Comparative Study of Numerical Modeling Methods for a Flux-Pumped Josephson Parametric Amplifier

Quantum-limited noise amplifiers based on superconducting Josephson junction elements are essential components for measuring low-power signals in a wide range of applications. The gain bandwidth of a flux-pumped Josephson parametric amplifier can be broadened by coupling junction elements with an impedance-matching network. Well-known modeling methods for these amplifiers typically assume ideal lumped-element circuits for passive components, but often overlook unexpected resonant modes arising from the bulk geometric features. To address this challenge, flux-pumped junction elements can be simulated using finite-element analysis (FEA) combined with the pumpistor modeling method, which accurately accounts for the geometric features of arbitrary impedance-matching circuits. Here, we present a benchmark study using a circuit topology to compare different modeling methods: (1) the coupled mode network method, (2) the harmonic balance method, (3) the analytical pumpistor method, and (4) the FEA-assisted pumpistor method. Our results highlight the importance of accurately reflecting geometric features to prevent unexpected resonant modes and avoid detuning from the target flux bias values.