Graphical impedance-matching method for a superconducting parametric amplifier

This work proposes a graphical impedance-matching method for superconducting parametric amplifiers with quantum-limited noise performance using a modified Smith chart. It enables one to quickly apply the impedance-matching methods in microwave engineering to the design of parametric amplifiers. When the matching networks are composed of resonators and their equivalents, the matching of a parametric amplifier can be reduced to that of a negative-resistance amplifier, which is generally invalid due to the connection between the signal-frequency and idler-frequency networks introduced by the parametrically modulated component. Several examples are presented to demonstrate the effective and efficient matching of parametric amplifiers using this method, circumventing the need for complex calculations. This method also offers intuitive insight into how variations in pump strength and bias affect the amplification behavior of the circuit, which is useful in characterizing the parametric amplifier and finding the optimal operating state.