UA-CAD – A Tool for Creating Broadband Material Models for Single-Ended
Transmission Lines
Lionelle F. Wells, Kathleen L. Melde
Center for Electronic Packaging Research
The University of Arizona
Tucson, AZ 85721-0104
(520) 626-2538
melde@ece.arizona.edu
Abstract
A tool is developed in MATLAB to extract frequency-dependent material parameters from Sparameter measurements of a pair of single-ended transmission lines. The tool contains a
command-line user interface which is capable of calculating several material quantities for
Coplanar Waveguide (CPW) and stripline given an input set of S-parameter measurements.
These include the complex propagation coefficient, the effective permittivity, and the relative
permittivity. The program is also capable of reading effective permittivity input data to calculate
the relative permittivity. The output data can be plotted as well as written to a file specified by
the user.
I. Introduction
There is a demand in industry for high-speed specialized software to determine the material
parameters of transmission lines in an “as-packaged” configuration. This deliverable report
discusses a software tool is based on a set of guidelines that have been experimentally verified.
While the program functions as a stand-alone tool for analysis of measurement data, it is also
written in such a way that it can function as a major component in a larger commercial software
tool. The input to the the software is a set of S21 measurements as a function of frequency for two
transmission lines having different lengths, or a set of effective permittivity values as a function
of frequency. In order to calculate the relative permittivity of the material, it is also necessary to
input the dimensions of the transmission line. Currently the software is designed to handle CPW
and stripline structures, but will be updated to fully support microstrip line in a future revision.
Section II of this report functions as a manual for the user of this program, Section III gives some
technical details on the implementation of the program, and Section IV contains some
conclusions. Fig. 1 shows the general building block model of the material extraction process.
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1.
Sample Preparation
& Characterization
2.
Wideband Measurements
3.
Determination of Complex
Propagation Coefficient
4.
Determination of
Effective Permittivity
Effective Permittivity to
5.
Relative Permittivity Conversion
6.
Create Causal, Frequency-Dependent Model
For Real and Imaginary Parts of Relative Permittivity
7. Validate and Assess Model Accuracy
8. Improve Model
9.Integrate into Frequency-Domain &
Time-Domain EDA Tools
Fig. 1 Material Characterization and Model Development Flow Diagram
II. Usage of the CAD Tool
A. Input
The command line interface can be started by typing uacad into the MATLAB command
window to run the function in the file uacad.m. The program will first request that the user
specify whether the input file contains S-parameter measurements or effective permittivity
values. The user will then be prompted to enter the names of the file(s), which should be ASCIIformatted and contain frequency data in the first column. The program is designed to handle files
containing a full set of 2-port S-parameter measurements as outputted from a Vector Network
Analyzer (VNA) in MDF or S2P format or alternatively, files containing only frequency and S21
data. Any non-numeric data at the beginning or end of the file will be ignored.
B. User Options
Once the input data has been successfully read, the user is prompted to select the desired output
data. The types of output include the complex propagation coefficient 𝛾, the effective
permittivity 𝜖𝑒𝑓𝑓 , and the relative permittivity 𝜖𝑟 . If the effective permittivity was inputted by the
user, the program will automatically select the option to calculate the relative permittivity. Each
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of the output quantities is frequency-dependent and will be written to the output file of the user’s
choosing. If the option for the relative permittivity is chosen, the user will be prompted for
information about the transmission line. This includes the dimensions of the line as well as the
conductivity of the metal. The default value of this conductivity is 5.8 ∙ 107 𝑆/𝑚 for copper
conductors. In the case of stripline, an assumption is made that 𝜖𝑟 ≈ 𝜖𝑒𝑓𝑓 , so the values of the
relative permittivity will be the same as the effective permittivity values.
C. Output
Once the desired quantity has been calculated, the data are plotted by MATLAB and written to
the output file. The data are written in an ASCII format as comma-separated values with a header
specifying the type of data.
D. Example Files for FR-4
A set of example files have been included in the CAD tool package. These include a set of two
S-parameter measurements for CPW lines and a set of effective permittivity data. Both of these
sets of data are for FR-4 material. The first CPW line (Line #1) has a length of 2.36 mm, while
the second CPW line (Line #2) has a length of 5.07 mm. Running the program and choosing the
option to compute the propagation coefficient will produce the results shown in Fig. 2. The
results for the effective permittivity using the same example data are shown in Fig. 3.
Fig. 2 – Real and imaginary parts of the complex propagation coefficient
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Fig. 3 – Real and imaginary parts of the effective permittivity
The two files containing S-parameters can be used to calculate the relative permittivity by
selecting the appropriate options and entering the dimensions listed in Table I. Alternatively, the
example file containing the effective permittivity can be directly input into the algorithm. After
the dimensions have been entered, the program will produce the plots of relative permittivity as
shown in Fig. 4.
Table I. Dimensions of the CPW lines
Property
Center Conductor Width
Gap Width
Substrate Height
Conductor Conductivity
Size
0.276 mm
0.077 mm
0.787 mm
5.8e7 S/m
Fig. 4 – Real and imaginary parts of the relative permittivity
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III. Technical Details
A. Complex Propagation Coefficient
The complex propagation coefficient is calculated using the two-line method [1], where 𝛾 is
given by:
𝛾=
1
𝐿1 −𝐿2
ln
𝑆21_𝑙𝑖𝑛𝑒1
𝑆21_𝑙𝑖𝑛𝑒2
(1)
where L1 > L2. This is a frequency-dependent quantity that can be split into the attenuation
coefficient 𝛼 and the propagation coefficient 𝛽 according to
𝛾 = 𝛼 + 𝑗𝛽
(2)
The complex propagation coefficient is also used to compute the effective permittivity.
B. Effective Permittivity
The effective permittivity is calculated from the complex propagation coefficient using the
following equation:
𝜖𝑒𝑓𝑓 (𝜔) = −
(𝛾/𝜔)
𝜖0 𝜇0
′
′′
(𝜔)
= 𝜖𝑒𝑓𝑓
(𝜔) − 𝑗𝜖𝑒𝑓𝑓
(3)
It is also possible to input the effective permittivity directly into the program.
C. Relative Permittivity (CPW)
The program calculates the relative permittivity from closed-form solutions found in [2]. A
quasi-static model is used to determine the permittivity as a function of frequency.
IV. Conclusion
A CAD tool was developed for broadband characterization of transmission lines. The tool is
capable of determining the complex propagation coefficient, effective permittivity, and relative
permittivity from an input set of S-parameter measurements for two transmission lines or
determining the relative permittivity values from a set of effective permittivity data.
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References
[1]
Zhen Zhou and K.L. Melde, "Physically-Consistent Broadband Material Model
Generation for Microstrip Transmission Lines," IEEE 16th Conference on Electrical
Performance of Electronic Packaging, pp.175-178, 29-31 Oct. 2007.
[2]
S. Gevorgian, T. Martinsson, A. Deleniv, E. Kollberg, and I. Vendik, "Simple and
accurate dispersion expression for the effective dielectric constant of coplanar
waveguides," IEEE Proceedings on Microwaves, Antennas and Propagation, vol. 144,
no. 2, pp.145-148, Apr 1997.
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