EQUIVALENT MODULATOR CIRCUITS 



45 



that the use of extreme values of R results in the maximum obtainable 

 power. 



The impedance conditions specified above permit the flow of any 

 generated products, so that an infinite network would be required in 



Fig. 9 — Equivalent modulator circuit showing connection between signal and 

 single-sideband circuits when a constant resistance R is effective to all other modu- 

 lation products. The primed coefficients {gk) apply to the conductance coefficients 

 when the series resistance R is included in the original modulator. 



general to bring out the relation of any one product to the others. 

 Discussion was limited, however, to signal and upper sideband ; the 

 amplitudes of other components did not appear explicitly. 



The section following deals with a different case involving an 

 infinite network in which individual meshes are treated explicitly. 



VI. Equivalent Network for the Idealized 



Resistance Microphone 



Other variable resistance systems may be put into equivalent form. 



For example, from the electrical side, an idealized variable resistance 



microphone actuated by a sinusoidal acoustic wave can be represented 



by the resistance 



r = Rq -\- R cos qt. 



This is exactly the form of the variable resistance already discussed, 

 with Tq = Ro, 2ri — R, and rn — for n > I. 



If one were interested in the modulation products with other 

 frequency components impressed electrically, the systems would be of 

 the same type as those of the previous section. In the case of the 

 microphone the d-c. voltage impressed leads to current components 

 which are d-c. and harmonics of the signal q. In this case, the equa- 

 tions are 



= Rolo + RIil2, 



= Roll + Rio + RI 2/2, 



= Roh + R{Ii + h)/2, 



Vo = Eo — Rblo 

 l\ = - R,h 



Viq = — R'iql2 



Vnq = — Rnqln = RqI n + R{I n-\ + In+l)l2, 



(16) 



