Theory of Single-Resonance Parametric Amplifiers

A parametric amplifier that supports a resonance at the idler frequency only is capable of unlimited gain when operated either as a straight-through amplifier or as a lower-sideband up-converter. In the latter case, the idler frequency becomes the output frequency. The analysis of the single-resonance parametric amplifier consists of determining the stability criteria and power gains associated with a nonlinear capacitance that is incorporated in a network producing a resonance at the idler frequency but not at the signal frequency. The admittance matrix of the network is first established; and then from this matrix the input admittances and the power-gain expressions for straight-through amplification and lower-sideband up-conversion are derived. The single-resonance parametric amplifier, as contrasted with one which is tuned at both the signal frequency and the idler frequency, is, in principle, easy to adjust because there is only one resonance. For this reason, the feasibility of continuously tunable parametric receivers becomes immediately evident.