FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1411 



1.0 



0.9 



0.8 



7 



0.6 



0.5 



0.4 



I 0.3 



0.2 



1 



7 

 X 



10 11 12 13 14 



Fig. 3 — Conductance contours for inverting transducer. 



CONDUCTANCE AND GAIN VERSUS X AND y 



By assigning a value to p, curves may be plotted showing how the 

 conductance and gain of the 4-pole change as the characteristics of the 

 nonlinear resistor and nonlinear capacitor are varied. The particular case 

 when /2 is about 160 times /i will be treated. This corresponds, for ex- 

 ample, to an intermediate frequency of 70 mc and a local oscillator f re- 

 fluency of 11,200 mc. 



Figs. 2 and 3 show the normalized conductance contours as functions 

 of .T and y as given by (24) for the noninverting and inverting cases re- 

 spectively. It wall be seen that in most instances, increasing the value of 

 X causes g/Go to decrease. An exception occurs in the noninverting case 

 (Fig. 2) when y is less than 2-\/p/(p + 1) or 0.157 where it is seen that 

 increasing x causes g/Go to increase. When x and y have values corre- 

 sponding to points above the g/Go = curve, the 4-pole cannot be 

 matched and (23) through (27) are not applicable. However, it will 

 be noted that connecting a resistor across either the nonlinear elements 

 or across the input and output terminals has the effect of increasing Go . 

 By this means the 4-pole can always be reduced to the condition w^here 

 it can be matched. 



Figs. 4 and 5 show the modulator gain contours as functions of x and y 



