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.

翻译：我们推导了改进节点分析法（MNA）方程到半显式指标1微分代数方程组的拓扑解耦。该解耦显式地允许受控源存在，而受控源在工程设计流程中起着关键作用。此外，该证明具有构造性，并提供了一个基于图的算法框架来实现该解耦，从而使其能够应用于多种工业问题，包括生成一致初始条件、模型降阶、（科学）机器学习以及加速传统电路仿真。此外，该解耦保留了MNA的结构，即所得系统保持稀疏性且关键部分保持正定性。我们通过多个示例（包括一些包含受控源的最常见子电路）来说明该解耦。最后，我们还提供了该解耦的首个软件实现。