REFLEX OSCILLATORS 487 



I'(. curve represents a change in frequency of oscillation; the shift along the 

 — Yc curve represents a change in the amplitude of oscillation. If we know 

 the variation of amplitude with position along the — 1% curve, and the varia- 

 tion of frequency with position along the Y ,■ curve, we can obtain both the 

 amplitude and frequency of oscillation as a function of the phase of — 1% , 

 which is in turn a function of repeller voltage. 



From (2.3) and (2.7) we can write — Ye in terms of the deviation of drift 

 angle M from n + f cycles. 



- Fe = yXlJ^)/Xy^\ (7.2) 



The equation relating frequency and Ad can be written immediately from 

 inspection of Fig. 12. 



2MAco/coo = -Gc tan Ad 



Aco/wo = -{Gc/2M) tan A0 (7.3) 



Aco/wo = - (1/2(3) tan M. 



Here Q is the loaded Q of the circuit. 



The maximum value of Ad for which oscillation can occur (at zero ampli- 

 tude) is an important quantity. From Fig. 12 this value, called A^o , is 

 obviously given by 



cosA^o = Gc/ye = {Gc/M)(M/ye) (7.4) 



= (M/ye)/Q. 

 From this we obtain 



tan A^o = ± {Q'(ye/My - 1)\ (7.5) 



By using (7.3) we obtain 



(Aa,/coo)o = ± (h) iye/M) (1 - {M/yeQYf (7.6) 



or 



(Aco/a;o)o - ±(§) (y./M) (1 - {Gc/yeYf. {1.1) 



These equations give the electronic tuning from maximum amplitude of 

 oscillation to zero amplitude of oscillation (extinction). 



The equation relating amplitudes may be as easily derived from Fig. 12 



Gl + (2MAa,/co)2 = y; {2J,{X)/xy (7.8) 



at 



Ao) = let X = Xo . Then 



Aco/a'o = {ye/2M) {{2J,{X)/XY - {2J ,{X ,) / X ,Y)\ (7.9) 



