Improved technique for radar absorbing coatings characterization with rectangular waveguide and numerical modeling

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 4, August 2022, pp. 3827~3837
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i4.pp3827-3837  3827
Journal homepage: http://ijece.iaescore.com
Improved technique for radar absorbing coatings
characterization with rectangular waveguide and numerical
modeling
Abdulkadhim Ameen Hassan1
, Janan Hameed Saadie2
1
Department of Electrical Engineering, Kufa University, Al-Najaf, Iraq
2
Department of Materials Engineering, Kufa University, Al-Najaf, Iraq
Article Info ABSTRACT
Article history:
Received Dec 19, 2020
Revised Mar 20, 2022
Accepted Apr 2, 2022
For materials characterization, several methods have been developed. Most
of them need a sample to be machined prior to testing process. Hence, they
are destructive and cannot be used for in-situ radar absorbing coatings
testing. This requires employing a suitable measurement technique to extract
their electromagnetic properties quickly and accurately. In this paper, the
swept frequency of probe reflection technique is proposed for broadband
nondestructive radar absorbing coatings characterization using finite flange
open-ended rectangular waveguide. The technique is based on the fact that
the frequency of measurement is an independent variable of probe’s
reflection coefficient by which its data set of selected frequency points can
be directly measured in one step by varying the frequency. Finite-difference
time-domain (FDTD) method was adopted to calculate probe reflection
coefficients at different test conditions. Simple interpolation approximation
was employed since they are frequency dependent parameters. Error analysis
was numerically performed to evaluate the influences of both flange size and
coated material thickness on the accuracy of the measurements, which are
carried out on several samples of radar absorbing coatings at X-band to
verify the proposed technique. Comparing with the existing methods, the
proposed technique simplifies and speeds up measurement process and
improves its repeatability and accuracy.
Keywords:
Absorbing coatings
Electromagnetic properties
Finite-difference time-domain
method
Microwave measurement
Rectangular waveguide
This is an open access article under the CC BY-SA license.
Corresponding Author:
Abdulkadhim Ameen Hassan
Department of Electrical Engineering, Kufa University
Al-Najaf, Iraq
Email: abdulkadhim.shlash@uokufa.edu.iq
1. INTRODUCTION
In diverse areas of microwave and millimeter wave’s practical applications, it is required to reduce
electromagnetic waves reflections from metallic surfaces or for shielding. In these situations, radar absorbing
materials made from wideband composite materials coated on metal plates with one layer (or layers) can be
used to solve these problems [1]–[5]. These materials can be designed with specific values of both relative
complex permittivity (εr) and relative complex permeability (µr) such that they can effectively absorb
electromagnetic wave energy either over broadband or at discrete points of frequency band. For the cases
when it is required to study the frequency dependence of reflections from the designed radar absorbing
coatings or where damage or misapplication of radar absorbing coating, the in the field testing is essential to
evaluate their performance over the operating frequency range [6]. Hence, it becomes necessary, in these
situations, to develop measurement techniques to achieve these purposes in a convenient way quickly and

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 4, August 2022: 3827-3837
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accurately. The microwave usage for industrial testing is increased due to its ability in accurately performing
frequency dependence measurement of material's electromagnetic properties (εr and µr). For materials
characterization, several techniques have been developed to extract simultaneously εr and µr such as cavity
resonator method, free space method [7], reflection/transmission method [8] and methods of transmission
lines [9]. Most of these methods need a sample to be machined prior to testing process and, hence, they are
destructive and cannot be used for in-situ testing of radar absorbing coatings due to their metallic structures,
which limit testing process using the aforementioned methods. However, practically, radar absorbing
coatings need to be tested or characterized as fabricated. This can be done by employing measurement
technique suitable to extract these parameters using a probe, which provides the necessary conditions of such
applications of measurements. Currently, radar absorbing coatings are characterized by directly measuring
the reflection coefficient using horn antenna from reflected wave of a plane wave incident normally on
coatings at a given frequency point [10]. The drawback of this method is that the horn antenna should be
carefully designed in order to obtain approximated plane wave at the aperture of the antenna. To the best
knowledge of the author, no appreciate work is available in the open literatures used for broadband testing of
radar absorbing coatings indirectly except [11], [12] where instead of determining these parameters from the
measured reflection coefficients, a loading fraction table is utilized to determine both εr and µr. Despite that
the method is indirect, a relationship between εr and µr and the loading fraction should be prepared at each
frequency point prior to the measurement process.
Because of the metallic structure and high loss nature of radar absorbing coatings, there are several
advantages which make using of open-ended rectangular waveguide probe suitable to perform nondestructive
in-situ radar absorbing coatings testing. The openness in its structure and a relatively handling high power are
the most important reasons. This probe was investigated both in theoretical and technical by many interests
and used for nondestructive measurement of both εr, µr of high-loss sheet composite materials at single
frequency points, among the others [13]–[20]. Also, in the most of theoretical formulations, the probe
reflection coefficient, symbolized as Γ (f, a, b, d, εr, µr), has been developed analytically under the
assumption that the probe flange is infinitely large, which cannot be physically realized. For practical use, the
flange size of the probe is finite in length. Hence, to ensure measurement accuracy, an alternative numerical
technique can be employed, instead, to obtain a better approximation of determination of probe reflection
coefficients, where using analytical methods, in this case is too difficult.
The objective of this paper is to present a technique for in- situ broadband simultaneously εr and µr
determination of radar absorbing coatings with single layer using reflection-only flanged rectangular
waveguide probe placed in close contact with test material. The fact on which the technique based is that the
probe reflection coefficient is a complex function of different variables; the most important of which is the
measurement frequency (f). Consequently, a broadband measurement process can be performed by varying
measurement frequency in one step on the same sample using frequency sweep measurement of probe
reflection coefficients over the entire of the given frequency band. The probe reflection coefficient is
numerically formulated using finite-difference time-domain (FDTD) method to calculate reflection
coefficients seen by the probe aperture at different measurement conditions. Simple interpolation
approximation is employed to reconstruct εr and µr of tested material from two measured independent
reflection coefficients of two neighbor points of frequency since they are frequency dependent parameters.
Also, FDTD simulation is performed to analyze the probe flange size and coated material thickness
influences on accuracy of reflection coefficient measurement. The extraction of these parameters is
performed iteratively using optimum cost function. The results of experiment of εr and µr are presented for
several radar absorbing coatings to demonstrate the validity and feasibility of the proposed technique.
2. PRINCIPLES OF THE MEASUREMENT
Figure 1 depicts the problem configuration, where a rectangular waveguide probe with the broad
and narrow dimensions (a and b) connected to finite size flange is placed against single layer radar absorbing
coating as test material with unknown EM-properties (εr and µr) and known thickness d. Assuming the
dominant TE10 mode is excited inside the waveguide, the measured probe reflection coefficient (ρ) is
described using (1) [16]:
𝜌 = 𝛤(𝑎, 𝑏, 𝑓𝑖 , 𝜀𝑟(𝑓), 𝜇𝑟(𝑓), 𝑑) (1)
It is clear in from (1) that the measured probe reflection coefficient is governed by more than one variable.
This makes the probe reflection coefficient to be a complicated function of probe dimensions (a and b),
measurement frequency (f), the test material thickness (d) and both complex permittivity εr (f)=ε'(1-jtanδε)
and complex permeability µr (f)=μ'(1-jtanδµ). For multi-parameter measurement, the associated mathematical

