Some General Properties of Nonlinear Elements. II. Small Signal Theory

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Abstract
The simplest types of nonlinear capacitor modulators, demodulators, and negative conductance amplifiers, in which components at only two signal frequencies are present, are studied by means of the well-known small-signal analysis. The results of this analysis of course agree with the general energy relations of Part I, but in addition give the gain, bandwidth, terminal admittances, and sensitivity (to changes in the terminal admittances or in the local oscillator drive) of these devices, and show the way in which these quantities depend on the amount of nonlinearity. In general, the bandwidth of all of these devices approaches zero as the nonlinearity approaches zero. Three cases are considered; f1 is the local oscillator frequency. 1) Noninverting modulator and demodulator-signal frequencies fl and f+=f1+fl. This device is stable and yields maximum gain with matched source and load. Under matched conditions the gain is equal to the ratio of output to input frequency; for widely separated signal frequencies the modulator has substantial gain, the demodulator an equal loss. Only a relatively small amount of nonlinearity is required to attain a bandwidth equal to the low-signal frequency. Since source and load are matched the sensitivity is zero. 2) Inverting modulator and demodulator-signal frequencies fl and f-=f1-fl. This device is potentially unstable; its input conductance is negative and match is impossible.