COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 329 



ship between their voltages and currents, as a result of using the same 

 amplitude and frequency of carrier harmonic multiplier of their 

 respective voltages to modulate between the two frequency positions. 

 Although reciprocity has been proved valid here only for short-circuit 

 terminations at the modulation product frequencies, it can also be 

 proved under numerous other conditions of circuit operation. It 

 seems that, regardless of modulator complexity of impedance termina- 

 tions or frequency loss effects, the reciprocal theorem is a necessary 

 attribute of such a linear and bilateral system in which there are no internal 

 energy sources. Two-way systems in which an aniplifier for example, 

 is included as an internal energy source in one or both directions will, 

 of course, violate the reciprocal theorem if the gains in the two direc- 

 tions are different. This arrangement is, however, both bilateral and 

 linear. 



Complete Performance Criteria 



The laws for transmission between a signal input frequency and a 

 •signal output frequency can be completely specified from open and 

 short circuit impedance measurements at the signal input and output 

 frequencies, regardless of the complexity of the modulator. (From 

 such measurements optimum impedance terminations can even be 

 determined for linear-bilateral systems with internal energy sources.) 



The four-terminal network of Fig. 7 is assumed to represent a modu- 



Rp 



2 

 — ^>- 



Q 



Fig. 7 — Four terminal network equivalent of a linear modulator. 



lator with a large carrier amplitude and having small signal voltage P 

 of frequency p applied at the input terminals 1-2 at the left. Current 

 of the output signal frequency q flows out of the terminals 3-4 into 

 the impedance Rq. The generator P is assumed to have zero internal 

 impedance at its own frequency. Impedance terminations at the 1-2 

 and 3-4 terminals at all other modulation product frequencies are 

 perfectly general; whatever they are in a particular case, it is assumed 

 that they are undisturbed as the terminations of the input and output 

 at the signal frequencies are varied between open circuit and short 

 circuit. The following symbols are used for the impedances looking 

 into the modulator at the input terminals at input signal frequency p 

 and at the output terminals at signal output frequency q. 



