518 BELL SYSTEM TECHNICAL JOURNAL 



conductance Gi is large the effect is to shift the constant frequency contours 

 along the sink boundary away from the zero susceptance line to larger sus- 

 ceptance values. Hence, the constant frequency contours no longer coincide 

 with the constant susceptance contours, not even for A0 = 0. 



The change in the power contours is considerably more marked. As the 

 frequency of the oscillator changes the transit angle is shifted from the 

 optimum value by an amount bd = (Aco/coo)c<;or. Thus the electronic 



conductance is reduced in magnitude by a factor cos — coot. In particular. 



Wo 



for the sink contour where the load conductance is just equal to the elec- 

 tronic conductance we see that when the repeller voltage is held constant 

 the power contour lies not on the Gi = 1 — G2 contour but on the locus of 



Ao) 

 values Gi = cos — wot — d . 



In order to determine the power contours when the transit time rather 

 than the transit angle is held constant we make use of (9.3) with addition of 

 resonator loss. In normalized coordinates ((9.6) and (9.12)) and for a phase 

 angle of electronic admittance 86 we have 



Gi + G2 = '^^^^ cos 89 . (9.18) 



From (9.5) and (9.13) we have for the power output 



Gi 2XJi{X) ,_ . . 



Along any constant frequency contour 86 is constant and has the value 

 given by (9.15) in terms of wo and coqt. Hence, it will be convenient to plot 

 (Gi + G2) vs X for various values of 86 as a parameter. This has been 

 done in Fig. 35. The angle 86 has been specified in terms of a parameter A 

 which appears in the Rieke diagrams as a measure of frequency deviation. 



^=^^ (9.20) 



ye Wo 



In terms of the parameter A 



86 = (y,/2A/)(coor)/l . (9.21) 



Once we have the curves of Fig. 35 we can find the power for any point 

 on the impedance performance chart. We may, for instance, choose to 

 find the power along the constant frequency contours, for each of which 

 A (or 86) has certain constant values. We assume some constant resonator 

 loss G2 . Choosing a point along the contour is merely taking a particular 

 value of Gi . Having 86, G2 and Gi we can obtain A^ from Fig. 35. Then, 

 knowing A^, we can calculate the power from (9.19). 



