EQUIVALENT MODULATOR CIRCUITS 



39 



The term power efficiency — as used here — means the ratio of the power 

 delivered to the load resistance {Ri+) to that introduced at the input 

 side of the network by the signal source. The corresponding current 

 ratio of sideband to signal is the square root of r}. If the sideband 

 resistance is shorted the current ratio rises to its maximum. The 

 ratio of voltage at the network output to that at the network input 

 when the load resistance is made infinite coincides with this value 



If we consider the various possible kinds of resistance variation with 

 time under the restrictions noted, it appears that the greatest attain- 

 able value of the power ratio is unity. It is evident from the equiva- 

 lent circuit that this limit corresponds to no loss from signal to side- 

 band. The closest approach to this no-loss condition is obtained in a 

 modulating element presenting a resistance which, over a carrier 

 cycle, varies between widely different resistances, taking on one 

 extreme value for a small fraction of the cycle and remaining near the 

 other extreme for the remainder of the cycle. Under these conditions 

 the series arm of the equivalent net tends to zero, the shunt arm to 

 infinity. There are practical limitations to the extent to which these 

 conditions can be approached in practical modulators. For example 

 the best attainable values of the two resistance extremes usually 

 depend upon the modulator characteristic, and upon the carrier 

 amplitude employed which may be limited by heat dissipation or by 

 voltage breakdown. Further limitation is imposed by parasitic 

 capacitances, which effectively limit the maximum attainable modu- 

 lator resistance. 



The commutator modulator may be used to illustrate the results of 

 analysis above. Figure 4 shows the variation of the resistance of 



■pn 



pn 



2n 



pt 



Fig. 4 — Variation of resistance with time in a commutator modulator, in which 

 the resistance is switched from A to B, remaining at the higher value B for the 

 fraction /3 of the carrier cycle. 



such a modulator over a carrier cycle. B and A are the two values 

 of the resistance {B > A) and j8 is the fraction of the carrier cycle 



