An efficient method for finding DC solutions for Josephson circuits

The formulation of Josephson circuit equations in the DC state is discussed and a mixed-mode approach that combines the nonlinear solution method of source-stepping and time-domain method of numerical integration is proposed. Since Josephson circuit equations are often multivalued, the mixed-mode algorithm follows the paths of the independent sources, detects ill-conditioned points, and converges to stable points on the characteristic curves of the simulated circuit. The algorithm uses a combination of source stepping and transient calculation with resistive damping. An adaption of method to superconducting quantum interference device (SQUID) threshold curve calculation is also discussed. The techniques are suitable and presented in sufficient detail, so that a reader may implement them as part of a general simulation program such as JSIM or SPICE.<>