Capacitance of circularly symmetric via for microstrip transmission line

Vias connecting different traces of a multilayered circuit board generally cross at least one ground plane and introduce a capacitance to a transmission line circuit. At sufficiently low frequencies this capacitance can be ignored, but at high frequencies it must be accounted for in the circuit design. The via structure of interest consists of a hollow cylinder with lips that passes through a circular hole in a ground plane. The cylinder has lips at its ends that facilitate connection to a trace of a microstrip transmission line that is supported by and resides on the surface of a dielectric slab, which itself rests on the ground plane. An integral equation is derived for the charge induced on the cylindrical centre of the via, from which one can compute via capacitance, under the condition that the cylinder is raised to a potential V relative to that of the ground plane. The differential equation for the Green´s function, which accounts for the dielectric substrate, is solved by a simple technique involving the Hankel transform. Data depicting via capacitance and its dependence on the dielectric constant of the slab and its geometric dimensions are presented for numerous configurations. From the data one can assess the importance of incorporating the effect of the dielectric substrate into the analysis