Unified Network Equation for Both Normal RLC Circuits and Josephson Junction Circuits

TL;DR

This paper introduces a unified network equation that bridges the analysis of Josephson junction circuits and conventional RLC circuits by modeling both as magnetic-flux-generator networks, enabling unified analysis and simulation.

Contribution

The paper presents a novel MFG model that unifies Josephson junctions and RLC components into a common circuit framework, deriving a general network equation for both types.

Findings

Unified analysis of superconducting and normal circuits.

Circuit simulation can be performed uniformly.

Josephson junctions modeled as superconducting RLC networks.

Abstract

Josephson junction circuits, such as superconducting quantum interference devices (SQUIDs) and single-flux-quantum (SFQ) circuits, have been successfully applied in both analog and digital electronic domains. They are considered to be distinct from the normal resistor-inductor-capacitor (RLC) circuits, due to the superconducting physics. To bridge the gap between Josephson junction circuits and conventional RLC circuits, we introduce a magnetic-flux-generator (MFG) model to unify the definitions of Josephson junctions and normal noninductive components, and transform their circuits uniformly into MFG networks. A general network equation for both superconducting and normal MFG networks is derived. It shows that, Josephson junction circuits are the superconducting RLC networks modulated by Josephson currents; their analysis and simulation are unified with that of the normal RLC circuits by solving the general network equation.