FREQUENCY CONVERSION BY A NONLINEAR ADMITTANCE 1413 



1.0 

 0.9 

 0.8 

 0.7 

 0.6 

 0.5 

 0.4 

 0.3 

 0.2 

 0.1 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4,0 4.5 5.0 

 X 



Fig. 6 — Gain contours for converter. 



as given by (26) . Here it is seen that increasing the value of x causes the 

 gain to increase. For values of x less than about 3, the gains in the non- 

 inverting and inverting cases are the same. In the nonin verting case, x 

 may increase indefinitely, provided y is less than 0.157, and a gain equal 

 to the ratio of the output frequency to the input frequency eventually 

 reached, 22.1 db in this case. In the inverting case, the maximum gain 

 obtainable is 19.3 db, and it occurs when y is zero. 



Fig. 6 shows the converter gain contours as given by equation (27). 

 Here we see that increasing x causes a decrease in the loss, but the de- 

 crease is small and in no case can the gain be greater than db. This oc- 

 curs when X is zero. The nonlinear capacitor is thus of small benefit in 

 the converter case. About the most benefit that can be obtained is a de- 

 crease in loss of perhaps 1 db. For example, if the nonlinear resistor alone 

 has a loss of 6 db {y = 0.8), this could be reduced to 5 db by adding a 

 nonlinear capacitor of such value as to make x = 1.3. 



BANDWIDTH 



Since both the admittance and gain of the 4-pole vary with frequency, 

 the bandwidth over which it can be used is limited. Figs. 7 and 8 show 

 the modulator gain as a function of x for input frequencies of 50, 70 and 

 90 mc, and a local oscillator frequency of 11,200 mc. These curves were 



