A method and system for reducing noise in a power grid of an integrated circuit,
which optimizes the placement and sizing of decoupling capacitors in the power
grid. Logic cells are located in a first layout of the integrated circuit with
empty spaces between the adjacent cells, and the placement of the cells is changed
to a second layout wherein the size of the empty spaces between the adjacent cells
also change. The decoupling capacitors are placed in the empty spaces of the second
layout. In the example of a row-oriented cell structure, the empty spaces may be
uniformly distributed along each row for the initial layout. An adjoint sensitivity
analysis is performed of the sensitivity of a noise function of the integrated
circuit with respect to sizes of the empty spaces between adjacent cells, and an
original noise waveform is convolved with an adjoint noise waveform. The convolution
may use piecewise linear compressions of the original and adjoint noise waveforms.
A quadratic programming solver is then used to iteratively determine the sizes
of the empty spaces between adjacent cells.
