A novel method based on two different thicknesses of the sample for determining complex permittivity of materials using electromagnetic wave propagation in free space at X-band
VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
A Novel Method Based on Two Different Thicknesses
of The Sample for Determining Complex Permittivity
of Materials Using Electromagnetic Wave Propagation
in Free Space at X-Band
Ho Manh Cuong1,*, Vu Van Yem2
1Electric Power University
2Hanoi University of Science and Technology, Vietnam
Abstract
In this paper, we present a method for determining complex permittivity of materials using two different
thicknesses of the sample placed in free space. The proposed method is based on the use of transmission having
the same geometry with different thicknesses with the aim to determine the complex propagation constant (γ).
The reflection and transmission coefficients (S11 and S21) of material samples are determined using a free-space
measurement system. The system consists of transmit and receive horn antennas operating at X-band. The
complex permittivity of materials is calculated from the values of γ, in turns received from S11 and S21. The
proposed method is tested with different material samples in the frequency range of 8.0 – 12.0 GHz. The results
show that the complex permittivity determination of low-loss material samples is more accurate than that of
high-loss ones. However, the dielectric loss tangent of high-loss material samples is negligibly affected.
Received 04 February 2017; Revised 17 May 2017; Accepted 11 July 2017
Keywords: Complex permittivity, Dielectric loss tangent, Complex propagation constant, S-parameters.
1. Introduction*
measurements such as printed circuit board
(PCB) materials [6-12]. Although the proposed
methods are simple, quick, and reliable to use.
However, it has drawbacks such as the material
samples to determine the complex permittivity
require structures the type printed circuit board.
The measurement of complex permittivity of
material can be made by using the
transmission/reflection method developed by
Weir [13]. The method for determining
S-parameters of material in free space are
nondestructive and contactless; hence, they are
especially suitable for measurement of the
The complex propagation constant is
determined from scattering S-parameters
measurements performed on two lines
(Line-Line Method) having the same
characteristic impedance but different lengths
[1]. Once the parameters are measured either
the ABCD [2] or wave cascading matrix
(WCM) [3-5] may be used for determining
complex propagation constant. The proposed
method for determining complex permittivity of
materials are structure to connected with device
________
complex permittivity
(
ε*
)
and complex
material under
* Corresponding author. E-mail: [email protected]
*
μ
permeability
(
)
of
57
H.M. Cuong, V.V. Yem / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
58
high-temperature conditions. The most popular
thicknesses. Diffraction effects at the edges of
the sample and multiple reflections between the
antennas are minimized by using two different
thicknesses of the sample placed in free space.
Our results indicate that the permittivity of
material is quite stable in the frequency range of
8.0 – 12.0 GHz. In addition, for materials with
dielectric loss tangent less than 0.1, the loss
factor measurements are accuracy in the entire
frequency band.
methods for determining the parameter of
materials are proposed in [14-21]. The errors in
free-space measurements are presumed to be
due to diffraction effects at the edges of the
sample and multiple reflections between the
antennas. Diffraction effects at the edges of the
sample are minimized by using spot-focusing
horn lens antennas as transmitters and receivers.
The method proposed by D. K. Ghodgaonkar et
al. [14] have developed a free-space TRL (thru,
reflect, line) calibration technique which
eliminates errors due to multiple reflections.
This method is especially suitable for quick,
routine, and broad-band measurement of
complex permittivity of high-loss materials.
However, for materials with dielectric loss
tangent less than 0.1, the loss factor
measurements are found to be inaccurate
because of errors in reflection and transmission
coefficient measurements.
The next section describes the theory of our
method in detail. The modeling and results are
presented in section 3. Finally, section 4
concludes this paper.
2. Theory
The complex permittivity of materials is
defined as
ε* =ε, - jε,, =ε,(1- jtanδε )
(1)
In this paper, we propose a method in free
space for determining complex permittivity of
materials based on the use of transmission
having the same geometry with different
where, ε, and ε,, are the real and imaginary
parts of complex permittivity, and tanδε is the
dielectric loss tangent.
