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

Josephson junctions and the quantum phase-slip (QPS) junctions are two\nquantum circuit elements introduced by superconducting electronics to create\nvarious hybrid circuits. Josephson junctions bring the developments of\nsuperconducting quantum interference devices (SQUIDs) and single-flux quantum\n(SFQ) digital circuits; as the dual element of Josephson junctions, QPS\njunctions are used to design the new devices dual to Josephson junction\ncircuits. In order to bridge the gap between superconducting and\nnon-superconducting circuits, this article presents an\nelectromagnetic-flux-distribution model to unify the superconducting and\nnon-superconducting circuit analyses. This model redefines the circuit laws and\nfunctions of circuit elements using the conventional electric variables; it\nprovides the unified circuit equations to depict the working principles of\ncircuits viewed from electric and magnetic fields; it also derives the\nmathematical expression of duality principles between Josephson junction and\nQPS Junction circuits. The application of this\nelectromagnetic-flux-distribution model is demonstrated in the analyses of a\nJosephson junction circuit and its dual QPS junction circuit. It shows that\nJosephson junction circuits are the magnetic-flux-distribution systems, while\nQPS junction circuits are the electric-flux-distribution systems, they are\nmodulated by the Josephson effect and the phase-slip effect.\n