The Bell System Technical Journal 



Vol. XXVII October, 1948 No. 4 



Equivalent Circuits of Linear Active Four-Terminal Networks* 



By 

 LISS C. PETERSON 



Introduction 



THE art of equivalent network representation has grown very con- 

 siderably since its inception by Dr. G. A. Campbell. In his paper 

 "Cissoidal Oscillations" which was published in 1911 he proved that any 

 passive network made up of a finite number of invariable elements and hav- 

 ing one pair of input terminals and one pair of output terminals is externally 

 equivalent to an unsymmetrical T or 11 network. From this modest be- 

 ginning the field of applications of the equivalent circuit concept has steadily 

 expanded so that by now the whole field of linear passive circuit theory has 

 been subjected to equivalent circuit interpretation. 



With the advent of the thermionic vacuum tube amplifier, linear active 

 network theory had to be considered and almost immediately the attempt 

 was made to obtain an equivalent circuit whose performance would depict 

 the linear characteristic of the tube. The equivalent circuit art has also, 

 in recent years, been used to describe the performance of certain classes of 

 non-linear devices, such as mixers, and further applications in this field will 

 no doubt be made. 



Equivalent circuit concepts have played an important part in electrical 



* This paper appears substantially as it was originally prepared some years ago as a 

 technical memorandum for internal distribution within Bell Telephone Laboratories. 

 Its publication is rendered timely by the applicabiUty to the recently announced transis- 

 tor devices. Present experience indicates, in fact, that the configuration of Fig. 13 

 furnishes the most useful equivalent four-pole network for the transistor. 



Mr. J. A. Morton has called my attention to an early paper in this field by Strecker and 

 Feldtkeller (E.N.T. Vol. 6, page 93, 1929) in which the general theory of active networks 

 has been well developed. However, the early state of the then prevailing art prevented the 

 full demonstration of the power of the method and of course precluded the possibility of 

 apphcation to modern devices. This paper enlarges the general theory and makes logical 

 applications of the method to modern devices. Since the appearance of the Strecker- 

 Feldtkeller paper several other papers touching upon this subject have appeared. How- 

 ever, no attempt at giving a complete bibliography will be made, except to call attention 

 to the contributions of Prof. M. J. O. Strutt, who also has adopted the four-pole point of 

 view. 



The I.R.E. Electron Tube Committee has adopted the four-pole viewpoint and has 

 proposed methods of tests for experimentally determining the four-pole parameters of elec- 

 tron tubes. This material will be pubhshed in the new I.R.E. standards on electron 

 tubes. 



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