A study of the fields associated with vertical dipole sources in stripline circuits

A prototype, integral-equation-based, full-wave layered interconnect simulator (UA-FWLIS) has recently been developed. In this simulator, the method of moments (MoM) reaction integrals are evaluated analytically, thereby dramatically improving the computational efficiency compared with standard numerical integration techniques. The closed-form representation for the reaction elements takes the form of a modal series expansion. Since the reaction between closely-spaced elements requires the dominant mode and a significant number of higher-order modes, an investigation of the behavior of the fields associated with both the propagating and higher-order evanescent wave modes will be beneficial for the further development of the simulator. The simulator can currently handle homogeneously-filled stripline structures only. In this paper, the electric field analysis is extended to an inhomogeneously-filled stripline structure. The knowledge gained from these studies will allow for the extension of the simulator to the analysis of inhomogeneously-filled stripline structures. The spectral domain technique is first used to obtain the field expressions in the spectral domain. Analytically performing the two-dimensional inverse Fourier transform results in electric fields that are expressed as closed-form solutions in terms of special functions that are free from any numerical integration. Computational results for the fields are presented and the physical phenomenology of the fields is studied.