Resistive modeling of periodically perforated mesh planes in multilayer packaging structures

The DC resistance of a periodically perforated mesh plane in a multilayer packaging structure is modeled by a network consisting of the equivalent resistances between any two holes. Through the use of the spectral analysis together with conformal mapping, analytic formulas for the equivalent resistances are derived for the mesh planes with holes of common shapes. For mesh planes with medium-size holes, the one-shell network constructed of the equivalent resistances between the nearest-neighbor and cross-corner holes is sufficient. However, if the hole size is small, the two-shell network which contains resistances to next-nearest holes should be used