Application of a reduced-order model to transmission line analysis

Systems with transmission lines and lumped linear elements are commonly used for modeling interconnections on integrated circuits, printed circuit boards, and multichip modules. Conventionally, the transmission lines are characterized by distributed parameters determined on the basis of a quasi-TEM approximation. With rapid increase in operating frequencies, distributed parameter models for interconnects are no longer adequate and electromagnetic field models that take into account all possible field components are needed to accurately analyze signal propagation. However, the solution of electromagnetic problems based on these more complex models using traditional techniques generally involves high computational cost. To circumvent this difficulty, a reduced-order model technique employing the asymptotic waveform evaluation (AWE) [1],[2] has recently been developed. The AWE is a moment-matching method where the s-domain transfer function of a linear system is approximated by using a reduced-order model function containing only a relative small number of dominant poles and residues. The resultant reduced-order model can be used to compute the time-domain and frequency-domain responses of the system in an efficient manner. In this paper, we utilize a reduced-order model technique to compute the transient response of hybrid systems containing both transmission lines and lumped linear elements. By taking into account the effect of the lumped elements into Maxwell's equations, we present a frequency-domain analysis of the entire hybrid system comprising lumped elements and transmission lines by using an electromagnetic field model, instead of treating various components separately by different techniques. This way, a global solution for hybrid systems can be obtained efficiently. Numerical examples of the proposed method are presented.