336 



BELL SYSTEM TECHNICAL JOURNAL 



Generalized Reflection Theory 



Superposition permits us to apply simultaneously driving forces of 

 the frequencies tabulated above in any relative phases and ampli- 

 tudes that we care to choose on either side of the modulator. If 

 simultaneously /o is applied on one side of the modulator and 

 Z^^- R 



is applied to the other set of modulator terminals, 



2k 



v Zi+ + K 



then the total current at the output terminals at the sideband fre- 

 quency (1+) will be 



(/h-) 



2k 



1 - 



R 



Zi+-\-R 



(34) 



This is equivalent to saying that a resistance R at the sideband 

 frequency (1 + ) has been connected to the output terminals of the 

 modulator and in this resistance is an internal zero impedance generator 

 of voltage 



2k Zi+ - R 



2R(h+) 



Zx+ + R 



(35) 



This resistance R at sideband frequency (1 +) must be infinite at 

 all other frequencies, if in parallel we assume another resistance of R 

 at all frequencies except (1 +) at which it is infinite. 



The equivalent impedance at frequency (1 +) at the modulator 

 terminals connected to the (1 +) resistance with its internal gen- 

 erator, is the ratio of (1 +) voltage to (1 +) current. 



which reduces to 



Z = Zi 



(36) 



(37) 



Zi+ may be real or complex as it involves only the amplitude and 

 phase of the superimposed voltage of upper sideband frequency. It 

 can readily be seen then that the solution for current flow at this 

 frequency of equation (34) is identical with the case of linear networks 

 in which the current is expressed as that flowing in a matched circuit 

 modified by a reflection factor. Reflection from any modulation 

 product frequency can be similarly treated. 



