EQUIVALENT MODULATOR CIRCUITS 



43 



These expressions are identical in form with corresponding ones 

 obtained for the high-impedance single-sideband case, in which 

 conductance components replace resistance components. This con- 



Fig. 7 — Equivalent modulator circuit showing connection between signal and a 

 single sideband. AH other modulation voltage components are suppressed by 

 means of low circuit impedances. The use of a 11 network and the specification 

 of element values as conductances are both matters of convenience. 



firms what has been observed in several special cases : that there is no 

 theoretical advantage of either impedance extreme over the other in 

 the general case.^ Which one to use in any particular case depends 

 upon the special characteristics of the modulator or upon the practica- 

 bility of obtaining required impedance conditions. 



The equivalent network for the corresponding double sideband 

 system is shown in Fig. 8. Similarly to the previous double sideband 

 case, the symmetry shows that when i?i+ = i?i_ the sideband current 

 amplitudes are equal and there is no potential across the coupling 

 resistance — (l/£2). Thus it may be shorted, reducing the circuit to 

 a simple unsymmetric tf. The matching resistances and maximum 

 efficiency may be obtained as before. 



The results again are identical with the high-impedance case, if 

 resistances are replaced by conductances. The comment made on 

 the single-sideband case still holds — that there is no general theoretical 

 advantage of either a high- or low-impedance system over the other 

 as far as maximum possible efficiency is concerned. 



The curves of Fig. 5 are evidently immediately applicable to the 

 low-impedance circuits provided all resistances are replaced by 

 conductances. 



There are, of course, practical advantages of the high- or the low- 

 impedance circuit in particular cases. For example, it is commonly 

 easier to make the terminating impedance to unwanted frequency 



* The form of the equations in corresponding high- and low-impedance cases 

 suggests that the impedance and efficiency relations for one case could be deduced 

 from those of the other through the principle of duality. See Guillemin, "Com- 

 munication Networks," Vol. 2. 



