Equivalent Modulator Circuits 



By E. PETERSON and L. W. HUSSEY 



Equivalent modulator circuits are developed in the form of 

 linear resistance networks. They are equivalent in the sense that 

 the current magnitude in any mesh of the network is equal to the 

 current amplitude of a corresponding frequency component in the 

 modulator. The elements of the network are determined by the 

 properties of the modulator, while the terminating resistances are 

 those physically existent in the connected circuit. 



With this correspondence demonstrated, the operating features 

 of the modulator may be deduced from the known properties of 

 linear networks. Among the properties considered are the trans- 

 fer efficiency from signal to sideband, and the input resistance to 

 signal as affected by the sideband load resistance. 



Equivalent networks are worked out for a number of interesting 

 cases, involving different impedances to unwanted modulation 

 products, together with different non-linear characteristics. The 

 equivalents come out comparatively simple in form under the 

 restrictions noted and followed in the te.xt, which make the carrier 

 large compared to the signal, and the circuit elements purely 

 resistive. 



CONSIDERED from the circuit standpoint, a number of modulator 

 performance features are important in any application. Among 

 these features might be mentioned the efificiency of power transfer 

 from signal input to sideband output, and associated with it the 

 question of how the signal input energy is distributed among the 

 different frequency components and dissipated in the modulator itself. 

 Then, too, we need to know how the impedance of the modulator to 

 any component depends upon the modulator structure and upon the 

 connected impedances to other products. 



In attempting to get answers to these questions by mathematical 

 analysis, we encounter lengthy and cumbersome expressions in general 

 which do not lend themselves to ready physical interpretation. The 

 physical interpretation of these equations may be facilitated by intro- 

 ducing equivalent circuits of familiar form. One form commonly 

 used in the past replaces the non-linear system by a circuit including 

 a series of generators and linear impedances. 



This may be illustrated by reference to a simple non-linear circuit, 

 in which carrier and signal generators are connected through an 



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