Magnetic-Flux-Flow Diagrams for Design and Analysis of Josephson Junction Circuits

Josephson junction circuits, such as superconducting quantum interference devices (SQUIDs) and single-flux-quantum circuits, have been successfully applied in both the analog and digital domains. Due to phase-based working principles, their analyses are not well supported by charge-based analysis methods and conventional circuit diagrams. This article introduces a type of magnetic-flux-flow (MFF) diagrams to simplify the design and analysis of Josephson junction circuits. MFF diagrams are the graphical expression of circuit equations derived by loop analysis methods. They vividly depict the functions of Josephson junctions and superconducting loops and visualize how Josephson junctions transfer flux quanta among superconducting loops. The applications of MFF diagrams in the design and analysis of typical Josephson junction circuits are demonstrated case by case; it is shown that MFF diagrams are complementary to conventional circuit diagrams for both Josephson junction circuits and normal electric circuits.