A Semianalytical Model for Vias With Arbitrarily Shaped Antipads Based on the Reciprocity Theorem

We present a semianalytical model for a dense layout of vias in an infinite parallel-plate environment. An arbitrarily shaped antipad configuration is addressed. The network parameters for the multi-via structure are calculated based on the reciprocity theorem, where a unit-strength magnetic testing ring frill is used to compute the currents flowing on the surface of the via barrels. The motivation for using reciprocity is to bypass the sophisticated computation of the radiation from the irregular-shaped antipad aperture; instead, a much simpler field from the reciprocal testing source is formulated. Also the higher-order parallel-plate mode radiation from this testing frill is highly localized and hence there is little interaction among vias through higher-order modes. This rapidly-decaying field makes the mode-matching computation converge very fast. Furthermore, the testing frill radiates an omnidirectional reactive near field that can be expressed in a closed-form, making the method computationally efficient. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithm.