Analytical modeling and tolerance analysis of parameter variations in superconducting quantum interference device arrays

Abstract Superconducting quantum interference device series SQUID arrays (SSAs) are essential for enhancing signal-to-noise ratio in ultra-sensitive applications, but their performance is highly susceptible to fabrication-induced parameter variations. This work presents analytical models that quantitatively describe the impact of parameter variations on SSA performance. We identify and model three distinct degradation mechanisms: shunt resistance variations introduce stochastic voltage amplitude fluctuations, critical current variations cause switching desynchronization characterized by a derived sensitivity factor | S | , and mutual inductance variations result in an exponential decay of the voltage envelope with increasing applied flux. We establish quantitative tolerance limits for each parameter, revealing that these parameter variations require tighter control than previously recognized. The derived analytical expressions provide quantitative relationships between parameter tolerances and performance metrics, offering theoretical basis for optimizing SSA performance.