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BELL SYSTEM TECHNICAL JOURNAL 



components very small rather than very large. The impedance 

 matching may be simpler in one case than in the other since, for the 

 same efficiency, the matching resistances are quite different in the 

 two cases. 



vW^ 



Fig. 8 — Equivalent modulator circuit showing connection between signal and 

 two sidebands. All other modulation voltage components are suppressed by low 

 circuit impedances. When one of the sideband paths is shorted, the network reduces 

 to that of Fig. 7. 



V. Finite Resistance to Distortion Products 



One more extension may be made, without excessively complicating 

 the equivalent circuit. This is an extension to the case of a constant 

 resistance R to all unwanted products, which yields information 

 unobtainable from the limiting cases previously treated oi R — ^ 

 and i? = 0. 



This problem can be handled in a simple way by the artifice of 

 incorporating R within the modulator proper. In that case the 

 external impedances to signal and sideband must be reduced by R 

 to keep the total circuit resistance at its correct value, while the ex- 

 ternal resistance to any other modulation product then becomes zero. 

 This brings the situation down to that considered and solved in the 

 section immediately preceding. 



By this manipulation the equivalent circuit is obtained as that of 

 Fig. 9 in the single sideband case. The primes indicate coefficients in 

 the expansion of the modified characteristic. These coefficients are 

 immediately available in the case of the commutator, since the sole 

 change there is an increase in both values of the variable resistance by 

 the amount R. Comparing the efficiency of transformation with that 

 obtained with extreme values of R as in the cases preceding, it appears 



