Analytical extraction of via-via inductance by using SMM for power-ground planes

In this paper, the via-via inductance between power-ground plane in printed circuit board is extracted analytically by using the scattering matrix method (SMM). A gap voltage source is used to excited the higher order modes between parallel plates, by solving the linear scattering matrix equation, the scattered wave coefficient is obtained, furthermore, the admittance parameter between two vias is calculated, and the analytical inductance formula with frequency dependence is obtained and validated by quasi-static numerical method.