Effect of ZnO-PCL Nanocomposite Thickness on Attenuation in a

Transcription

Journal of Microwave Power and Electromagnetic Energy, 49 (2), 2015, pp. 112-118.
A Publication of the International Microwave Power Institute
Effect of ZnO-PCL Nanocomposite
Thickness on Attenuation in a
Rectangular Waveguide at Microwave
Frequency using FEM
Abubakar Yakubu, Zulkifly Abbas
Departament of Physics, Universiti Putra, Malaysia
Nor Azowa Ibrahim
Department of Chemistry, Universiti Putra, Malaysia
Received: January 9, 2015
Accepted: June 1, 2015
ABSTRACT
Presented in this work is an essential and basic approach to compute the attenuation
of electromagnetic waves propagating through a rectangular waveguides with lossy material
sample placed inside the waveguide. The rectangular waveguide (WR 90) technique is used to
theoretically calculate the attenuation of electromagnetic wave as it interacts with ZnO-PCL
nanocomposites of different sample thicknesses from measurements of transmission /reflection
coefficients in the X-Band. Finite element method (FEM) was also used to calculate attenuation
for the same sample thicknesses at X-Band. Comparison of the attenuation results obtained
from experiment and FEM were analysed. Among other findings, it was found that the composite
with 6.8 mm thickness gave the highest attenuation within the frequency range measured. The
comparative study between the techniques showed close measurement system agreement. The
value of attenuation for the different thicknesses measured showed that the composites is a
good material for microwave low absorption. This material composites can be applied to mobile
communication devices as thin layer circuit board for electromagnetic wave absorption.
KEYWORDS: Rectangular waveguide; transmission coefficients; attenuation; nanocomposites.
INTRODUCTION
Induced currents flowing in the metal walls of waveguides produce losses which can be
calculated from formulae derived on the assumption that the surfaces are perfectly smooth
[Benson and Stephen, 1963; Pomeroy and Suarez, 1956]. This analogy, can be ascribed to a
sample placed inside a rectangular waveguide such that the radiation flowing into the sample
produces losses and the losses can be calculated assuming the sample surfaces are smooth
and placed parallel to the port surface without any air gap. Rectangular waveguides are
employed extensively in microwave and millimeter wave receiver since they are much easier
to manipulate than circular waveguides and also offer significantly lower cross polarization
component [Withington et al., 2003].
The approximate power-loss method has been widely used in analyzing wave attenuation
in lossy rectangular waveguides as a result of its simplicity when the frequency of the signal
112
International Microwave Power Institute
Abubakar Yakubu et al., Effect of ZnO-PCL Nanocomposite Thickness on Attenuation in a Rectangular Waveguide ...
is well above cutoff frequency [Seida, 2003].
In this method, the field expressions are
derived assuming perfectly conducting walls,
allowing the solution to be separated into TE
and TM modes. To calculate the attenuation,
ohmic losses are assumed to exist due to small
field penetration into the conductor walls.
The power-loss method however fails near
cutoff frequency, as the attenuation obtained
using this method diverges to infinity when
the signal frequency approaches the cutoff
frequency. Bladel [1971], and Robson [1963]
reported degenerate modes propagation in
lossy rectangular waveguides, but neither of
them was able to compute the attenuation
values accurately near cutoff. Like the
power-loss method, their theories predict
infinite attenuation at cutoff. An expression
valid at all frequencies is reported by Kohler
and Bayer [1964] which was later re-reported
by Somlo and Hunter [1996]. This expression
however is only applicable to the transverse
electric (TE¬10) dominant mode. However,
no report has been published on analyzing
the guided propagation of electromagnetic
signals through Lossy substrates of different
thicknesses close to the cutoff frequency.
The three principal factors which affect
the attenuation of samples placed in a
waveguide are the internal dimensions of
the waveguide, and the effective resistivity
of the conducting surfaces and size of the
sample used [Abbas, 2001]. The effective
losses depends on the roughness of the
conducting surfaces of the sample, the
radiation, resistivity of the sample, and
the nature of the sample at the excitation
surfaces of the rectangular waveguide.
The roughness of the conducting surfaces
is important because of the increased
path length due to the roughness, since
radiation at microwave frequencies travels
