TUNED AMPLIFIERS 



input, by appropriate operation of the potentiometer — the Q control — then the 

 overall gain at high frequencies is AI{1 + AB). At some intermediate 

 frequency m,. the phase shift per filter section becomes 60 degrees and the 

 overall phase shift is therefore 180 degrees. The feedback is now positive. 



Q control 



Output 



Figure 13.12 



The overall gain rises to a maximum of ^4/(1 — ABF(co^)) where F(<d) is the 

 transmission factor of the filter. 



The value of F(co^) depends on the filter tapering factor a. If all the sections 

 are identical, a = 1, it can be shown that |F(co^)| is 1/29 and cd^ = ll(6y/^CR. 

 In our analysis we shall assume that the taper factor is sufficient for sections 

 not to load their predecessors significantly, say a = 10. If this is true, it is 

 easily seen that when the phase shift per section is 60 degrees, the output from 

 each section is half the input and for three sections F(co^) = 1/8. Thus for a 

 phase shift tuned amplifier employing tapered sections the overall gain (and 

 therefore the Q) rises to infinity when the denominator of the gain expression 

 equals O, i.e. 1/8 AB = 1. Thus if B is made 1 the gain required of the 

 amplifier in the dotted box of Figure 13.12 is only 8. If all the sections are 

 identical the gain required is 29, but due to the mixing resistances, the gains 

 required of the valve must be 16 and 58 respectively. 



To show the performance more precisely we have for a single RC high- 

 pass section 



F, 



out 



R 



jcoCR 



m 



R + 



1 jcoCR + 1 



jcoC 



So for 3 highly tapered sections 

 Fout „, , / JcuCRY 



■J 



\(^o/ 



Km 



CO 



.CO, 



J 



3^ 



CO 



.CO. 



where 



'^'>^CR 



204 



