MIXED FEEDBACK METHOD— PHASE SHIFT ACCEPTOR AMPLIFIER 



Thus 



Af(co) 

 Overall gam = YT^^^X^ 



1 



/M 



+ AB 



/ oj Y~] r CO / CO Y~ 

 1-3 — +y 3 — - - 



[f^ol 



+ AB 



And 



1 Overall gain| 



:&f- ^ gv [3 fcf -('+-) 



1211/2 



This has a maximum near {(oJcSf — 3(cojco), i.e. where w = coJ(3y^^. By 

 differentiating the above with respect to (o and equating to zero, it can be 

 shown that the exact frequency at which the maximum occurs is given by: 



1 



CO = O), 



0) 



" ' {Viae - \yi^ 



Evidently m^ approaches ojJ{3y-/^ as AB approaches 8. It can also be shown 

 that, at cOj., 



[Overall gain| = 2(2^5)V2 _ AB 



An expression for the Q, based on the points at which the 'resonant' gain is 

 reduced by the factor \l(2y'^, has so far eluded the writer; some very cumber- 

 some equations seem unavoidable, but we can get at least a measure of the 

 selectivity of the amplifier by remarking the resemblance between the curves 

 of Graph 32 and those for the voltage across the inductance in a series 

 L-C-R circuit (Figure 5.41). In the latter case Q was seen to be defined by 



Output at resonant frequency 



Output at frequencies much above resonance 

 Defining the selectivity of the amplifier in an analogous manner, and calling 



it e, 



Q 



2{2ABy'^ — AB 



1 +AB 

 1 -\-AB 



2{2ABfl^ - AB 



Some performance curves for this type of amplifier are shown in Graph 32. 

 The design of these amplifiers has been more fully discussed by Shaw^, 



205 



