Analysis of LC-Resonance in DC SQUID Using Dynamic System Model

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.