How to Model and Simulate Flux-Quantizing Josephson Junction Circuits

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Model Flux-Aware Superconducting Circuits

Modeling a flux-quantizing superconducting circuit requires representing magnetic flux and Josephson phase in addition to conventional circuit voltages and currents. Flux-aware Josephson junction and inductor models expose auxiliary flux nodes that allow the circuit to express phase and flux relationships directly. These components can be assembled into superconducting loops and biased with externally applied flux to model devices such as radio-frequency superconducting quantum interference devices (rf-SQUIDs) and direct-current SQUIDs.

The simulation can use transient analysis when flux quantization arises naturally from the circuit's time evolution, or an auxiliary flux circuit can impose the quantization constraint for direct current (DC), S-parameter, alternating current (AC), and harmonic balance analyses. Flux-dependent phase, circulating current, inductance, transmission, gain, compression, and intermodulation behavior can then be evaluated for individual SQUIDs and more complex multi-junction circuits and arrays.

Flux-Quantizing Josephson Circuit Modeling Solution

Model the superconducting loop by connecting flux-aware Josephson junction and inductance components so the sum of component fluxes satisfies the required flux-quantization condition. Keysight Advanced Design System (ADS) provides Josephson junction models with auxiliary phase/flux terminals and flux-aware inductor and mutual-inductance models that connect conventional electrical behavior with the circuit's normalized flux. Designers can use transient simulation or explicitly construct an auxiliary flux loop for frequency-domain analysis. The approach supports DC, S-parameter, and harmonic balance analysis and is demonstrated for rf-SQUIDs, dc-SQUIDs, SNAIL nonlinear elements, snake arrays, and Josephson parametric amplifiers.

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