REGENERATION THEORY AND EXPERIMENT 



699 



dotted lines. By direct circuit analysis, the current and voltage ampli- 

 tudes in the feed-back condition are related by 



E= (Z + Zo + Z,)(l - A)r, 



where A and the Z's are functions of frequency. The total effective 

 circuit impedance is obtained as the multiplifier of / in the right mem- 



Fig. 13 — Series type feed-back circuit. The dotted resistances indicate the termi- 

 nations applied when the feed-back circuit was broken, to which the passive impe- 

 dances {ZiZo) apply. Zi„ represents the effective input impedance with the feed-back 

 circuit connected through. 



ber. Subtracting the generator impedance Z from the total, the input 

 impedance becomes 



Z/^ = (Zo-f Zi)(l - A) ~ AZ, 



from which. 



1 



A = 



Z + Zo + z, 



1 + 



Zi. 



Of the two factors of the right member, the first one, involving pas- 

 sive impedances alone, can have no roots with positive real part. Any 

 such roots must, therefore, be contained in the second bracketed fac- 

 tor and then only when Ztn is negative. Hence paraphrasing the 

 transfer factor criterion, if we plot — Zin/Z over the frequency range, 

 the circuit is stable when the point (1, 0) is not enclosed by the result- 

 ant curve. 



Shunt Feed-Back 

 Proceeding as in the series case with the circuit of Fig. 14 we get 



Fig. 14 — Shunt type feed-back circuit. The notation corresponds to that of Fig. 13. 