essentially on the surface [Sadiku, 2008].
For this paper, the authors are interested in
investigating the effect of sample thickness
on attenuation close to the cutoff frequency.
We shall in addition show the effects of
sample thickness on the transmission and
reflection coefficients obtained. In our
method, the solution for the attenuation is
found by solving logarithm equations derived
from transmission coefficients values of the
propagating electromagnetic wave through
the waveguide walls and interaction of the
waves on the surface of the composites
placed inside the waveguide.
THEORY AND METHOD
The attenuation in a rectangular
waveguide carrying the normal mode, and
having irregularities on its surfaces which
are, in general, much greater than the skin
depth and closer to the cutoff frequency
can be solved assuming having a sample
with negligible surface roughness, then
attenuation can be expressed as [Khun,
1946; Ajoy and Thyagarajan, 2000];
(1)
Where, Rs is the surface resistivity of the
waveguide material in ohms per square
meter. For a waveguide having nominal
dimensions a and b, then the expression is
given as;
(2)
Where, ∂a and ∂b are the fractional tolerances
on a, and b. The cut-off wavelength is also
affected by a change in b, so,
(3)
Where, m = λc/λcr and λcr is the nominal value.
Substituting the values of Equation (2) and
(3) into Equation (1), attenuation α, can be
written as;
Journal of Microwave Power and Electromagnetic Energy, 49 (2), 2015
(4)
113
Further simplification of Equation (4), will
lead to attenuation becoming;
(5)
Where, αn is the nominal attenuation given
as;
(6)
samples into the waveguide is very essential
so as to avoid air gaps. Figure 1 is a photo of
both a sample placed inside a waveguide and
different sample sizes used in this study.
In
a
transmission/reflection
measurement method, the material under
test is inserted in a piece of transmission
line, and the properties of the material
are deduced on the basis of the rejection
from the material and the transmission
through the material [Bayrakdar, 2011]. This
method is widely used in the measurement
of electromagnetic properties of materials.
Therefore, attenuation would become;
(7)
In dimensional tolerance, attenuation is
given as;
(8)
In the case of the sample placed inside the
rectangular waveguide, the attenuation is
given as;
(9)
Where r is the transmission coefficient
measured from the vector network analyzer.
Equation (9), can be further simplified to
give, [Yakubu et al., 2014];
(10)
EXPERIMENTAL
Different ZnO-PCL nanocomposite
sample sizes were fabricated using the
melt blend and cold press technique with a
hydraulic press at 5 tonnes. The samples were
molded in a mold of dimension of 11.4 mm
by 22.8 mm. This dimension is the dimension
of the WR 90 (rectangular waveguide used
in this study). Precision in the fitting of the
114
Figure 1. Rectangular waveguide filled with ZnO-PCL
sample (top) and prepared different samples sizes
(bottom).
Figure 3. Magnitude of reflection coefficient for all
samples measured.
Figure 2. Scattering parameter measurement set-up.
This is because microwave guides have
field focusing ability which is possible to
make accurate measurements at microwave
frequencies. It is important to note that the
ZnO nanoparticles used in the synthesis of
the composites was prepared via microwave
irradiation technique. After successful
fitting of the samples inside the waveguides,
measurement of the scattering parameter
was then carried out via the vector network
analyser (VNA), Agilent 8570B as shown in
Figure 2. The scattering parameter of the
different samples were further used in the
calculation of attenuation for each of the
samples used in the study. For this study,
sample sizes used are 4.3 mm, 4.8 mm,
6.0 mm, and 6.8 mm thick.
RESULTS AND DISCUSSION
The measured S11 and S21 magnitudes
using rectangular waveguide for the ZnOPCL nanocomposite for different sample
thickness are presented in Figure 3 and 4
respectively. Careful observation on Figure
3 shows that the reflection coefficients
decreases with increasing frequency
whilst Figure 4 showed that S21 increases
as sample thickness and frequency
increases. The sinusoidal-like wave form
in the profile of the S11 was attributed to
the impedance mismatched between the
input impedance of the waveguide and the
surface impedance of the sample as well as
Figure 4. Magnitude of transmission coefficient for all
samples measured.
the characteristic impedance of the coaxial
cable [Pozar, 2009]. While the curve shaped
rabbles in the |S21| measurements were
due to the internal surface roughness of the
waveguide, possibility of air gap between
the sample and the internal walls of the
