Efficient MPIE approach for the analysis of three-dimensional microstrip structures in layered media

A full-wave space-domain method is presented for the rigorous and fast investigation of printed circuit structures of arbitrary shape on uniaxial anisotropic layered substrates including three-dimensional (3-D) metallizations. The electromagnetic (EM) fields are described in terms of a mixed-poteneial-integral-equation (MPIE) formulation. Two different techniques-the matrix pencil (MP) technique and a cross-sectional eigenvalue (CSEV) approach-are employed to extract the S-parameters of the circuit under consideration. The usage of a triangular mesh allows the convenient modeling of arbitrarily shaped structures, Therefore, the main advantage of this method is its generality, which allows a large variety of printed circuit structures to be characterized. The flexibility of the method is demonstrated at the example of spiral inductors including air-bridges with finite-metallization thickness.