Chong-Jin Ong

Evaluation of the Green's function for the mixed potential integral equation (MPIE) method in the time domain for layered media

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Greens function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Greens functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/s and ts simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Greens function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Greens functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

Full-Wave Solver for Microstrip Trace and Through-Hole Via in Layered Media

This paper reports major improvements to a 3-D full wave solver for a microstrip line and through-hole via in layered media. The interior layer problem, consisting of vias between two reference planes, is solved using the Foldy-Lax multiple scattering equations. The exterior layer problem is solved using the method of moments (MoM) with the layered media Greens functions. The exterior layer and interior layer problems are combined to obtain the S-parameters of the trace and through-hole via. A fast approach for calculating the layered-medium Greens functions using the numerical modified steepest descent path method is utilized. The Greens functions require milliseconds to compute per point. Schemes for efficiently computing image contributions for the static portion of the mixed potential Greens function are also implemented to solve the neighboring or self-RWG (basis function) interaction in the MoM problem. To validate the accuracy of the solution, extensive comparison with Ansofts HFSS versions 9 and 11 for different pad sizes and antipad sizes are presented. The CPU per frequency is also tabulated to demonstrate the speed of the approach in this paper.

Full-Wave Analysis of Large-Scale Interconnects Using the Multilevel UV Method With the Sparse Matrix Iterative Approach (SMIA)

Moving towards the goal of analyzing whole printed circuit boards (PCBs) and packages using full-wave electromagnetic (EM) methods, the multilevel UV method is applied to the method-of-moments (MoM) solution of the current on large-scale interconnects. The MoM solution uses the layered media Greens functions computed using the numerical modified steepest-descent path (NMSP) method, and is applied to the exterior layers of the interconnect structure. The sparse matrix iterative approach (SMIA) is used to speed up the solution of the iterative matrix solver. The iterative solver is also accelerated by using larger blocks in the block diagonal inverse preconditioner. With the multilevel UV method, a fast solution is presented for solving the current on large-scale interconnects on thin layered structures at high frequencies. We show an example of an interconnect structure that has horizontal dimensions of 12.675 lambda × 12.876 lambda with 24\thinspace 848 current unknowns and an interconnect fractional area of approximately 31%. This problem takes a total of 21 min 20 s to solve for the current on the traces on a Pentium 3.2-GHz CPU with 4 GB of RAM.

Electromagnetic Fields of Hertzian Dipoles in Thin-Layered Media

Fast numerical methods are developed to compute the electromagnetic (EM) fields for thin-layered media for the entire distance range. Thin-layered media are defined to be the case when there are only surface wave modes but no leaky modes between the Sommerfeld integration path (SIP) and the vertical branch cut. Fields for distances larger than twice the layer thickness are computed by the numerical modified steepest-descent path (NMSP) method. The NMSP consists of integration along the branch cut with the pole proximity accounted for by using incomplete error functions. The fields for distances less than twice the layer thickness are computed by the first two orders of low-frequency approximation up to frequency squared. These two methods are used to compute the electromagnetic fields for all distance ranges. The CPU per point is of the order of milliseconds using a Pentium IV 3.2 GHz CPU and Matlab. The CPU for each point as a function of distance range is tabulated

Application of the Multilevel UV Method to Analyze Large Microstrip Patch Structures

The analysis of a plane wave incident on a large microstrip patch is studied using the method of moments (MoM) with the layered medium Greens functions and the rooftop basis functions. A fast numerical approach, the multilevel UV method, is employed to speed up the method of moment solution. A conjugate gradient method solver with preconditioning is applied as an iterative matrix solver to accelerate the matrix-vector multiplication. The multilevel UV method has O(N log N) complexity for CPU per iteration and memory.

A numerical solution of the layered media Green's function for the MPIE in the time domain

Layered media Greens functions in the frequency domain have been extensively studied previously. Interest has increased in the evaluation of the layered media Greens functions in the time domain, to be subsequently used for time domain integral equations (TDIEs). This is because of critical time-domain applications including the analysis of transients in high speed digital interconnects and for analyzing wideband microstrip antennas. In using time domain layered Greens functions in conjuction with TDIEs, it is necessary to compute the layered medium Greens function for many source-to-field distances /spl rho/ and time intervals t. In this paper, a numerical solution of the layered media Greens function in the time domain for the mixed potential integral equation (MPIE) is reported. The particular case where the source and field points are on the top layer is presented. The method is applicable to multi-layered structures and to both lossless and lossy media. The technique also computes the Greens function for many /spl rho/ and t values simultaneously.

Full-wave analysis of microstrip line coupling and fast solution of multi-via scattering in PCBs

We present a full wave solver for coupled microstrip lines and multiple vias on printed circuit boards. The formulation is broken down into the interior problem and the exterior problem. The interior problem solves the scattering from a large number of vias inside a parallel plate waveguide, using cylindrical expansion of the magnetic field Greens function. The multiple interactions among vias are evaluated using the Foldy-Lax scattering formula and the solution is accelerated by the sparse matrix canonical grid (SMCG) method. The exterior problem includes coupled microstrip lines with traces passing over anti-pads and is solved using the method of moments (MoM), where RWG basis functions are applied.