| Model order reduction methodologies are presented for semi-discrete electromagnetic systems obtained from the spatial discretization of the hyperbolic system of Maxwell's equations. Different reduced-order modeling algorithms, i.e., Pade via Lanczos (PVL), multiple point PVL, Krylov, rational Krylov, PVL with expansion at infinity, are presented and applied for model order reduction and the properties of these algorithms are discussed. The implementation of the model order reduction methodologies to a full-wave frequency domain electromagnetic system simulator (ROMES) is discussed in detail. Scattering parameters are calculated for several electromagnetic systems with discontinuities.; A time domain simulation framework is also introduced for transmission line embedded systems described by the Telegrapher's equations. The time domain convolution approach is selected to perform the transmission line embedded circuit simulations. Derivations for Closed-form triangle impulse responses (TIR) are discussed and numerical examples are presented. The developed triangle impulse responses are used to perform time-domain circuit simulations. The effects of frequency-dependent lossy transmission lines on signal integrity and causality issues associated with the transmission line parameters ( R, L, C, and G) in Telegrapher's equation are discussed. The presented research provides an accurate and efficient way to characterize electromagnetic systems for high-speed circuit applications in the frequency domain and methods to simulate these circuits in the time domain. |