T1
X
Y
Antenna 1
Antenna 2
S211
S111
Port 1
Port 2
Free Space
d0
Free Space
d0
d1
(a)
X
Y
T2
Antenna 1
Antenna 2
S221
S121
Port 2
Port 1
Free Space
d0
Free Space
d0
d2
(b)
Figure 1. Schematic diagram of two transmissions (a) and (b).
H.M. Cuong, V.V. Yem / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
59
Figure 1 shows two planar sample of
d1
1
cosh-1 Tr M M -1
1
2
d
> 1 ) placed in free
d
2
thicknesses
and d2
(
2
(8)
γ=
space. For both transmissions (a) and (b), the
determined two port parameters expressed in
ABCD matrix form can be considered as a
Δd
The real part of
γ
is unique and single valued, but
the imaginary part of
defined as
γ
has multiple values. It is
product of three parts: an input matrix
including the input coax-to-antenna transition,
Y
transmission , and an output matrix ,
X
,
T
(Δφ-360n)
(9)
γ= α+ jβ = α+ j
including the output coax-to-antenna transition.
It can be shown that the M1 and M2 matrices
Δd
are the real and imaginary parts
of the complex propagation constant, is an
where
α
and
β
are related to
equations [2]:
X
,
T
and
Y
by the following
n
integer (
), Δφ is the reading of
n=0,±1,±2,
M1 = XT1Y
M2 = XT2Y
(2)
(3)
0
the instrument (
0 ). The phase
-180 Δφ 180
is defined as
constant
β
where Mi
,
X
,
Ti , and
Y
are ABCD matrices
360
β =
ε,
(10)
for the corresponding sections as in the Figure
1. Mi can be related to measurable scattering
λ0
where λ0 is the wavelength in free space.
parameters [22] by equation (4).
The phase shift of complex propagation
constant is the difference between the phase
angle ΔΦ measured with two material sample
between the two antennas, namely:
i
i
i
i
s12s21 - s11s22 si
1
11
Mi =
(4)
i
-s2i2
1
s21
The cascade matrix Ti of the homogenous
transmission line , is defined as
ΔΦ =Φ2 -Φ1
(11)
is the phase angle of
). Consequently the
i
-360di ε,
-γdi
e
0
where Φ =
i
T =
(5)
λ0
i
γdi
0
e
material sample (
i=1,2
phase shift is given by
di
are the complex propagation
where
γ
and
-360Δd ε,
constant and length of the line. Multiplying the
ΔΦ=
(12)
matrix M1 by the inverse matrix of
M
2 , we
(6)
λ0
obtain (6)
On the other hand, it can be expressed from
(9) and (10) as
M1M2-1 = XTT-1X-1
1
2
M1M2-1
ΔΦ= Δφ-360n
(13)
In (6), notice that
is the similar
transformation of
-1 . Using the fact that the
TT2
Measurements at two frequencies can also
be used to solve the phase ambiguity problem
[23]. The frequencies are selected in a region
such that the difference between dielectric
1
trace, which is defined as the sum of the diagonal
elements, does not change under the similar
transformation in the matrix calculation, we can
deduce (7)
ε1,
ε2,
at 2 , is small enough
f
constants,
at f1
,
Tr(M1M2-1 )=Tr(TT-1 )=2cosh(γΔd)
to permit the following assumption, using (12)
and (13):
(7)
1
2
where Δd = d - d is the length difference of
1
2
λ01 Δφ - 360n = λ Δφ - 360n
1 02 2
(14)
1
2
two transmission lines. The complex propagation
constant is found from (8)
H.M. Cuong, V.V. Yem / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
60
where λ01 and λ02 are the wavelengths in free
space at f1 and f2 , respectively, with f1
f2
In figure 2, two same pyramidal antennas
are designed to operate well in the frequency
range of 8.0 – 12.0 GHz. The gain and voltage
standing wave ratio of the pyramidal horn
antennas are 20 dBi and 1.15 at center
frequency. In this model, the distance between
the antenna and the material sample is 250mm
<
,
n1 and n2 are the integers to be determined.
