Geometrically Parameterized Circuit Models of Printed Circuit Board Traces Inclusive of Antenna Coupling

This paper presents a systematic methodology for the characterization of mutual couplings between antennas and printed circuit board (PCB) traces in modern mobile devices. The main approach is based on the assumption that the interfering fields produced by the antennas are not perturbed significantly by the PCB traces. The one-way coupling can thus be computed using the theory of field-excited transmission lines. The incident field patterns excited by each antenna are computed via a single preliminary full-wave analysis. We adopt a generalized scattering formulation for the electromagnetic system. Some ports define the terminals of the PCB traces, the other “electromagnetic” ports correspond to the antennas feed points. The main achievement of this paper is a parameterization scheme for this generalized scattering form in terms of the trace-routing path. This parameterization further approximates the frequency dependence of each response in terms of rational functions, enabling the direct synthesis of path-dependent macromodels in an SPICE environment. Fast optimization, what-if, and sensitivity analyses can thus be performed directly via transient SPICE runs, possibly including realistic (transistor-level or behavioral) models for driver and receiver circuits.