An Electromagnetic-Flux-Distribution Model for Analyses of Superconducting Josephson Junction Circuits and Quantum Phase-Slip Junction Circuits

Superconducting Josephson junctions and quantum phase slip (QPS) junctions create various hybrid circuits combined with nonsuperconducting elements. Those circuits require a common analysis method to bridge the gap between superconducting and nonsuperconducting electronics. This article presents an electromagnetic-flux-distribution model to unify the analyses of superconducting and non-superconducting circuits. This model uses electric and magnetic fluxes as the variables to unify the definitions of circuit elements and circuit laws; it derives general circuit equations of the circuits viewed from both electric and magnetic fields, to depict their dynamics and duality principles. This method is demonstrated in the analyses of a Josephson junction circuit and its dual QPS junction circuit. It shows that Josephson junction circuits are the magnetic-flux distribution network tuned by the Josephson current, while QPS junction circuits are the electric-flux distribution network modulated by the QPS voltage.