EQUIVALENT MODULATOR CIRCUITS 



33 



external resistance to a two-terminal non-linear element such as a 

 diode, or a copper oxide rectifier. The effects of non-linearity show- 

 up in the change of modulator resistance with changes in applied 

 potentials and in the appearance of new frequency components. 

 These efifects may be reproduced quantitatively if we replace the 

 non-linear element by its equivalent consisting of a linear internal 

 resistance together with a series of internal generators — indicated at 

 the right of the dashed line of Fig. \-A. It is easy to see from this 



Eq© 



LINEAR 

 NETWORK 



A B 



Fig. 1 — {A) Equivalent modulator circuit in which the modulator is replaced 

 by a fixed internal resistance together with a series of generators. (5) Equivalent 

 modulator circuit replacing the modulator by a network of linear elements which 

 serves to couple the signal circuit into the paths followed by the modulation products. 

 In this circuit the mesh currents represent the amplitudes of the various frequency 

 components. 



circuit^ what the amplitude of any current component should be; 

 for the general component 



Despite the apparent simplicity of this relation, a difficulty arises as 

 soon as we attempt to state the internal generator e.m.f.'s explicitly, 

 since they are found to be tied up with the impressed potentials, the 



' Here we denote the carrier frequency by />/2n and the signal frequency by g/2n ; 

 the corresponding generator potentials are Ep and Eq respectively, and the external 

 resistance is Rk where k indicates the frequency at which the resistance is effective. 



The new frequencies are usually made up of sums and differences of integral 

 multiples of carrier and signal frequencies. In general, they may be represented 

 by {mp ± nq)/2ll, where m and n are integers or zero. It is advantageous to adopt 

 an abbreviated notation for the voltage component, say, of any frequency by which 

 the general component is indicated as £„,+„. Further when n is unity it is omitted 

 from the subscript, so that the generator e.m.f. of frequency (mp ± q)/2ll is indicated 

 as £m+. One of the restrictions mentioned further on results in limiting n to unity. 



