Evaluating noise pulses in RC networks due to capacitive coupling

Closed form solutions are introduced that describe the area, width, and maximum value of a noise pulse induced on a quiet net (line, tree, or mesh) due to capacitive coupling with switching neighbor nets. These solutions are highly efficient to evaluate with a complexity linearly proportional to the number of elements in the RC network. The pulse area calculated based on these solutions is exact while the width and maximum value of the noise pulse are within 15% from SPICE simulations for a wide range of typical interconnect structures. The effects of the coupled line impedances and line length on the amount of noise induced on a quiet line are investigated based on these solutions. It is shown that the energy of a noise pulse is quadratic with the length of an interconnect line, illustrating the need for accurate noise estimation for large interconnects.