Applications of Convex Optimization in Power and Ground Network Design and Wire Sizing

Lieven Vandenberghe

(Joint work with Abbas El Gamal and Stephen Boyd, Stanford University)

We describe two important optimization problems in digital circuit design, and solution methods based on recent interior-point methods for convex optimization. First, we consider the problem of determining optimal wire widths for a power or ground network, subject to to limits on wire widths, voltage drops, total wire area, current density, and power dissipation. To account for the variation of the current demand, we model it as a random vector with known statistics. We show that when the current variation is taken into account, the optimal network topology is usually not a tree. We formulate a heuristic method based on minimizing a linear combination of total average power and total wire area. This problem can be formulated as a convex optimization problem that can be globally solved very efficiently.

As a second problem, we consider optimal wire sizing of interconnect networks based on linear RC models. We describe a method based on minimizing the dominant time constant instead of the Elmore delay. The advantage of the method is that it leads to convex optimization problems, even in circuits with a non-tree topology.

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