A circuit approach to compute near-field interactions based on an efficient implementation of the spherical wave expansion

This paper describes an efficient evaluation of a spherical wave based generalized scattering matrix formulation for electronic subsystems (Printed Circuit Boards, ICs, small antennas,...). This generalized S-matrix consists of four subparts: the classical scattering matrix of the modes at the circuit ports, an array describing the outward traveling modes at the radiation ports, an array describing the inward traveling modes at the radiation ports, and a matrix containing the reflection of inward traveling modes at the radiation ports. The S-matrix is derived from one full-wave simulation, based on a new and efficient evaluation of the orthogonality integrals of spherical wave functions. Special attention is paid to a fast and easy-to-implement evaluation of the translation and rotation of spherical waves. The proposed formulation is especially suitable to integrate in a circuit simulator, without resorting to computationally complex methods which are difficult to implement or rely on unstable approximate formulations. This approach allows to generate a library of models of electronic subparts that do not contain any confidential data; and enables the use of a circuit simulator to analyze the coupling between these subparts both in frequency domain and time domain.