In this paper, we formulate closed-form expressions for the fields excited by an x-directed dipole source in both homogeneously-filled and inhomogeneously-filled stripline structures. These expressions are obtained by first employing spectral domain techniques, which yields a spectral-domain Green's function that involves simple algebraic and trigonometric functions. Then we take the inverse two-dimensional Fourier transform of that expression and represent it as a Sommerfield-type integral in the space domain. This Sommerfield integral has a highly oscillatory and slowly convergent nature. Therefore, we analytically evaluate this Sommerfield integral by applying Residue theory. Summing over the residues evaluated at the pole locations in the complex plane yields a rapidly computable modal series expansion that is free from any nmnerical integration. The special functions that occur in the modal series expansions are rapidly computable Bessel functions. This method greatly improves the computational efficiency as compared with numerical integration. The field study carried out in this paper will help to extend the capabilities of a recently developed full-wave layered interconnect simulator (UA-FWLIS). This simulator can currently handle method of moment (MOM) reaction element evaluations in homogeneously-filled stripline structures, where the dominant mode and numerous higher order decaying modes may be required. After a robust algorithm has been developed for the computation of all the modes for the inhomogeneous case, the Green's function can be directly plugged into UA-FWLIS to allow for the evaluation of the MoM reaction elements in inhomogeneously layered stripline structures. In this paper, we compare the field behavior for the homogeneous and inbomogeneous cases. Computational results for the fields are presented and the physical pbenomenology of the fields is studied.
- Integral equation
- Newton's method
ASJC Scopus subject areas
- Electrical and Electronic Engineering