[SI-LIST] Re: Question on 2D field solver
- From: Chris Cheng <Chris.Cheng@xxxxxxxxxxxx>
- To: "'ray.anderson@xxxxxxxxxx'" <ray.anderson@xxxxxxxxxx>, si-list@xxxxxxxxxxxxx
- Date: Wed, 10 Nov 2004 16:25:51 -0800
Ray,
Boundary element method solves the charge density with the green's function
pivot against the voltage boundary conduction. The common BEM discretization
assume a constant charge density per filament. The problem is the Green
function is an integral like 1/(r-r') so when filaments are getting close,
the average integral value is always under estimate, when you pivot the
matrix to solve for charge density, you get an over estimate of the average
charge density of the filament resulting in larger capacitance matrix than
real value. The impedance is just solve by generating L matrix by inverting
the over estimated C matrix against propagation matrix (assumig a
homogeneous media). The end result is a double under estimation of
impedance.
Back in grad school days I tried using an adaptive rediscretize scheme to
refine the grid near high charge density area (sharp edges, corners,
conductor placing too close to each other etc) and I believe if the
discretization is based on a log scale grid instead of linear grid the
results will be closer to close form solutions. But I don't know if there is
any commerical venodr out there using the non-linear scheme.
HTH
-----Original Message-----
From: Raymond Anderson [mailto:ray.anderson@xxxxxxxxxx]
Sent: Wednesday, November 10, 2004 3:25 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Question on 2D field solver
Here's a question for the field solver guru's on the list:
I'm currently taking a critical look at the Mayo MMTL BEM 2D field
solver (TNT 1.2.2) that the developers at Mayo have so graciously made
freely available under the GNU GPL to the world. See the si-list
message announcing it for download links:
(//www.freelists.org/archives/si-list/07-2004/msg00311.html)
In preparation for doing a series of simulations on some via geometries
in packages I decided to validate the accuracy of the MMTL program on
some simple geometries that independent high accuracy answers were known
for.
I first tried the zero thickness stripline benchmark suggested by Dr.
Rautio at Sonnet Software.
(http://www.sonnetusa.com/products/benchmarking/eval_ch3.asp). The
results were about -0.4% low at 49.8002 ohms. This compares
comparably with a selection of other solvers I've had access to (but on
the low end of the range).
Mayo MTTL 49.8002
Polar CITS25 49.96
Agilent Appcad 3.0.2 49.8
AWR TXLINE 50.0346
LINPAR 2.0 50.03
LINPAR 1.0 50.027
Next I selected the case of a pair of parallel round elements as a test
case. The analytical solution for the inductance of this geometry is
given by Grover in chapter 5 of "Inductance Calculations". His formula
is an analytic solution based on first principles.
Using a test case of conductors 150 microns in diameter on a 500
micron pitch, Grover's equations yields a loop inductance of
758.84797 nH for 1 meter long conductors. The same problem modeled in
the MMTL field solver gives an answer of 749.4645 nH. I'm trying to
understand why the field solver answer is about 1.2% low. Is this
reasonable for a 2D MOM BEM solver using quasi-TEM assumptions? I've
tried modeling it several ways (as a pair of parallel circular
conductors far from ground and as a single circular conductor with it's
image reflected across a ground plane) and am getting the same answer
out to at least 2 decimal places. I've also tried upping the density of
the meshing with little real improvement.
Comments, suggestions and ideas solicited. Thanks!
-Ray Anderson
Senior Signal Integrity Staff Engineer
Advanced Packaging R&D
Xilinx Inc.
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