Optimizing Dominant Time Constant in RC Circuits

L. Vandenberghe, S. Boyd, and A. El Gamal

IEEE Transactions on Computer Aided Design, 17(2):110-125, February 1998.

We propose to use the dominant time constant of a resistor-capacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interesting design problems as convex optimization problems, specifically, semidefinite programs (SDPs). For example, assuming that the conductances and capacitances are affine functions of the design parameters (which is a common model in transistor or interconnect wire sizing), one can minimize the power consumption or the area subject to an upper bound on the dominant time constant, or compute the optimal tradeoff surface between power, dominant time constant, and area. We will also note that, to a certain extent, convex optimization can be used to design the topology of the interconnect wires. This approach has two advantages over methods based on Elmore delay optimization. First, it handles a far wider class of circuits, e.g., those with non-grounded capacitors. Second, it always results in convex optimization problems for which very efficient interior-point methods have recently been developed. We illustrate the method, and extensions, with several examples involving optimal wire and transistor sizing.