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

Abstract

Abstract-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).

Broadband Calculations of Band Diagrams in Periodic Structures Using the Broadband Green's Function With Low Wavenumber Extraction (Bbgfl)

“…Note that the above expansion is similar to the waveguide mode expansion [23]. In the problem considered in this paper, the band problem consists of the scatterer being perfect electric conductor and the background has permittivity ε (Figure 1(a)).…”

“…We choose a low wavenumber k L . Then we apply BBGFL, in a manner similar to waveguide/cavity problem [20][21][22][23]. The periodic Green's function is expressed as the sum of the Green's function at that single low wavenumber k L and the Floquet mode expansion with that low wavenumber counterpart subtracted.…”

“…If the periodic Green's function is used for the surface integral equation to calculate the eigenvalues, the equation is nonlinear and an iterative search needs to be performed with one band at a time. Recently, the Broadband Green's Function with Low wavenumber extraction (BBGFL) [20][21][22][23] has been applied to wave propagation in waveguide/cavity of arbitrary shape. By using a single low wavenumber extraction, the convergence of the modal expansion of the Green's function is accelerated.…”

Reduction of PCB PDN Impedance and Radiated Emissions Using a Hybrid Technique With Absorbing Materials and Decoupling Capacitors

“…Passive interconnects are commonly used to help improve electrical performances of high speed digital systems and power delivery networks (PDN) for several decades and have been shown to impact each other [1][2][3][4][5][6][7][8][9][10][11][12][13]. For instance, the PDN impedance has significant influence on the signal, power integrity, and EMI of electronic systems.…”

“…If we can reduce resonant impedance amplitude, then we will effectively lower behavior modes (TE and TM modes) along PCB edges [1][2][3][4][5][6][7][8][9][10][11]. We employ the use of absorption material to mitigate cavity resonant effect and PDN impedance noise from powerground planes.…”