Constrained multivariable optimization of transmission lines with general topologies

The design of system level interconnects to meet signal integrity objectives is a challenging problem. This paper formulates the transmission line synthesis problem as a constrained multi-dimensional optimization of the complete net, taking into account factors like loading conditions on the line loss in the line and rise-time of the input signal. Different design variables such as width or resistivity of the interconnect, resistive source or far-end termination, etc. can all be considered concurrently. The termination metric is based upon forcing the impulse response waveform to be symmetric using the first three exact moments of the distributed system. An efficient means to trade-off between signal rise-time and ringing is presented and no time-domain simulations are needed. Several examples are presented to demonstrate the efficacy of the proposed methodology.