waveguide, surface irregularity of the ZnOPCL nanocomposite pellets and certain voids
in the sample. In addition, the effect of the
multiple reflections can be clearly seen
in |S21| especially at the lower frequency
range but was significantly reduced with
increasing frequency where the wavelength
is comparable to the sample thickness close
to the cutoff frequency. However, from the
profiles of both |S11| and |S21|, there was
overlapping in the lower frequency ranges,
this might due to the close size ratio of the
materials used although this overlapping was
not observed at the high frequency range.
Table I is the summary for the mean values
of S11 and S21 of the electromagnetic wave in
the frequency range of 8 GHz to 12 GHz for
115
Table I. Summary of mean values of S11 and S21.
Sample Thickness (mm)
S11
S21
4.3
0.587
0.621
4.8
0.570
0.641
6.0
0.518
0.672
6.8
0.407
0.710
the different sample sizes. Increase from
4.3 mm to 6.8 mm of ZnO-PCL nanocomposite
pellets corresponds to a decrement in S11
from 0.587 to 0.407 which represents
18 % decrease in reflection coefficient whilst
the S21 had a 9 % increment. Based on the
result presented in Table I, it is concluded
that the ZnO-PCL nanocomposites are good
electromagnetic wave absorbing substrate
within the frequency range measured.
CALCULATION OF ATTENUATION USING
MEASUREMENT AND FEM
The values of attenuation due to
the ZnO-PCL nanocomposites with different
thicknesses were calculated using Equation
(10). The variation for the different
thicknesses is shown in Figure 5 whilst
Figure 5. Measured attenuation for all ZnO-PCL
nanocomposite samples.
Figure 6 is the comparison of attenuation
from both measurement and calculation
(FEM). Careful observation on Figure 5
showed that the thicker the sample the
higher were the attenuation values. It is
also observed that attenuation increases as
the frequency increases. Liu et al., [2012],
reported the increase of attenuation
as frequency increases. The results of
attenuation obtained from measurement
are in complete agreement with the results
obtained for the S21 magnitude.
The FEM calculated of attenuation
was achieved using a COMSOL version 4.3.
Figure 6. Comparison of measured and calculated attenuation for all ZnO-PCL nanocomposite samples.
116
Table II. Summary of calculated mean attenuation with
respect to sample size for ZnO/PCL nanocomposites.
Sample
thickness (mm)
Attenuation (dB)
Measurement
FEM
4.3
-4.196
-3.619
4.8
-3.917
-3.618
6.0
-3.527
-3.303
6.8
-3.077
-3.042
The software was used to calculate the
transmission and reflection coefficients of
the different nanocomposite thickness. The
result obtained for the scattering parameters
are then used as raw data for the calculation
of attenuation using Equation (10).
Figure 6 is the comparison of attenuation
obtained from both the measurement and
FEM techniques. Evidence from Figure 6
showed that attenuation is dependent on
material sample thickness. As expected for
a rectangular waveguide, the attenuation
increases as the sample thickness increases
for both FEM and measurement techniques.
Generally, there was a good measurement
system agreement between the FEM and
measurement techniques especially at
higher frequency range.
The mean values of attenuation due
to the ZnO-PCL nanocomposite samples were
calculated to be in the range of -4.196 dB to
-3.077 dB using measurement method (VNA)
whilst the mean attenuation of the same
samples using FEM is the range of -3.619 dB
to -3.042 dB.
Table II is the summary of mean
attenuation obtained from both techniques
for the frequency range measured. Based on
Table III. Relative error of attenuation for FEM.
Thickness
(mm)
Attenuation (dB)
Relative
error
Measurement
FEM
4.3
-4.196
-3.619
0.13
4.8
-3.917
-3.618
0.07
6.0
-3.527
-3.303
0.06
6.8
-3.077
-3.042
0.01
the results in Table II, it is concluded that
attenuation is highest for materials with
thickest sizes. As reported by Jurvelin et
al., [2014] and Yamasaki et al., [2014], they
showed that the increase in attenuation
quality of materials increases with sample
thickness.
The entire result showed that there
is a high order of correlation between the
two methods as evident in the calculated
error analysis tabulated in Table III. Based
on analysis carried out, it is suggested that
FEM method is also good in the calculation
of attenuation of material samples at
microwave frequency.
CONCLUSION
In this work, a simple fast and accurate
technique to compute the attenuation of
electromagnetic waves propagating through
a rectangular waveguide loaded with lossy
material was presented. The technique is
based on measuring the transmission and
reflection coefficients, and using the data
to compute the magnitude of attenuation.
The finite element method was also used to
