EQUIVALENT MODULATOR CIRCUITS 41 



ciency with these parameters. It is evident from the equivalent 

 circuit that best efficiency is obtained with r^ — ri small and ri large. 

 In this case ro increases linearly with /?, and ri varies sinusoidally 

 with /? — having its maximum at |8 = 0.5. The immediate conclusion 

 is that the optimum conditions are obtained when (3 is less than 0.5. 

 In fact the efficiency approaches the limiting value of 100 per cent 

 when j8 is very small and B is much greater than A, as may be seen 

 from (11) and (12). 



III. Double Sideband — High Impedance Outside Band 



In double sideband operation both upper and lower sideband 

 currents flow, but all other modulation products are suppressed as in 

 the previous case. Here the equations for signal and upper and 

 lower sideband respectively are 



(ro + R,)Q + ri/i+ + rj,^ = E„ 

 nQ + (ro + i?i+)/i+ + rJx- = 0, (13) 



rxQ + rJx+ + (ro + Rx-)h- = 0. 



Comparing (13) with the equations for a three-mesh circuit, we 

 obtain the equivalent network of Fig. 6. It is obvious from the 

 symmetry of this network that the two sidebands are equal when 

 Ri+ = 2?i_. Conditions for optimum efficiency may be put in form 

 permitting convenient comparison with the single sideband case when 

 we assume equal resistances to both sidebands. 



Efficiency curves of a commutator modulator are shown on Fig. 5 

 for both single and double sideband cases. They differ primarily in 

 that the utilization of two sidebands gives greater efficiency, except in 

 limiting cases. The outstanding difference is that the unsymmetric 

 network has optimum signal and sideband resistances which are not 

 equal except at three values of /S equal to 0, 1/2 and 1. Modulators 

 are often operated with /3 approximately 1/2, so that in this case the 

 results here check with the common experience that the two terminating 

 resistances should be equal. It may be remarked that only in highly 

 efficient modulators would unequal terminations make an appreciable 

 difference in the efficiency of power transfer. 



A comparison of Figs. 3 and 6 gives some light on the difference in 

 efficiency of the single and double sideband cases. The comparison 

 is made when Ri+ = i?i_. From the symmetry of the circuit of 

 Fig. 6, /]+ then equals /i_ and the mutual resistance (— ra) may be 

 eliminated, leaving a simple T network connecting the input and the 

 load. This is, with two exceptions, the T network of Fig. 3 with all 