For this purpose, a second equation is needed.
This equation can be
n2 - n1 = k
is an integer.
The integers n1 and n2 can be either equal
k = 0
(15)
where
k
(
d0 = 250mm ).
The two selected material samples have
(
) or different (
) depending on
parameters as follows: The width and length of
150mm, the thicknesses of 7mm and 12mm.
The complex permittivity of material samples:
k =1,2,
the frequency difference and dielectric
properties and thickness of material under test.
Therefore, two cases can be distinguished:
*
*
*
,
,
ε = 2.8- j0 ε = 2.8- j0.14 ε = 2.8- j0.28
*
k = 0
+
+
Δd = 5mm
is the
and
. With
ε = 2.8- j0.84
λ01Δφ1 - λ02 Δφ2
length difference of two material samples. The
frequencies f1 and f2 2 ) are selected in
f1
(16)
n1 = n2 =
360(λ01 - λ02 )
(
<
f
the frequency range of 8.0 – 12.0 GHz. The
results show that in the entire frequency band.
k 0
λ01Δφ1 - λ02 Δφ
λ02
(17)
(18)
n1 =
2 +k
360(λ01 - λ02 )
λ01 - λ02
3.2. Results
with
The reflection and transmission coefficients
of two planar material samples are determined
using the proposed model in section 3.1. The
complex permittivity of material samples is
calculated by equation (19) in section 2.
3.0
n2 = n1 + k
The complex permittivity of the material is
calculated from (7), we obtain
2
cγ
ε* =
(19)
2.5
2.0
1.5
1.0
0.5
0
'=2.8
''=0
''=0.14
''=0.28
''=0.84
j2πf
c
where
f
is the frequency and
is the light
velocity.
3. Modeling and results
3.1. Modeling
8
8.5
9
9.5
10
10.5
11
11.5
12
Frequency [GHz]
In this part, using the Computer Simulation
Technology (CST) software to model system
which presented in section 2, matrix S are
determined from this modeling.
Figure 3. Complex permittivity of material samples
Δd = 5mm
(
).
Figure 3 shows the data obtained using the
proposed method. The real part of the complex
permittivity are quite stable and the mean error
difference of 0.2% in the entire frequency band.
The imaginary part of the complex permittivity
are also stable and small the errors. The error of
complex permittivity for materials with
different dielectric loss tangent as shown in
figure 4.
Figure 2. Modeling determining the parameters of
material sample by CST.
H.M. Cuong, V.V. Yem / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
61
0.5
0.4
0.3
0.2
0.1
0
4. Conclusion
tan=0
tan=0.05
tan=0.1
tan=0.3
We propose a method for determining the
complex permittivity of materials using two
different thicknesses of the sample in free
space. The method consists of two antennas
placed in free space and the two different
thicknesses material samples placed in the
middle of the two antennas. The results show
that the permittivity of material is quite stable
in the frequency range 8.0 - 12.0 GHz. In
addition, the dielectric loss tangent of low-loss
material samples is determined accurately by
using proposed method. Our proposed method
is especially suitable for determining complex
permittivity of low-loss materials.
This method is applicable in many scientific
fields such as: electronics, communications,
metrology, mining, surveying, etc. Because this
method is nondestructive and contactless, it can
be used for broad-band measurement of
permittivity under high-temperature conditions.
-0.1
-0.2
-0.3
-0.4
-0.5
8
8.5
9
9.5
10
10.5
11
11.5
12
Frequency [GHz]
Figure 4. The root mean squared error of dielectric
loss tangent the materials ( Δd = 5mm ).
