FEEDBACK AMPLIFIER DESIGN 445 



of (10) shows how the feedback depends upon the intrinsic band width 

 of the available tubes. In low-power tubes especially designed for the 

 purpose /t may be 50 mc or more, but if/o is small the first term will be 

 substantial even if tubes with much lower values of ft are selected. 

 The second term gives the loss in feedback which can be ascribed to the 

 rest of the circuit. It is evidently not possible to provide input and 

 output circuits and a /3-path without making some contribution to the 

 asymptotic loss, so that At cannot be zero. In an amplifier designed 

 with particular attention to this question, however, it is frequently 

 possible to assign A t a comparatively low value, of the order of 20 to 

 30 db or less. Without such special attention, on the other hand, A t is 

 likely to be very much larger, with a consequent diminution in available 

 feedback. 



In addition toft and At, (10) includes the quantity n, which repre- 

 sents the final asymptotic slope in multiples of 6 db per octave. Since 

 the tubes make no contribution to the asymptotic loss at f = ft we 

 can vary n without affecting A t by changing the number of tubes in the 

 circuit. This makes it possible to compute the optimum number of 

 tubes which should be used in any given situation in order to provide 

 the maximum possible feedback, li At'is small the first term of (10) 

 will be the dominant one and it is evidently desirable to have a small 

 number of stages. The limit may be taken as w = 2 since with only 

 one stage the feedback is restricted by the available forward gain, 

 which is not taken into account in this analysis. On the other hand 

 since the second term varies more rapidly than the first with n, the 

 optimum number of stages will increase as At is increased. It is given 

 generally by 



or in other words the optimum n is equal to the asymptotic loss at the 

 tube crossover in nepers. 



This relation is of particular interest for high-power circuits, such as 

 radio transmitters, where circuit limitations are usually severe but the 

 cost of additional tubes, at least in low-power stages, is relatively un- 

 important. As an extreme example, we may consider the problem of 

 providing envelope feedback around a transmitter. With the rela- 

 tively sharp tuning ordinarily used in the high-frequency circuits of a 

 transmitter the asymptotic characteristics of the feedback path will be 

 comparatively unfavorable. For illustrative purposes we may assume 

 that/a = 40 kc. and « = 6. In accordance with (7) this would provide 

 a maximum available feedback over a 10 kc. voice band of 17 db. It 



