Broad band Green's function with low wavenumber extraction (BBGFL) for inhomogeneous waveguide of arbitrary shape

Abstract

Recently, we have developed the method of broadband Green's function with low wavenumber extraction (BBGFL) to investigate the problem of arbitrary shaped waveguides [1]. In the past, the Boundary Integral-the Resonant Mode Expansion (BIRME) [2, 3] method was applied to calculate the modes of an arbitrary shaped waveguide with a homogenous dielectric. In BIRME, a DC extraction is applied to remove the singularity. In BBGFL, the broadband Green's function is expressed in modal expansion of modes that are frequency independent. To accelerate the convergence in computing the Green's function, a low wavenumber extraction is implemented which was shown to be a robust method of extraction. We apply the BBGFL method to the signal integrity problem where the broadband simulations of signal interaction with vias in printed circuit boards (PCBs) are carried out by combining with the Foldy-Lax multiple scattering equations [1]. The BBGFL method is also used in the dielectric problem with periodic structures [4]. Recently, the broadband Green's function method is further employed in the fast modeling of radiated emissions from PCBs with power bus structures for electromagnetic interference/compatibility (EMI/EMC) studies [5]. In EMI/EMC problems, PCBs usually consist of inhomogeneous dielectrics and arbitrary shaped power/ground planes. The complication for this case is because of the two different wavenumbers in the two dielectrics. In this paper, the BBGFL technique is extended to treat the inhomogeneous waveguide problem where the waveguide is filled with two different dielectrics. We apply BBGFL to fast model the irregular shaped PEC boundary for inhomogeneous waveguides. The extinction theorem is applied twice, respectively from outside and inside the boundary separating the two dielectrics. Low wavenumber extractions are next used. With this technique we obtain a linear matrix eigenvalue problem from which the modal solutions for all modes are calculated simultaneously. The broadband Green's function is next constructed using the mode solutions for broadband application. We compare simulation results and computational efficiency with HFSS.