Fast calculation of electromagnetic interference by through-silicon vias

A methodology is presented for the expedient calculation of radiated electromagnetic interference by dense arrays of through-silicon vias in layered substrates. The proposed methodology builds upon the efficiency of the Foldy-Lax scheme for the fast calculation of the electromagnetic interactions between multiple vias in planar substrates, by exploiting translation invariant expressions of the governing equations that lend themselves to fast calculation of the convolution integrals for the radiated fields using Fast Fourier Transform. Applications of the developed model and algorithm involving the investigation of radiated emissions from through-silicon via clusters are used to demonstrate the efficiency of the proposed algorithm.