Broadband Green's Function with Low Wavenumber Extraction for Arbitrary Shaped Waveguide and Applications to Modeling of Vias in Finite Power/Ground Plane

In this paper we developed the method of broadband Green's function with low wavenumber extraction (BBGFL) for arbitrary shaped waveguide. The case of Neumann boundary condition is treated. The BBGFL has the advantage that when using it to solve boundary value problems in a waveguide, the boundary conditions have been satisfied already. The broadband Green's function is expressed in modal expansion of modes that are frequency independent. To accelerate the convergence of the Green's function, a low wavenumber extraction is performed. The singularity of the Green's function is also extracted by such low wavenumber extraction. Numerical results show that BBGLF and direct MoM are in good agreement. We next illustrate the application of BBGFL for broadband simulations of vias in printed circuit boards (PCB) by combining with the method of Foldy-Lax multiple scattering equation. The results show that BBGFL are in good agreement with MoM and HFSS. It is also shown that BBGFL is many times faster than direct MoM and HFSS. The computational efficiency in broadband simulations makes this technique useful for fast computer-aided design (CAD). The effects of waveguide or cavity structures are critical for the electrical performance of electronic devices and components in signal integrity (SI), power integrity (PI), electromagnetic interference (EMI), and electromagnetic compatibility (EMC). Harmful electromagnetic signal noises or interferences are often generated and amplified at the resonant frequencies of the waveguide or cavity structures. The issues deteriorate when the electronic devices or computer systems operate at higher frequency or faster speed. In printed circuited boards (PCBs), two adjacent power/ground planes form a waveguide/cavity structure. The propagating modes satisfy the PMC (Neumann boundary conditions) at the edges of PCB power/ground plane structures. The power/ground plane structures are the key root causes in SI/PI and EMI/EMC problems. Vias are used for vertical interconnects for multilayer PCBs. At frequencies near the resonant frequencies, the propagating electromagnetic waves excite resonant modes, that result in strong edge radiations. These cause EMI/EMC problems. The switching noises induced by voltage regulator module (VRM) generate voltage fluctuations and lead to PI problems. The high frequency power noise can also couple into signal vias and cause SI/PI coupling issues. Therefore, the modeling of PCB cavity with vias is critical in practical designs and applications of high speed PCBs and packages. Fast and accurate modeling technique is desired for broadband simulations in electronic design and application. The finiteness of the parallel power/ground planes make them waveguide/cavity structures. The power/ground planes are also of arbitrary shape. Commercial tools such as HFSS provide solutions for the analysis of the via-cavity coupling problem. The tools require large CPU and memory and are not suited for broadband analysis. The physical problem is that of TM modes in a cavity with PMC boundary conditions on the side walls. Various methods have been used for waveguide