, Gn/ye = /o(Xo), we can find the 

 value of A^o that is, A' at Ao; = 0, for various ratios of GrIj^ . For Gr — ^ 

 (zero resonator loss) the optimum power value of A^o is 2.4. When there is 

 some resonator loss, the optimum total conductance for best power output 

 is greater and hence the optimum value of A^o is lower. 



In Fig. 13 use is made of (7.3) Aw/wo in plotted vs. A0 (which decreases 

 as the repeller is made more negative) for several values of (), and in Fig. 14, 

 (7.9), is used to plot (A7.A0)" vs. (2M/ye)Aw/ajo , which is a generalized 

 electronic tuning variable, for several values of Xo . These curv^es illustrate 

 typical behavior of frequenc}- vs. drift angle or repeller voltage and power 

 vs. frequency for a given reflex oscillator for various loads. In practice, 

 the S shape of the frequency vs. repeller voltage curves for light loads 

 (high Q) is particularly noticeable. The sharpening of the amplitude vs. 

 frequency curves for light loads is also noticeable, though of course the cusp- 

 like appearance for zero load and resonator loss cannot be reproduced ex- 

 perimentally. It is important to notice that while the plot of output vs. 

 frequency for zero load is sharp topped, the plot of output vs. repeller volt- 

 age for zero load is not. 



Having considered the general shape of frequency vs. repeller voltage 

 curves and power vs. frequency curves, it is interesting to consider curves of 

 electronic tuning to extinction ((Aa'/a-o)o) and electronic tuning to half power 

 ((Aw/coo)i) vs. the loading parameter, {MjyeQ) = Gdye . Such curves are 

 shown in Fig. 15. These curves can be obtained using (7.7) and (7.10). 

 In using (7.10) X can be related to Gdye by the relation previously derived 

 from 2J\iX)/X = Gc/ye and given in Fig. 5 as a function of A'. It is to 

 be noted that the tuning to the half power point, (Aoo/a'o)> , and the tuning 

 to the extinction point, (Aa)/coo)o , vary quite differently with loading. 



