34 BELL SYSTEM TECHNICAL JOURNAL 



modulator characteristics, and the external circuit impedances. For 

 this reason the equivalent circuit of Fig. X-A reveals only part of the 

 story, and in general the relation between the amplitudes of impressed 

 and generated components remains somewhat obscured. 



In a number of cases of practical interest it is possible to represent 

 the connection between the amplitudes of various frequency compo- 

 nents by means of a different type of equivalent circuit. Figure \-B 

 is an illustration of this type, in which the paths of the current compo- 

 nents are shown individually. The connection between the various 

 circuits is effected by means of a linear network which contains no 

 internal generators. In this equivalent network the magnitude of 

 any mesh current is equal to the amplitude of a corresponding fre- 

 quency component in the modulator circuit. The purpose of this 

 paper is to demonstrate the validity of this representation, and to 

 show in detail what the linear network looks like when applied to 

 various types of modulating elements, in a variety of interesting cases. 



In order to develop such equivalent networks in simple and useful 

 form, the following restrictions are imposed. The system includes 

 only one non-linear element.^ The terminating impedances are purely 

 resistive, although they may be functions of frequency. The signal 

 amplitude must be much smaller than that of the carrier. Finally, 

 the slope of the modulator current- voltage characteristic never becomes 

 negative. Under these conditions a number of modulating systems 

 can be treated, including variable resistance modulators with a 

 variety of current-voltage characteristics, and the variable resistance 

 microphone. 



The section following deals with the modulator as a resistance 

 (or conductance) varying at carrier frequency. Succeeding sections 

 consider the behavior of such variable elements under different 

 circuit conditions. 



I. Carrier Controlled Resistance 

 In setting up equations from which the equivalent networks are 

 obtained, the restriction on signal amplitude permits us to assume 

 the modulator to be a resistance or conductance varying at carrier 

 frequency. This commonly used assumption may be arrived at with 

 the aid of Fig. 2, which shows a typical non-linear current-voltage 



2 Other cases are to be found in a paper by R. S. Caruthers on "Copper Oxide 

 Modulators in Carrier Telephone Systems," presented at the A.I.E.E. Winter Con- 

 vention, January 1939. 



Modulators including a plurality of elements can frequently be replaced by an 

 equivalent structure with a single modulating element. This is true of the rectifier 

 type of modulator. In the double-balanced or ring type, however, under certain 

 conditions the equivalent circuit involves merely an ideal transformer connecting 

 signal and sideband circuits. 



