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).
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