An Algorithmic Approach to Formulate Well-Conditioned Stable Reduced-Order Models of Active Circuits

A model order reduction technique was introduced to preserve the stability of large full-order models and efficiently handle the complexity of large stable active circuits. The key principle of this approach was to ensure that the reduced model satisfies the Lyapunov equation, thereby guaranteeing stability at the time of construction. However, this method relied on an oblique projection operation involving two distinct bases applied to the large matrices of the full-order model. While the oblique projection theoretically preserved stability and maintained the accuracy of the reduced model, it often led to numerical anomalies that caused simulation failures. This paper presents an algorithmic approach designed to detect and, when necessary, correct numerical ill-conditioning in the matrices generated by oblique projection. Numerical simulations validate the robustness of the proposed method by demonstrating its effectiveness in restoring the accuracy of models that would have, otherwise, yielded erroneous simulation results.