compute the attenuation for materials placed
in a rectangular waveguide. The results
from both techniques were then compared
and analyzed. Our calculated attenuation
curves are in good agreement with the
experimental results for all sample thickness.
An important consequence of this work is
the demonstration that the attenuation
of materials are dependent on the size of
sample used. In other words, attenuation is
higher in sample with larger thicknesses for
electromagnetic waves propagating through
a rectangular waveguide. For the materials
used in the studies, the attenuation obtained
experimentally ranged from -4.196 dB to
-3.077 dB whilst for the calculated (FEM)
attenuation, the value ranged from -3.619 dB
to -3.042 dB. The 6.8 mm thick sample had
the largest attenuation in both instances.
The calculated attenuation of the different
sample thicknesses showed that as the
frequency increases, the attenuation of all
117
the samples also increases in both methods
used. The rectangular waveguide method
is another technique that can be used to
calculate the attenuation of material sample
close to cutoff frequency provided that the
sample is devoid of surface roughness, air gap
between sample and port of the rectangular
waveguide.
ACKNOWLEDGMENT
The authors wish to thank the
Universiti Putra Malaysia (UPM) for its
support and for the provision of enabling
environment to carry out this research work.
REFERENCES
Abbas Z., Pollard R. D., and Kelsall
R. W. (2001) “Complex Permittivity
Measurements at Ka-Band Using Rectangular
Dielectric Waveguide”. IEEE Transactions on
instrumentation and measurement, Vol. 50,
No. 5
Ajoy G. and Thyagarajan K. (2000)
“Fundamentals
of
Photonics:
Optical
Waveguides and Fibers”. University of
Connecticut.
Bayrakdar H. (2011) ”Complex
permittivity, complex permeability and
microwave absorption properties of ferriteparaffin polymer composites”. Journal of
Magnetism and Magnetic Materials, Vol. 323,
p. 1882-1885.
Benson F. A. and Steven D. H. (1963)
“Rectangular-waveguide
attenuation
at
millimetre wavelengths”. PROC. I.E.E., Vol.
110, No. 6.
Bladel J. V. (1971) “Mode coupling
through wall losses in a waveguide”.
Electronics Letters, Vol. 7, p. 178 – 180.
Jurvelin J., Riekkinen O., and
Hakulinen M. (2014) U.S. Patent No.
8,679,019. Washington, DC: U.S. Patent and
Trademark Office.
Kohler M. and Bayer H. (1964) “Feld und
ausbreitungskontante im rechteckhohlrohr
bei endlicher leifahigkeit des wandmaterials”.
Zeitschrift Fur Angewandte Physik, Vol. 18, p.
16 – 22.
118
Kuhn S. (1946) “Calculation of
attenuation in waveguides”.
J. Instn.
Electrical Engrs. 93, Part III A, p. 663.
Liu J., Jackson D. R., and Long Y. (2012)
“Substrate integrated waveguide (SIW) leakywave antenna with transverse slot”. IEEE
Transactions on Antennas and Propagation,
60(1), 20-29.
Pomeroy A. F. and Suarez E. M. (1956)
“Determining Attenuation of Waveguide from
Electrical Measurements on Short Samples”.
IRE Transactions on Microwave Theory and
Techniques, 4(2), 122-129.
Robson P. N. A. (1963) “Variational
integral for the propagation coefficient of
a cylindrical waveguide with imperfectly
conducting walls”. Proceedings of IEEE, Vol.
110, p. 859 – 864.
Sadiku M. N. O (2008) “Elements of
Electromagnetics”. 4th Edition, New-York,
Oxford University Press, America.
Seida O. M. A. (2003) “Propagation
of electromagnetic waves in a rectangular
tunnel”.
Applied
Mathematics
and
Computation, Vol. 136, p. 405 – 413.
Somlo P. I. and Hunter J. D. (1996)
“On the TE10 mode cutoff frequency in
lossy-walled
rectangular
waveguides”.
IEEE Transactions on Instrumentation and
Measurement, Vol. 45, p. 301 – 304.
Withington S., Campbell E., Yassin G.,
Tham C. Y., Wolfe S., and Jacobs K. (2003)
“Beam combining superconducting detector
for
submillimetre-wave
astronomical
interferometry”. Electronics Letters, Vol. 39,
p. 605 – 606.
Yakubu A., Abbas Z. and Hashim
M. (2014) “Effect of Material Thickness on
Attenuation (dB) of PTFE Using Finite Element
Method at X-Band Frequency”. Advances in
Materials Science and Engineering, ID 965912.
Yamasaki J., Mutoh M., Ohta S., Yuasa
S., Arai S., Sasaki K., and Tanaka N. (2014)
“Analysis of nonlinear intensity attenuation
in bright-field TEM images for correct 3D
reconstruction of the density in micron-sized
materials”. Japan Society of Microscopy, Vol.
63 (5), p. 345-355.

Effect of ZnO-PCL Nanocomposite Thickness on Attenuation in a

Transcription

Similar documents

SuDS Case Study – Project Red Dragon, RAF St Athan

Ironman II Mini Product Details

ECHOGRAPH 1095 - karldeutsch.de

Clarity® Earplug

HAZTURK Için Istanbul`da Deprem Sonrasi Yersel Ivme Dagiliminin

waveguide technologies and academics

Omelette

TrueWave® LA Fiber

Atmosphere Attenuation