Determination of Quasi-Coaxial Via Capacitance using Conformal Mapping Technique

This paper presents an analytical investigation on a static capacitance of a quasi-coaxial via, which consists of a signal via and two surrounding ground vias. To determine the capacitance we propose an analytical equation derived from a modified mapping function for parallel circular conductors under the condition of a ground-signal-ground (GSG) symmetrical configuration. The validity of the derived equation as a function of via diameters and the distance between the signal via and the ground vias was examined by comparison of analytical capacitance per unit length with Q2D static numerical simulations, which results in good agreements within a few percentages of the error. Moreover, a 3D model of quasi-coaxial is designed with an existing design rule for a microvia. Its capacitance at 30 GHz is numerically extracted by full-wave electromagnetic simulation and compared to the analytical capacitance. As a result, we have observed that the difference between them is up to a few femtofarads.