Analysis and Simulation of Multi-Loop SQUID-Based Electric Circuits With Mesh-Current Method

Practical superconducting quantum interference devices (SQUIDs) have been developed into multiloop hybrid electric circuits with Josephson junctions and normal elements such as resistor, inductor and capacitor. To find a common circuit analysis and simulation method for different types of SQUID hybrid circuits consist of both superconducting and normal components, we introduce a mesh-current method, which can derive both the general system model and uniform circuit equations directly from the equivalent circuit. The mesh-current method is demonstrated in the simulation of a SQUID additional positive feedback circuit. The numerical simulation results are presented and verified with the measurements. Compared with the conventional nodal analysis method, the mesh-current method is excellent in dealing with the relations including external flux, self and mutual inductances in multiloop hybrid circuit analysis; its final circuit equations directly exhibit the physical theorems; its general system model reveals the quantum interference mechanism inside SQUID circuits, and is applicable for further dynamics studies.