FEEDBACK AMPLIFIER DESIGN 423 



may lead to enormous effective ranges. For example, In a 4 megacycle 

 amplifier they indicate an effective range of about 60 megacycles for 30 

 db feedback, or of more than 400 megacycles if the feedback is 60 db. 



The general engineering implications of this result are obvious. It 

 evidently places a burden upon the designer far in excess of that which 

 one might anticipate from a consideration of the useful band alone. 

 In fact, if the required total range exceeds the band over which effective 

 control of the amplifier loop characteristics is physically possible, be- 

 cause of parasitic effects, he is helpless. Like the young man, he 

 simply can't pay for his ticket. The manufacturer, who must con- 

 struct and test the apparatus to realize a prescribed characteristic over 

 such wide bands, has perhaps a still more difficult problem. Un- 

 fortunately, the situation appears to be an inevitable one. The 

 mathematical laws are inexorable. 



Aside from sounding this warning, the relations between loop gain 

 and loop phase can also be used to establish a definite method of 

 design. The method depends upon the development of overall loop 

 characteristics which give the optimum result, in a certain sense, con- 

 sistent with the general laws. This reduces actual design procedure to 

 the simulation of these characteristics by processes which are essen- 

 tially equivalent to routine equalizer design. The laws may also be 

 used to show how the characteristics should be modified when the 

 cutoff interval approaches the limiting band width established by the 

 parasitic elements of the circuit, and to determine how the maximum 

 realizable feedback in any given situation can be calculated. These 

 methods are developed at some length in the writer's U. S. Patent No. 

 2,123,178 and are explained in somewhat briefer terms here. 



Relations Between Attenuation and Phase in 

 Physical Networks ^ 



The amplifier design theory advanced here depends upon a study of 

 the transmission around the feedback loop in terms of a number of 

 general laws relating the attenuation and phase characteristics of 

 physical networks. In attacking this problem an immediate difficulty 

 presents itself. It is apparent that no entirely definite and universal 



^ Network literature includes a long list of relations between attenuation and 

 phase discovered by a variety of authors. They are derived typically from a Fourier 

 analysis of the transient response of assumed structures and are frequently ambigu- 

 ous, because of failure to recognize the minimum phase shift condition. No attempt 

 is made to review this work here, although special mention should be made of Y. W. 

 Lee's paper in the Journal for Mathematics and Physics for June, 1932. The proof 

 of the relations given in the present paper depends upon a contour integration in the 

 complex frequency plane and can be understood from the disclosure in the patent 

 referred to previously. 



