A topological decoupling of modified nodal analysis including controlled sources

TL;DR

This paper introduces a topological decoupling method for modified nodal analysis that explicitly includes controlled sources, facilitating various engineering applications and preserving system structure.

Contribution

It presents a novel graph-based algorithmic framework for decoupling MNA equations with controlled sources, enabling efficient simulation and analysis.

Findings

Decoupling results in a semi-explicit index one differential-algebraic system.

The approach preserves sparsity and positive definiteness of the original MNA structure.

Software implementation of the decoupling is provided.

Abstract

We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling.