Variance-Based Iterative Model Order Reduction of Equivalent Circuits for EMC Analysis

Abstract

This paper proposes a novel and iterative way to conduct model order reduction (MOR) of linear equivalent circuit models (ECMs) without the use of a state-space representation as a surrogate model. The result is an ECM with a reduced total number of circuit elements but same system behavior. The proposed method is as follows: first, the original ECM is decomposed into smaller subcircuits after which a variance-based global sensitivity analysis by means of polynomial chaos expansion is conducted in order to extract the Sobol indices which measure the relative impact of the circuit elements. The least influential ones are then removed by either shorting them or replacing them by an electric open. The frequency responses of the resulting reduced circuits are then fitted against the original frequency response through nonlinear least squares optimization and by subsequently updating the element values. As opposed to the traditional MOR techniques from systems theory, the proposed approach operates on the ECM themselves directly. Thus, it not only offers additional physical insight into the system at any iteration step but also inherently leads to reduced-order models that are at once stable, causal, and passive. This makes the approach especially useful for practical electromagnetic compatibility problems and analysis. In the following, this novel approach is first described in detail and then applied to different test cases. Finally, a discussion of its limitations will be given.