  Josephson junction circuits, such as superconducting quantum interference
devices (SQUIDs) and single-flux-quantum (SFQ) circuits, have been applied in
both analog and digital systems for their ultralow-noise, high-speed, and
power-efficient features. However, their analyses are not well supported by the
conventional circuit diagrams and the charge-based analysis methods, due to the
Josephson effects and flux quantization phenomena. This article introduces a
type of magnetic-flux-flow (MFF) diagrams for the design and analysis of
Josephson junction circuits. The MFF diagram of a Josephson junction circuit is
the graphical expression of circuit equations. It not only gives the behaviors
of Josephson junctions and superconducting loops new physical meanings, but
also visualizes how the flux quanta are transferred among superconducting
loops. The advantages of MFF diagrams are demonstrated in the design and
analysis of typical Josephson junction circuits. It is shown that the MFF
diagram and flux-based analysis method are the indispensable complement to the
conventional circuit methodologies for Josephson junction circuits.
