Full-Circuit Modeling and Nonlinear Analysis of Flux-Pumped SQUID Amplifiers in Keysight Advanced Design System (ADS)

SQUID-based parametric amplifiers offer high gain, quantum-limited added noise, and wide tunability in the GHz spectrum. In this work, we present a full-circuit modeling of flux-pumped SQUID amplifiers for the first time in a commercial circuit solver (Keysight ADS) that rigorously incorporates flux quantization in the SQUID loop and the nonlinear dynamics of the Josephson junctions. Harmonic-balance analysis reproduces published small-signal gain characteristics and, in addition, reveals Duffing-type hysteresis responsible for amplifier bistability in the large-signal regime. This paper aims to provide microwave engineers with a comprehensive circuit-level framework for flux-pumped quantum amplifiers design that ensures monostable behavior.