Boping Wu

Modeling Multiple Vias With Arbitrary Shape of Antipads and Pads in High Speed Interconnect Circuits

This letter successfully extends the full-wave semi-analytical approach, based on Foldy-Lax multiple scattering equations and modal expansions, to solve massively-coupled multiple vias with arbitrary shape of antipads and pads in high speed interconnect circuits. The magnetic frill current at the antipad aperture is calculated using finite difference method. Numerical examples of as many as 16-by-16 via array demonstrate that this approach is able to model the multiple vias problem at about five thousand times faster than Ansoft HFSS and yet is within 5% difference of accuracy up to 20 GHz.

Signal Integrity Analysis of Package and Printed Circuit Board With Multiple Vias in Substrate of Layered Dielectrics

This paper successfully extends the Foldy-Lax multiple scattering approach to model massively-coupled multiple vias in substrate of layered dielectrics between two horizontal power/ ground plates. The dyadic Greens functions of layered dielectrics are expressed in vector cylindrical waves and modal representations. Formulations are derived for admittances and S-parameters of single via and multiple vias structures. The CPUs and results of S-parameters are illustrated for various sizes of via array. For the case of 16 × 16 via array through hybrid dielectrics in single interior layer, the CPU is about 0.8 s per frequency and is at least three orders of magnitude faster than Ansoft HFSS. The results are within 5% difference of accuracy up to 20 GHz. This full-wave method is able to include all the coupling effects among the multiple vias. It is also shown that the approach of using effective dielectric constant by assuming an effective homogeneous media does not give accurate results.

Full-wave modeling of multiple vias using differential signaling and shared antipad in multilayered high speed vertical interconnects

A 3D full-wave approach, based on the Foldy-Lax multiple scattering equations, is successfully extended to model massively- coupled multiple vias using difierential signaling and shared antipad in high speed vertical interconnects. For the flrst time, this method has been used and tested on via-pair with shared antipad in multilayered structure. The magnetic frill current source on the port is calculated by using the flnite difierence method. Banded matrix iterative method is applied to accelerate the flnite difierence calculation. Numerical example of 15 signal via-pairs and 20 ground shielding vias in 6- layer board demonstrates that this approach is able to model the via-pair with shared antipad and to include all the coupling efiects among multiple vias. The electrical performances of difierent signal driving schemes are provided and discussed. The coupling crosstalk on various via-pairs is compared. The improvement of signal integrity is shown by using difierential signaling and shared antipad for via-pair in multilayered structure. The results are compared with HFSS and SIwave in accuracy and CPU. The CPU using Foldy-Lax approach is three orders of magnitude faster than using HFSS, and two orders of magnitude faster than using SIwave. The accuracy of Foldy-Lax is within 2% difierence from HFSS up to 20GHz, and outperforms SIwave in accuracy.

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.

Electromagnetic Fields of Hertzian Dipoles in Layered Media of Moderate Thickness Including the Effects of All Modes

Fast numerical methods are developed to compute the electromagnetic fields of Hertzian dipole of layered media (layered medium Greens function) of moderate thickness for the entire distance range. The method consists of using a fast all modes (FAM) method of determining all mode locations in the complex plane. The modes include surface wave modes, leaky wave modes, and improper modes. For the case of layer thickness of one wavelength, it requires only 0.12 CPU seconds as preprocessing to determine 400 mode locations accurately in the complex plane using a Pentium IV 3.2 GHz PC with Matlab. The mode locations are required only to be computed once. The numerical modified steepest descent method (NMSP) is then used to compute the steepest descent integral with all the pole proximities extracted and accounted for by using incomplete error functions. With the extraction of the poles, the NMSP requires no more than six quadrature points to compute fields at distances larger than 0.02 wavelength. The CPU per distance point based on the FAM/NMSP method is less than 3 ms for all distance ranges. The accuracy of the method has been confirmed to within 0.2% from the benchmark calculations of the half-space extraction method.

Fast Computation of Layered Medium Green's Functions of Multilayers and Lossy Media Using Fast All-Modes Method and Numerical Modified Steepest Descent Path Method

A fast and accurate approach, based on the fast all-modes method (FAM) and the numerical modified steepest descent path method (NMSP), was previously used to calculate the spatial Greens function for a single-layer lossless dielectric medium over a perfect electric conductor. This paper successfully extends that approach to two new cases. The first is the multilayer case where the medium has an arbitrary number of layers. The second is lossy media over an imperfect conductor. The FAM locates all modes accurately on the complex plane. The modes include surface wave modes, leaky wave modes, and improper modes. For a typical six-layer case over a ground plane, the FAM requires only 2.265 s of pre-processing that includes computing 200 mode locations by using a P4 3.2-GHz PC with Matlab. The NMSP is then used to evaluate the steepest descent path integral. Accuracy within 0.2% is achieved in comparison with the benchmark calculations. Within this context of accuracy, the total CPU per distance point is less than 7.6 ms for distances larger than 0.02 free-space wavelength and is less than 2.7 ms for distances larger than two free-space wavelengths. This method is shown to be fast and accurate, even for large-distance interactions in the multilayer and lossy media.

Efficient full-wave modeling of high density TSVs for 3D integration

This paper presents a full-wave electromagnetic approach for modeling the electrical performance of massively-coupled and coated through silicon vias in a sandwiched SiO2-Si-SiO2 substrate. The planar guided wave is analyzed to determine the fundamental mode and high order modes in stratified media. Cylindrical wave expansions and Foldy-Lax equations for multiple scattering techniques are used to efficiently calculate the couplings among the vias. The effect of SiO2 coating around the via is modeled by general T-matrix coefficients. Both silicon loss and copper loss are included in this approach. Numerical simulations of insertion loss, return loss and crosstalk of 1-by-3 and 4-by-4 through silicon via arrays are presented and compared with general-purpose field-solver.

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

Fast full wave analysis of PCB via arrays with model-to-hardware correlation

This paper applies a methodology based on a mostly-analytical Foldy-Lax full wave scattering model to analyze via arrays in a multilayered printed circuit board. We have demonstrated good model-to-hardware correlation up to 20 GHz by simulating and measuring 8×8 via arrays including 29 signal vias and 35 ground vias in a 18-layer test board. The required CPU in the 64-via case is 4 seconds which is more than four orders of magnitude faster than the market leading general-purpose 3D full wave solver.

Electromagnetic fields and modal excitations on a thin silver film

In this paper we extend the fast-all-modes method and the numerical modified steepest-descent-path method to the optical frequency range by finding all modes and solving the total electric field in three dimensions that is due to a point source above a lossy thin metal film with a negative permittivity situated between two dissimilar dielectric materials. We show that up to four proper surface wave modes may propagate on the film surface, including both backward and forward waves. We also solve for the electric field below the lossy thin metal film and verify the existence of superlensing of the electric field, comparing that case to the case of a dielectric film where no superlensing occurs. The CPU time using the fast-all-modes method and the numerical modified steepest-descent-path method is considerably less than that using the conventional method of integration along the Sommerfeld integration path.