Theory of variable-capacitance parametric amplifiers

An analysis is presented of variable-capacitance parametric amplifiers for the case where there is a loss resistance in series with the capacitance. Such a resistance provides the major form of loss in a reverse-biased semiconductor diode. It is shown that the coupling of two circuits by a pumped variable capacitance can be described by a simple equivalent circuit which has a direct physical interpretation. The characteristics of regenerative amplifiers and convertors, and of non-inverting convertors, are deduced from the equivalent circuits. The gain, bandwidth and noise properties of these amplifiers or convertors are shown to depend on two parameters of the pumped variable capacitance C, the mean Q at the signal frequency and the normalized amplitude of the variation of 1/C at the pump frequency. The noise temperature in each case is a function only of the product of these two parameters and the ratio of signal to idler (or output) frequencies. Particular attention is given to finding the optimum operating conditions and a brief discussion is given of the effects of variations of the capacitance at harmonics of the pump frequency, and of higher sidebands.