520 BELL SYSTEM TECHNICAL JOURNAL 



These values are roughly those for the 2K25 reflex oscillator. Figure 36 

 shows p vs Gi for the particular parameters assumed above. The curves 

 were obtained by assuming values of Gi for an approj)riate .1 and so obtain- 

 ing values of .V from Fig. 35. Then the power was calculated using (9.19) 

 and so a curve of j)ower vs d for a })articular value of .1 was constructed. 



Figure 37 shows an impedance performance chart obtained from (9.16) 

 and Fig. 36. In using Fig. 36 to obtain constant power contours, we need 

 merely note the values of Gi at which a horizontal line on Fig. 36 intersects 

 the curves for various values of A. Each curve either intersects such a 

 horizontal (constant power) line at two points, or it is tangent or it does not 

 intersect. The point of tangency represents the largest value of A at which 

 the power can be obtained, and corresponds to the points of the crescent 

 shaped power contours of the impedance performance chart. The maximum 

 power contour contracts to a point. 



Along the boundary of the sink, for which p — 0, X = and we have from 

 (9.18) 



Gi = cos bd - Gi. (9.22) 



The results which we have obtained can be extended to include the case 

 in which Id 9^ 0. Further, as we know from Appendix I, we can take into 

 account losses in the output circuit by assuming a resistance in series with 

 the load. In a well-designed reflex oscillator the output circuit has little 

 loss. The chief effect of this small loss is to round off the points of the 

 constant power contours. 



In actually measuring the performance of an oscillator, output and fre- 

 quency are plotted vs load impedance as referred to the characteristic 

 impedance of the output line. Also, frequently the coupling is adjusted so 

 that for a match (the center of the Smith chart) optimum power is obtained. 

 We can transform our impedance performance chart to correspond to such a 

 plot by shifting each point G, B on a contour to a new point 



Gi = G/Gxaax 

 Bi = B/Gmas 



where Gmax is the conductance for which maximum power is obtained. 

 Such a transformation of Fig. 37 is shown in Fig. 38. 



It will be noted in Fig. 38 that the standing wave ratio for power, the 

 sink margin, is about 2.3. This sink margin is nearly independent of the 

 resonator loss for oscillators loaded to give maximum power at unity stand- 

 ing wave ratio, as has been discussed and illustrated in Fig. 10. If the sink 

 margin must be increased or the pulling figure must be decreased^" the coup- 



'" The pulling figure is arbitrarily defined as the maximum frequency excursion pro- 

 duced when a voltage standing wave ratio of v 2 is presented to the oscillator and the 

 phase is varied through 180°. 



