Analytical formulas for the barrel-plate and pad-plate capacitance in the physics-based via circuit model for signal integrity analysis of PCBs

The current distribution along via barrel and pad is obtained by the Green's function of a generalized coaxial cavity for a magnetic frill current. An analytical formula for both the barrel-plate and pad-plate capacitances are derived by observing the current difference along the via barrel and pad. Finite difference method has been used to validate the formula derived here. Analytical formula presented facilitates the implementation of the physics-based via circuit model in practical via designs for printed circuit boards and packages. The impact of various via geometric parameters on the parasitic capacitances has been investigated.