Characteristic Mode and Reduced Order Modeling at Low Frequencies

We present a stabilized theory to address the breakdown or inaccuracy issue for low-frequency (LF) characteristic mode analysis (CMA). At LFs, to properly preserve the governing quasi-static circuit physics, the eigenvalue decomposition technique is leveraged to formulate a stabilized eigenvalue problem regarding low-order CMs, which dominate the scattering, radiation, and energy storage properties of arbitrarily shaped conducting bodies. Several efficient schemes are introduced for the computation of the low-order CMs in the LF regime, including the augmented electric-field integral equation, the potential (A-Φ)-based integral equation, and the Calderón multiplicative preconditioner. The LF stabilized CMA enables one to understand and interpret the behaviors of complicated conducting objects with a reduced “modal” representation at LFs, which offers an insightful tool for reduced order modeling in circuit design and analysis.