EQUIVALENT MODULATOR CIRCUITS 47 



desired, they may be obtained from equations (16), using the known 

 values of 7o and /i. 



The two-mesh circuit for /o and Q can immediately be put in the 

 form of an unsymmetric T terminated at one end by the battery and 

 its internal impedance and at the other end by Rq. The optimum 

 terminating resistances and corresponding efficiencies are obtainable 

 as in previous cases but it is evident from the network, without further 

 computation, that losses are minimized (with suitable termination) 

 \i Rq — R and Ri are small compared with R. Ri is decreased by 

 decreasing Rnq (n > 1). These conditions mean that the best elec- 

 trical efficiency is obtained when the resistance variation is large and 

 the unwanted signal harmonics are short circuited. 



VII. Extensions and Summary 



Equivalent networks can be obtained in some cases when the 

 restrictions on the relative amplitudes of signal and carrier are re- 

 moved. It is evident from Fig. 2 that the value of the variable 

 resistance at any instant then depends not only on the carrier ampli- 

 tude but also on the signal amplitude. Thus the equivalent networks 

 are no longer made up of constant resistances, but depend upon the 

 magnitudes of both signal and sideband components. Further, new 

 components appear involving multiples of the signal frequency. The 

 equivalent for this case lacks the simplicity of those discussed here, a 

 simplicity which appears when one of the two input components is 

 much greater than the other. 



The reason for the restriction to pure resistances becomes evident 

 when one attempts to generalize the results. The current components 

 will then have phase angles differing from zero in general. Consider- 

 ation of lower sidebands then shows that the phase angles must have 

 their signs reversed in certain circumstances, which leads to obvious 

 complexities. Again in purely resistive circuits it is possible to 

 determine the instantaneous current-voltage relation and hence to 

 specify the resistance variation as a function of time. In a reactive 

 circuit, however, additional difficulty arises in that the relations are 

 much more complex and in general impossible to specify in simple 

 terms. 



To summarize, the presentation has been limited to the simplest 

 circuits used for modulation by means of a variable resistance. In 

 each example, the inter-relations between modulation product ampli- 

 tudes, terminating resistances, and types of modulator characteristics 

 are shown in terms of familiar linear resistance networks. From these, 

 qualitative information concerning the properties of the system is 



