REFLEX OSCILLATORS 547 



Yc = Gc+2Mao/wo (12.5) 



Thus in this special case we have for oscillation 



yco = Gc+ IMaJwo (12.6) 



and 



ao = ^{Y,o-Gc)- (12.7) 



The amplitude, then, builds up initially according to the law 



V = Voe""'. (12.8) 



If the amplitude does not change too rapidly, the build-up characteristic 

 of an oscillator can be obtained step-by-step from a number of contours 

 for constant a and from a — Ye curve marked with amplitude points. The 



Ye curve might, for instance, be obtained from a Rieke diagram and an 

 admittance curve. 



Consider the example shown in Fig. 56. Fig. 56a shows curves con- 

 structed for complex frequencies from the admittance curve for the resonant 

 circuit for real frequency. In addition the negative of the electronic ad- 

 mittance is shown. Oscillation will start from some very small amplitude, 

 V = Vo , and build-up at an average rate given by a = 2.5 X 10~ until 

 F = 1. Let Vo = .1. Then the interval to build-up from F = .1 to 

 F= lis 



In 



Ah = 



© 



2.5 X 10-« 



= .92 X 10"^ seconds. 



From amplitude 1 to amplitude 2 the average value of a will be 1.5 X 10' 

 and the time interval will be 



At. = 



-1 



Similarly, from 2 to 3 



Ah = 



1.5 X 10-« 



.46 X 10"^ seconds. 



M 



.5 X 10-6 



.80 X 10"^ seconds. 



The build-up curve is shown in Fig. 56b. 



Similarly, from a family of admittance contours constructed from a cold 

 impedance curve, and from a knowledge of frequency and amplitude vs time, 



