MCM interconnect design using two-pole approximation

In this paper, an optimization scheme is proposed for interconnect design with wire width and series resistance being design variables. Due to the distributed nature of interconnects, poles of such systems are transcendental and infinite in number. First, a two-pole approximation is used to capture the system behavior. Lower-order moments are employed to obtain two approximate dominant poles. Then, the two parameters, damping ratio and natural undamped frequency, are expressed as functions of the two dominant poles. Since the output response is characterized by the two parameters, the parameters are used to define the objective function and constraints, which form a constrained multivariable nonlinear optimization problem. After that, the optimization problem is solved using the gradient projection method. One advantage of our approach is the ability to explicitly control the maximum overshoot of the observation points. Two numerical examples are given