# Benchmarking

## Evaluation of Electromagnetic Software

Revised: June 4, 1997

© Copyright 1994, 1999 Sonnet Software, Inc. All Rights Reserved

### Table of Contents

Chapter 1 - Introduction

Chapter 2 - Technical Overview

Chapter 3 - The Stripline Standard

Chapter 4 - The Stripline Standard and Triangular Subsections

Chapter 5 - The Microstrip Standard

Chapter 6 - The Coupled Microstrip Standard

Chapter 7 - Limit Tests

Chapter 8 - Lossy Ground Plane and Lossy Dielectric Tests

## Chapter 2 - Technical Overview

Stripline Standard | Triangle Subsections | Microstrip Standard | Coupled Microstrip Standard |

Ultra-thin Dielectric | Zero Length Through | Short Length Vias | Loss Tests

This chapter provides a brief technical description of the entire suite of benchmarks. Benchmarks which are of particular interest can then be reviewed in detail in the referenced chapter.

Each benchmark is designed to detect and quantify specific error sources as described below. All test structures have very simple geometry and allow precise quantitative evaluation of error. (Complex geometries, which do not allow precise evaluation of error, are appropriate for the more common GABMAC validation as described in the previous chapter.) Given familiarity with the software being tested, it should be possible to complete the entire suite of benchmarks in one to two days.

**1) The Stripline Standard**
(Chapter 3, "The Stripline Standard"). This standard consists of a simple through line. Since there is
an exact solution for stripline, the width of the line can be set so that an exact 50 Ohm
line results. The length of the line is set to exactly a quarter wavelength at 15 GHz.
Total error is determined by simply adding the magnitude of S11 to the percent phase
difference of S21 from -90 degrees. Use different subsection sizes to determine how error
changes with subsection size. We recommend starting with a very short subsection length
(512 per wavelength) and varying the number of subsections into which the width of the
line is divided. Start with one subsection per line width, then two, then four, etc.
Continue until analysis time becomes excessive. As subsection size becomes smaller, error
should decrease and analysis time should increase. Plot or tabulate the error versus
analysis time performance.

**2) Triangle Subsections** (Chapter 4, "The
Stripline Standard And Triangular Subsections"). Some analyses use triangular
subsections to allow representation of smooth curves. If improperly implemented, undesired
error can result. To detect and quantify this error, repeat the above Standard Stripline,
only now subsectioned with triangles, see Figure 6 in Chapter 2. Perform the analysis for
the line subsectioned only one (triangle) subsection wide. Determine the amount of error
due to triangles by comparing the result with the Stripline Standard subsectioned one
(rectangular) subsection wide as performed above. As explained in the chapter, this test
is not appropriate for Sonnet.

**3) The Microstrip Standard**
(Chapter 5, "The Microstrip Standard"). There is no exact solution for microstrip, thus an approach
similar to the Stripline Standard is not possible. Instead, the microstrip standard is a
frequency independent lumped component, a series capacitor, embedded in a microstrip line.
The dimensions and frequency of analysis are set so that the effect of fringing
discontinuities (series inductance) are very small relative to dispersion in the
connecting transmission line. To test an analysis for accuracy, simply analyze the
capacitor as a function of frequency. The analysis should have reference planes set to the
middle of the capacitor with results de-embedded to that point. The capacitance is
independent of frequency. Any calculated variation of capacitance with frequency is error
in the analysis of dispersion or error in the de-embedding. Since de-embedding is usually
an integral part of an electromagnetic analysis, de-embedding error is appropriate to
include in a quantitative benchmark. If the capacitance is not a standard output of the
analysis under test, use the linearity of Y22 as an equivalent metric. Unlike the previous
tests, this test is not intended to quantify error due to subsection size. Since some
electromagnetic analyses have difficulty analyzing capacitors, the dielectric on this
capacitor has been kept thick so that such analyses are not excluded from this benchmark.

**4) The Coupled Microstrip Standard** (Chapter 6,
"The Coupled Microstrip Standard"). Because de-embedding works for single lines,
does not mean it also works for coupled lines. This benchmark is a simple coupled line
version of the Microstrip standard. Error in de-embedding coupled lines or in coupled line
dispersion can be quantified using this standard. Some analyses are incapable of
de-embedding coupled lines. This standard can not be used on such analyses.

**5) Limit Tests** - see the section "Ultra-thin Dielectric" in Chapter 7. The
Green's Function (i.e., fields due to an "impulse function" of current) are very
singular near the source of current. If two subsections are very close to one another and
an analysis relies on numerical integration, very large error can result. This is
especially true in thin dielectric capacitors. This test is similar to the Microstrip
Standard except that the capacitor dielectric is now very thin, with dimensions and
parameters similar to Metal-Insulator-Metal (MIM) capacitors common on GaAs integrated
circuits. This test simply looks at the low frequency value of the capacitance and checks
to make sure it is close to the DC parallel plate capacitance. When an analysis fails this
test, it usually does so dramatically.

**6) Limit Tests** -- see the section "Zero Length Through" in Chapter 7. This test
is a simple microstrip through line de-embedded to zero length. Any error left over is
usually very small numerical noise due to finite precision. Any larger errors should be
investigated carefully.

**7) Limit Tests** -- see the section "Short Length Vias" in Chapter 7. Most analyses
have a low frequency limit where the small difference between two large numbers generates
large errors and an analysis becomes unusable. For example, if there is any need to deal
with integrated circuit dimensions at frequencies below 2 GHz, this test is absolutely
critical. The test consists of an ultra short via. With the frequencies and dimensions
suggested, if an analysis fails the test, it is likely to do so dramatically.

**8) Loss Tests** -- see the section "Lossy Ground
Plane And Lossy Dielectric Tests" in Chapter 8. In many designs, accurate calculation
of ground plane loss and dielectric loss can be important. These tests demonstrate
precisely how much error there is in the calculation of these quantities.

Please feel free to investigate in detail any of the above tests that you find interesting. Results of these benchmarks as applied to Sonnet are included in this report. As they become available, we will provide results of these benchmarks applied to other electromagnetic software. Contact Sonnet for current information.

**It is our hope that this document will initiate the transformation of the field
of electromagnetic software validation from a subjective hand-waving contest to one where
precise, quantitative evaluation of error is held in high regard.
Suggestions of additional benchmarks which can further this goal are welcome.**