STABILIZED FEEDBACK AMPLIFIERS 



11 



^-Circuit Equalization 

 Referring to equation (2), the output voltage, E, approaches — eo/iS 



1 



as 1 — yu/3 = — ;uj8 and equals it in absolute value if cos $ = 



2|/x^| 



where n^ = 1^/31 [_^- Under these circumstances increasing the loss 

 in the jS-circuit one db raises the gain of the amplifier one db and vice- 

 versa, thus giving any gain-frequency characteristic for which a like 

 loss-frequency characteristic can be inserted in the ^-circuit. This 

 procedure has been termed /3-circuit equalization. It possesses other 

 advantages which cannot be dwelt upon here. 



Avoid Singing 



Having considered the theory up to this point, experimental evidence 

 was readily acquired to demonstrate that /x/3 might assume large values. 



UNSTABLE 



Fig. 5 — -Measured m/S characteristics of two amplifiers. 



for example 10 or 10,000, provided $ was not at the same time zero. 

 However, one noticeable feature about the field of /i/3 (Figs. 3 and 4) is 

 that it implies that even though the phase shift is zero and the absolute 

 value of /x/3 exceeds unity, self-oscillations or singing will not result. 

 This may or may not be true. When the author first thought about 

 this matter he suspected that owing to practical non-linearity, singing 

 would result whenever the gain around the closed loop equalled or 

 exceeded the loss and simultaneously the phase shift was zero, i.e., 

 m/3 = |ju/3| -f JO ^ 1. Results of experiments, however, seemed to 

 indicate something more was involved and these matters were de- 

 scribed to Mr. H. Nyquist, who developed a more general criterion 



