38 



BELL SYSTEM TECHNICAL JOURNAL 



After multiplying, and separating out the different frequency compo- 

 nents, each frequency component of v is equated to the corresponding 

 terminating generator e.m.f. minus the potential drop across the 

 external impedance. Carrying out this process for signal and side- 

 band, respectively, 



£g = (i?, -f ro)(3 + ri/i+, (8) 



= ri(2 + (i?i+ + ro)/i+. 



If Q and /i+ are considered as mesh current amplitudes in a simple 

 linear circuit, it is evident that ri represents a mutual resistance, and 

 that Fig. 3 represents an equivalent network. In this system the 



VV\A- 





Fig. 3 — Equivalent modulator network connecting signal and sideband when other 

 modulation current components are suppressed by high circuit impedances. 



signal source is connected to the sideband load by a simple T network.* 

 It will be found in subsequent cases similarly, that the connection 

 between signal and sideband circuits may be effected by a network 

 comparatively simple in form. Hence we can make our deductions 

 concerning the performance of modulator circuits by reference to the 

 well known properties of such equivalent networks. In the present 

 case, for example, we can draw the following conclusions. 



1. The modulator loss becomes negligibly small if the series arm 



resistance, r^ — ri, is very small and the shunt arm resistance, 

 ri, is relatively large. 



2. Considering the modulator network as fixed, maximum power is 



transferred when the signal and sideband resistances match 

 the characteristic resistance of the network, so that 



R, = R,+ = V^o^ - n\ (9) 



3. Under matched impedance conditions the power efficiency is 



V 



ro 



+ Vro^ — ri^ 



(10) 



^ While the results come out most simply in terms of a 7" network, the various 

 possible transformations (for example to a jt or to a lattice network) are of course 

 equally valid. 



