A topological decoupling of modified nodal analysis including controlled sources
This work addresses a bottleneck in engineering design workflows by enabling more efficient circuit simulation and applications like model order reduction, though it appears incremental as it extends existing MNA methods to include controlled sources.
The paper tackles the problem of decoupling modified nodal analysis (MNA) equations for circuits with controlled sources, deriving a semi-explicit index one differential-algebraic equation that preserves sparsity and positive definiteness, and provides a constructive graph-based algorithm and software implementation.
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.