Development of A Temperature Dependent
Dielectric Constant Measurement System
Nan ChenˈBo Gao, Shu Zhou, Yu Tian, Ling Tong
Microwave and Remote Sensing Laboratory, College of Automation Engineering
University of Electronic Science and Technology of China
Cheng Du, China
e-mail: 1299496172@qq.com
Abstract—In this paper, a dielectric constant
measurement system is presented, which can work at
different temperatures from room temperature to 200
.This system is developed based on the theory of NRW
algorithm using coaxial line. The calibration standards
are also designed for TRL calibration. Temperature
distribution is analyzed and optimized carefully using
ANSYS thermal analysis to make sure temperature is
uniform on the test fixture and is safe enough to connect
to Vector Network Analyzer (VNA). Frequency range of
this system is from 1GHz to 18GHz.
Keywords—NRW algorithm; TRL calibration; dielectric
constant
I. INTRODUCTION
With the development of the dielectric material, it
has been played an important role in aerospace,
biomedical and other fields. The value of the material’s
dielectric constant is very important, its variation will
affect characteristics of the systems. So it is very
valuable to develop a system which can evaluate the
variation tendency of dielectric constant at different
temperature.
There are many methods developed to measure
dielectric constant of dielectric material at room
temperature such as NRW method[1,2], free-space
method[3], the open-ended coaxial probe method[4] and
resonant method[5]. Each method has its advantages and
defects. For example, the resonant method provides high
accuracies and suitable for low-loss dielectric materials,
and NRW method is a popular broadband measurement
method.
Following the working frequency and conditions
change, the environment temperature will change. For
example, when aircraft flies at high speed, temperature
of aircraft changes greatly. So, we need to know
dielectric constant of material at different temperatures.
Over the years, several methods proposed for
determining the dielectric constant of microwave
materials at high temperature. The American Society for
Testing and Materials(ASTM)[6] presents shorted
waveguide and cavity perturbation methods. There are
other literatures[7,8] proposed some methods for
determining the dielectric constant of dielectric
materials at high temperature.
In this paper, a dielectric constant measurement
system employing a VNA, NRW method and a TRL
calibration technique, proposed for determining the
dielectric constant of solids at different temperature.
NRW method is used by placing a precisely machined
specimen in a section of waveguide or coaxial line on
account of their relative simplicity and broadband
measurement. In this method, the dielectric constant of
sample is determined from scattering parameters. NRW
method has ill-behaved characteristic for low-loss
material, such as multi-valued, phase jumped and
corresponding to integer multiples of one-half
wavelength at frequency points. In past two decades,
researchers have found several methods to solve these
questions[9,10,11].
II. T
EMPERATURE DEPENDENT DIELECTRIC
CONSTANT MEASUREMENT SYSTEM
A. NRW Method
Fig.1 shows an annular disk of sample with
dielectric constant of H
r
and the length of sample is l. Z
r1
and Z
c
represent the characteristic impendence of
Teflon-filled coaxial line and sample-filled line. The
dielectric constant of materials can be obtained from
following relationships:
22
11 21
22 22
(1 ) (1 )
,
11
TT
SS
TT
* *
* *
(1)
22
2
21 11
21
1
=, 1
2
ss
KKK
s
7 r
(2)
According to the transmission line theory:
2
0
0
2
=
rr
c
j
O
S
JHP
OO
§·
¨¸
©¹
(3)
The work is supported by the National Natural Science
Foundation of China (Grant No. 61201006) and the Fundamental
Research Funds for the Central Universities.
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978-1-4673-7441-5 /15/$31.00 ©2015 IEEE