Transmission line synthesis via constrained multivariable optimization

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 multidimensional optimization task for performance-driven routing 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. A novel termination metric is described that is based upon forcing the impulse response waveform to be symmetric using the first three moments of the distributed system response. This metric provides an efficient means to trade off between signal rise time and ringing without requiring a time-domain simulation. Several examples are presented to demonstrate the efficacy of the proposed methodology