Transmission Line Representation of the Capacitive Via-Plate Interaction Toward a Capacitor-Free Via Model

Conventional physics-based via circuit model takes into account the capacitive coupling between via barrel and power/ground plane by a via-plate capacitor, whose calculation relies on a complex expression involving an infinite summation of Hankel functions. In this paper, a capacitor-free via model is proposed and realized by way of a novel transmission line representation of the via-plate capacitance. In particular, the via-plate capacitor is replaced by an open-circuited transmission line (OC-TL) with equal input admittance. The resultant capacitor-free model obviates the need of calculating the sum of infinite series. Instead, it only requires identifying the length of the OC-TL by simple closed-form expressions. Hence, the proposed efficient capacitor-free via model is able to facilitate the modeling of realistic multilayer printed circuit boards (PCBs) and packages. Both numerical and measurement results validate the proposed OC-TL-based via model.