Figure 4 shows for materials with the
dielectric loss tangent less than or equal to 0.1.
The root mean squared error (RMSE) changes
from 0 to 0.03. When dielectric loss tangent
more than 0.1, the RMSE changes from 0 to
0.08. So, the results show that for materials
with different dielectric loss tangent, the
complex permittivity is nearly identical with the
theoretical values. However, the dielectric loss
tangent more than 0.1, the complex permittivity
is effected by multiple reflections between the
antennas. These errors are small and acceptable
for high-loss materials.
The results show that the complex
permittivity of low-loss material samples
obtained by our method is more accurate than
that calculated by the method proposed in [14].
However, with high-loss material samples, the
root mean squared error of our method is larger
than that of the method in [14].
References
[1] N. K. Das, S. M. Voda, and D. M. Pozar,
"Two Methods for the Measurement of
Substrate Dielectric Constant," IEEE
Transactions on Microwave Theory and
Techniques, vol. 35, pp. 636-642, 1987.
[2] L. Moon-Que and N. Sangwook, "An
accurate broadband measurement of substrate
dielectric constant," IEEE Microwave and
0.05
'=2.8
0.04
''=0
''=0.14
0.03
Guided
pp. 168-170, 1996.
Wave
Letters,
vol.
6,
''=0.28
0.02
''=0.84
[3] R. B. Marks, "A multiline method of network
analyzer calibration," IEEE Transactions on
Microwave Theory and Techniques, vol. 39,
pp. 1205-1215, 1991.
0.01
0
-0.01
-0.02
[4] C. Wan, B. Nauwelaers, and W. D. Raedt, "A
simple error correction method for two-port
transmission parameter measurement," IEEE
Microwave and Guided Wave Letters, vol. 8,
pp. 58-59, 1998.
1
2
3
4
5
6
7
8
9
10
Length difference [mm]
Figure 5. Error versus length difference of two
transmission lines.
[5] J. A. Reynoso-Hernandez, C. F. Estrada-
Maldonado, T. Parra, K. Grenier, and J.
Graffeuil, "Computation of the wave
propagation constant γ in broadband
uniform millimeter wave transmission line,"
Figure 5 shows that the error versus the
length defferences of two transmission lines is
very small, so that the complex permitivity of
material samples is negligibly affected by the
different thicknesses of those samples.
H.M. Cuong, V.V. Yem / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 57-62
62
in Microwave Conference, 1999 Asia Pacific,
vol.2, pp. 266-269, 1999.
[15] E. Håkansson, A. Amiet, and A. Kaynak,
"Electromagnetic shielding properties of
polypyrrole/polyester composites in the
1-18GHz frequency range," Synthetic metals,
vol. 156, pp. 917-925, 2006.
[16] V. V. Varadan and R. Ro, "Unique Retrieval
of Complex Permittivity and Permeability of
Dispersive Materials From Reflection and
Transmitted Fields by Enforcing Causality,"
IEEE Transactions on Microwave Theory and
Techniques, vol. 55, pp. 2224-2230, 2007.
[6] J. A. Reynoso-Hernandez, "Unified method for
determining the complex propagation constant
of reflecting and nonreflecting transmission
lines," IEEE Microwave and Wireless
Components Letters, vol. 13, pp. 351-353, 2003.
[7] Y. Young, "A novel microstrip-line structure
employing a periodically perforated ground
metal and its application to highly
miniaturized and low-impedance passive
components fabricated on GaAs MMIC,"
IEEE Transactions on Microwave Theory and
Techniques, vol. 53, pp. 1951-1959, 2005.
[17] U. C. Hasar, "Unique permittivity
determination of low-loss dielectric materials
from
microwave
transmission
measurements
Progress
at
In
frequencies,"
[8] C. You, Y. Sun, and X. Zhu, "Novel wideband
bandpass filter design based on two
transformations of coupled microstrip line," in
Antennas and Propagation (APSURSI), IEEE
Electromagnetics Research, vol. 107, pp. 31-
46, 2010.
