On long-range and high frequency propagation alongparallel strip conductors in layered media : A simplified yet accurate method using the mode matching technique in the spectral domain

Sammanfattning: Electrical arcing in the railway environment radiates wideband noise that can disturb nearbysensitive electronics e.g. signaling systems. High frequency disturbances follow conducting wiresand rails. For Electromagnetic Compatibility reasons, radiation from wire structures is studied atspecific frequencies, to assess the risk to sensitive electrical devices further along the track.The specific problem is to construct a fast and accurate solver for computing the currents inducedby a dipole source on an arbitrary number of parallel wires inside a layered medium. In this project, atwo-layered medium is considered, each medium defined by arbitrary permittivity and permeability.Once the wire currents are known, the fields may be calculated everywhere.The approach is to transform the circular wires into equivalent strips, creating a planarly layeredstructure. The fields from a source in a layered structure may be expanded as a sum of planewaves propagating in the direction of stratification. The strip currents are expanded into Chebyshevpolynomials and together with the fields and boundary conditions, the currents are solved with themode matching technique in the spectral domain.Moreover, a simplified model for strips much narrower than the wavelength is derived, onlyconsidering axial currents, further reducing the complexity of the problem and still exhibiting highaccuracy.Unlike most full wave methods, the spectral domain approach does not rely on spatial discretisationof wires. Since infinitely long wires are considered, they are electrically large and thusconventional full wave methods yield to massive computations as many grid points are required, thusmotivating the spectral domain approach.The result is a linear system of integral equations solving the currents on an arbitrary numberof narrow strips. Results for different configurations of strips and dipole locations are shown andverified by comparing them with a commercial Method of Moments based solver, 4NEC2, using finitelengths of wire.In conclusion, a simple, fast and accurate method has been developed in Matlab for solving thecurrents along parallel strip conductors.