FEEDBACK AMPLIFIER DESIGN 



429 



characteristics. An example is furnished by Fig. 6, which is built up 

 from three solutions of the type shown by Fig. 5. By proceeding 

 sufficiently far in this way, an approximate computation of the phase 

 characteristic associated with almost any attenuation characteristic 

 can be made, without the labor of actually performing the integration 

 in (2). 



20k 



8:3 



5ulOk 



UJQ 



^^ 



1JJ< 



-k- 



0.2 0.3 0.4 0.5 



X 

 fo 

 Fig. 6 — Diagram to illustrate addition of elementary attenuation and phase char- 

 acteristics to produce more elaborate solutions of the loss-phase formula. 



Equations (1) and (2) are the most satisfactory expressions to use 

 in studying the relation between loss and phase in a broad physical 

 sense. The mechanics of constructing detailed loop cut-off character- 

 istics, however, are simplified by the inclusion of one other, somewhat 

 more complicated, formula. It appears as 



Jo ih' - 



Adf 



f if - P) 



+ 



r 



Bdf 



Vf^^^ (f - m 



_ -rr B(f,) 



2fc^U - fc 



A(fc) 



2/cV/e^-/0^' 



/c>/0. (4) 



where /o is some arbitrarily chosen frequency and the other symbols 

 have their previous significance. 



The meaning of (4) can be understood if it is recalled that (2) implies 

 that the minimum phase shift at any frequency can be computed if the 