[18] J. Roelvink and S. Trabelsi, "Measuring the
complex permittivity of thin grain samples by
the free-space transmission technique," in
International
Symposium
on,
pp. 3369-3372, 2011.
Instrumentation
Technology Conference (I2MTC), 2012 IEEE
International, pp. 310-313, 2012.
and
Measurement
[9] Q. Xue, L. Chiu, and H. T. Zhu, "A transition of
microstrip line to dielectric microstrip line for
millimeter wave circuits," in Wireless
Symposium (IWS), IEEE International,
pp. 1-4, 2013.
[19] R. A. Fenner and S. Keilson, "Free space
material characterization using genetic
algorithms," in Antenna Technology and
Applied Electromagnetics (ANTEM), 2014
[10] M. A. Suster and P. Mohseni, "An
RF/microwave microfluidic sensor based on a
center-gapped microstrip line for miniaturized
dielectric spectroscopy," in Microwave
Symposium Digest (IMS), IEEE MTT-S
International, pp. 1-3, 2013.
[11] J. Roelvink and S. Trabelsi, "A calibration
technique for measuring the complex
permittivity of materials with planar
transmission lines," in 2013 IEEE
16th
International
Symposium
on,
pp. 1-2, 2014.
[20] N. A. Andrushchak, I. D. Karbovnyk, K.
Godziszewski, Y. Yashchyshyn, M. V.
Lobur, and A. S. Andrushchak, "New
Interference Technique for Determination of
Low Loss Material Permittivity in the
Extremely High Frequency Range," IEEE
Transactions
Measurement, vol. 64, pp. 3005-3012, 2015.
on
Instrumentation
and
International
Measurement
Instrumentation
Technology Conference
and
(I2MTC), pp. 1445-1448, 2013.
[21] T. Tosaka, K. Fujii, K. Fukunaga, and A.
Kasamatsu, "Development of Complex
Relative Permittivity Measurement System
Based on Free-Space in 220–
330-GHz Range," IEEE Transactions on
Terahertz Science and Technology, vol. 5,
pp. 102-109, 2015.
[12] L. Tong, H. Zha, and Y. Tian, "Determining
the complex permittivity of powder materials
from l-40GHz using transmission-line
technique," in 2013 IEEE International
Geoscience and Remote Sensing Symposium
- IGARSS, pp. 1380-1382, 2013.
[22] P. M. Narayanan, "Microstrip Transmission
Line Method for Broadband Permittivity
Measurement of Dielectric Substrates," IEEE
Transactions on Microwave Theory and
Techniques, vol. 62, pp. 2784-2790, 2014.
[23] S. Trabelsi, A.W. Kraszewski, and S. O.
Nelson, “Phase-shift ambiguity in microwave
dielectric properties measurements,” IEEE
[13] W. B. Weir, "Automatic measurement of
complex dielectric constant and permeability
at microwave frequencies," Proceedings of
the IEEE, vol. 62, pp. 33-36, 1974.
[14] D. K. Ghodgaonkar. V. V. Varadan, and V.
K. Varadan. "A free-space method for
measurement of dielectric constants and loss
tangents at microwave frequencies," IEEE
Transactions
on
Instrumentation
and
Transactions
on
Instrumentation
and
Measurement, vol. 49, pp. 56-60, 2000.
Measurement, vol. 38, pp. 789-793, 1989.
6 trang
11480
Free
Bạn đang xem tài liệu "A novel method based on two different thicknesses of the sample for determining complex permittivity of materials using electromagnetic wave propagation in free space at X-band", để tải tài liệu gốc về máy hãy click vào nút Download ở trên
File đính kèm:
- a_novel_method_based_on_two_different_thicknesses_of_the_sam.pdf
