Simulation of a flux-pumped Josephson parametric amplifier with a detailed SQUID model using the harmonic balance method

Abstract

This work presents an analysis of a flux-pumped Josephson parametric amplifier (JPA) with a detailed superconducting quantum interference device (SQUID) model, using the harmonic balance (HB) method in Keysight’s Advanced Design System. The model is built using the generalized resistively shunted junction model of a Josephson junction and the quantization condition of a SQUID, incorporating the effects of the geometric inductance and parasitic parameters. This approach is used to simulate the behavior of an unmatched lumped element JPA and an impedance-matched JPA, showing the necessity of the detailed SQUID model for the simulation of a broadband JPA by comparison with the results based on a widely used, simplified model. Gain profiles obtained from the approach are consistent with existing experiments in the literature, with reasonable accuracy. Due to the HB method, the simulation is of high efficiency, making it feasible to sweep and optimize parameters. This provides a useful method for the analysis of Josephson parametric amplification and the design of a JPA.