Efficient generation of multi-parameter closed-form expressions for high-speed transmission line networks

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 predictions of these effects involve solution of large systems of equations, the direct simulation of which is prohibitively CPU expensive. In addition, 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. In this paper, we propose an algorithm that can efficiently extract multi-parameter closed-form expressions of the response of transmission line circuits at any output node of interest. This is achieved by the use of parameterized model reduction techniques in conjunction with neural networks. The proposed algorithm was applied to practical transmission line networks and a significant speed-up was achieved.