Modeling Flux-Quantizing Josephson Junction Circuits in Keysight ADS

We introduce Josephson junction and inductor models in Keysight Advanced Design System that feature an auxiliary flux port, and facilitate the expression of flux quantization conditions in simulation of superconducting microwave circuits. We present several examples that illustrate our methodology for constructing flux-quantizing circuits, including dc- andrf-SQUIDs, tunable couplers, and parametric amplifiers using superconducting nonlinear asymmetric inductive element and rf-SQUID arrays. We perform dc, S-parameter, and harmonic balance simulations to validate our models and methods against theory and published experimental results.