FEEDBACK AMPLIFIER DESIGN 



439 



cross over point G. This is illustrated by II and II' in Fig. 13. On 

 the other hand, if the zero gain intercept of the asymptote CEK had 

 occurred at a slightly lower frequency, no change in k alone would have 

 been sufficient. It would have been necessary to reduce the amount 

 of feedback in the transmitted range in order to secure stability. 



The final characteristic in Fig. 13 reaches the limiting phase shift 

 of 180° only at the crossover point. It is evident that a somewhat more 

 efficient solution for the extreme case is obtained if the limiting 180° 

 is approximated throughout the cutoff interval. This result is attained 

 by the cutofif characteristic shown in Fig. 14. The characteristic con- 



20 



-20 



0.5 0.6 0.8 1.0 



3 4 5 6 8 10 



fo 



20 30 40 50 



Fig. 14 — Ideal cutoff modified to take account of asymptotic characteristic. Drawn 

 for zero gain and phase margins. 



sists of the original theoretical characteristic, drawn for k — 2, from 

 the edge of the useful band to its intercept with the zero gain axis, the 

 zero gain axis from this frequency to the intercept with the high-fre- 

 quency asymptote, and the asymptote thereafter. It can be regarded 

 as a combination of the ideal cutoff characteristic and two character- 

 istics of the type shown by Fig. 5. One of the added characteristics 

 starts at B and has a positive slope of 12 db per octave, since the ideal 

 cutoff was drawn for the limiting value of k. The other starts at C and 

 has the negative slope, — 18 db per octave, of the asymptote itself. 

 As (3) shows, the added slopes correspond at lower frequencies to ap- 



