Broadband Green´s function and applications to fast electromagnetic modeling of high speed interconnects

In this paper we developed the method of broadband Green´s function with Low Frequency Extraction (BBGFL) for arbitrary shaped waveguide. To facilitate broadband modeling over a wide range of frequency, BBGFL consists of modal expansion of modes that are frequency independent. To accelerate convergence of the Green´s function, low wavenumber extraction is performed by calculating the Green´s function at a single low wavenumber. The singularity of the Green´s function is also extracted by such low wavenumber extractions. In applying BBGFL, only a small set of field points and source points are usually needed. These are readily computed once and used for all frequencies. We illustrate the application of BBGF for broadband simulations of vias in arbitrarily shaped power/ground planes by combining with the method of Foldy-Lax multiple scattering equation. Results show that BBGFL agrees with MoM and HFSS. But BBGFL is several hundred times faster than direct MoM and HFSS in CPU. The substantial improvement in computational efficiency enables this technique for fast computer-aided design (CAD).