A General Circuit Analysis and Simulation Method for Superconducting Quantum Interference Devices

The Superconducting Quantum Interference Device (SQUID) is an extremely sensitive flux-to-voltage converter widely used in weak magnetic signal detection systems. It is the superconducting circuit composed of Josephson junctions and superconducting loops. However, the analysis is usually based on superconducting physics rather than the conventional circuit theorems. This article presents a general circuit analysis method using only the conventional circuit variables and laws to simplify the analysis and simulation of SQUID circuits. The method unifies the descriptions of Josephson junctions and non-superconducting elements with a general non-linear inductance concept; and derives the uniform SQUID circuit equations with the common circuit laws used for both superconducting and normal circuits. The uniform circuit equation and dynamic model show that the only element making the SQUID distinct from the non-superconducting circuits is the cosine potential introduced by the Josephson current. This general analysis method bridges the gap between the superconductive SQUID circuits and the conventional normal circuits for the electronics engineers trained with the conventional circuit theory.