Closed-form parameterized simulation of high-speed transmission line networks using model-reduction techniques

During the design of microwave circuits there is a significant need for efficient and accurate analysis of components with respect to environmental effects, thermal effects, manufacturing variations and fluctuations in the critical dimensions of transmission lines. However, increased integration levels and higher signal speeds in microwave devices and modules have produced the need to include transmission line effects previously neglected during circuit simulation. Accurate prediction of these effects involve solution of large systems of equations, the direct simulation of which is prohibitively CPU expensive. In this paper, we propose an algorithm to form closed-form expressions for the response of microwave circuits as a function of any design parameter in the network. This is achieved by the use of parameterized model reduction techniques in conjunction with a popular rational approximation algorithm vector-fit. The proposed algorithm was applied to transmission line networks and a significant speed-up was achieved.