  Josephson junctions and the quantum phase-slip (QPS) junctions are two
quantum circuit elements introduced by superconducting electronics to create
various hybrid circuits. Josephson junctions bring the developments of
superconducting quantum interference devices (SQUIDs) and single-flux quantum
(SFQ) digital circuits; as the dual element of Josephson junctions, QPS
junctions are used to design the new devices dual to Josephson junction
circuits. In order to bridge the gap between superconducting and
non-superconducting circuits, this article presents an
electromagnetic-flux-distribution model to unify the superconducting and
non-superconducting circuit analyses. This model redefines the circuit laws and
functions of circuit elements using the conventional electric variables; it
provides the unified circuit equations to depict the working principles of
circuits viewed from electric and magnetic fields; it also derives the
mathematical expression of duality principles between Josephson junction and
QPS Junction circuits. The application of this
electromagnetic-flux-distribution model 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 systems, while
QPS junction circuits are the electric-flux-distribution systems, they are
modulated by the Josephson effect and the phase-slip effect.
