Double and single summation expression for the impedance of populated PCB power-bus structures including asymmetrically connected components

In this paper the impact of lumped elements connected asymmetrically to rectangular PCB power-bus structures is investigated and a double summation expression for the resulting impedance is derived. Further, the double summation expression is reduced to a single summation expression by using a summation formula of a Fourier series. The analytical results show good agreement with measurements