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Superconducting quantum interference devices (SQUIDs), single flux-quantum(SFQ) logic circuits, and quantum Josephson junction circuits have beendeveloped into a family of superconductor integrated circuit, and are widelyapplied for subtle magnetic-field measurements, energy-efficient computing, andquantum computing, respectively. They are Josephson junction networks composedof Josephson junctions and normal resistor-inductor-capacitor (RLC) components,working with the fluxoid-quantization principle and Josephson effects toachieve unique flux-modulated dynamics and characteristics; they react to thevector potential of magnetic fields rather than the electric potential.However, the conventional circuit diagrams and nodal analysis methods focus onthe electric charges flowing though branches and nodes, ignoring dynamics ofthe magnetic fluxes flowing from loop to loop. This article introduces ageneral flux-based circuit theory to unify the analyses of Josephson junctioncircuits and normal RLC circuits. This theory presents amagnetic-flux-generator (MFG) concept to unify Josephson junctions and normalcircuit elements, and abstract both Josephson junction circuits and normal RLCcircuits as MFG network; it derives a general network equation to describedynamics of Josephson junction circuits, and invents a kind of magnetic-fluxflow (MFF) diagram to depict the working principles of magnetic-flux flowsinside Josephson junction circuits. The flux-based theory is complementary tothe conventional circuit theories in the design and analysis of superconductorintegrated circuits.

A general flux-Based Circuit Theory for Superconducting Josephson Junction Circuits