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Direct current superconducting quantum interference device (dc SQUID) can be regarded as a hybrid system with two nonlinear Josephson currents driving a linear network consists of conventional resistors (R), inductors (L), and capacitors (C). There must be LC resonances inside the SQUID loop with influences on its static current-voltage characteristics. To study the working principle of the LC resonance, we build an equivalent dynamic system model transformed directly from the circuit equations of dc SQUID. With dynamic system analyses in both dc and alternating current (ac) domains, we derive the analytical expressions of the resonance point with only the RLC circuit parameters. The analytical derivation proves that the LC resonance inside a symmetrical dc SQUID with resonance frequency ω = 1/√LC results in the flux modulation suppression with I–V curves concentrated on one resonance point. Based on those mathematical expressions, the resonance point is easily indentified from the measured I–V curves, and can be utilized for practical SQUID parameters characterization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]