Int J Elec & Comp Eng ISSN: 2088-8708 
Improved technique for radar absorbing coatings characterization with… (Abdulkadhim Ameen Hassan)
3829
truth states that if there are n unknown to be determined, it needs to perform n measurements even to obtain
one of them. Hence, the extraction process of εr and µr of test material using reflection-only probe requires
measuring at least two complex reflection coefficients performed at two different conditions of testing. Based
on (1), different techniques have been proposed to measure probe reflection coefficient, via changing sample
thickness (d) or via changing part of test material or changing measurement frequency (f). These methods are
called thickness-varying method (TVM) and sample-varying method (SVM) [13] and frequency-varying
method [21] respectively. Each method has its own advantages and drawbacks making each one suitable to
meet a certain measurement requirement. In general, these methods cannot be employed for testing radar
absorbing coatings due to its metallic structure limitation. In this work, frequency sweep technique is
proposed to measure probe reflection coefficients by changing measurement frequency (f) for broadband εr
and µr parameters determination of radar absorbing coatings. The proposed technique allows to measure
reflection coefficients data sets in one step over a given frequency range at two different test conditions for
each frequency point. In his regard, the measurement frequency (f) is varied such that for a given frequency
point (fi), the required two reflection coefficients are measured at two adjacent frequencies fi and fi
'
respectively. These two frequencies must be spread from each other by a certain frequency interval (∆f) such
that the two measured reflection coefficients contain at least partly different information and can be
distinguished by network analyzer. The set of the two simultaneous equations, which represents the measured
reflection coefficients, can be described using (2) and (3).
Figure 1. Configuration of the problem
𝜌1 = 𝛤(𝑓𝑖, 𝜀𝑟(𝑓𝑖), 𝜇𝑟(𝑓𝑖), 𝑑 (2)
𝜌2 = 𝛤(𝑓𝑖
′
, 𝜀𝑟(𝑓𝑖
′
), 𝜇𝑟(𝑓𝑖
′
), 𝑑) (3)
𝑖 = 1,2,3, . . . . . 𝑁
where fi
'
= fi+Δf, ρ1 and ρ2 are the measured reflection coefficients at fi and fi
'
respectively and N is frequency
the points number. Most commonly, the material EM-properties are numerically extracted by imposing the
measured probe reflection coefficient (Γmeas) to the theoretical calculated one (Γthy) by iterative optimization
techniques using (4):
𝛤
𝑚𝑒𝑎𝑠(𝑓𝑖, 𝜀𝑟(𝑓), 𝜇𝑟(𝑓), 𝑑) = 𝛤
𝑡ℎ𝑦(𝑎, 𝑏, 𝑓𝑖, 𝜀𝑟(𝑓), 𝜇𝑟(𝑓), 𝑑) + 𝛾𝑖 (4)
where γi is the measurement error, which is frequency dependent and the other symbols defining are
pictorially depicted in Figure 1. In general, the proposed technique is based on two facts to perform
broadband reconstruction of both εr and µr of radar absorbing coatings. Firstly, as can be seen in (1), that
frequency of measurement is an independent variable, hence, the reflection coefficient can be changed by
changing frequency of measurement. Secondly, for most of solid materials, both εr(f) and µr(f) themselves
are functions of measurement frequency, which may vary slowly or rapidly with the frequency depending on
the nature characteristics of radar absorbers. Therefore, simple approximation interpolation technique is
introduced in εr and µr reconstruction process to improve the accuracy of measurement from reflection data

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3830
of the frequency sweep. Considering two facts, both εr(f) and µr(f) can be reconstructed from the two
reflection coefficients measured at fi and fi
'
respectively by using the following simple interpolation
approximation:
𝜀𝑟(𝑓𝑖) ≈ 𝜀𝑟(
𝑓𝑖+𝑓𝑖
′
2
) ≈ 𝜀𝑟(𝑓𝑖
′
) (5)
𝜇𝑟(𝑓𝑖) ≈ 𝜇𝑟(
𝑓𝑖+𝑓𝑖
′
2
) ≈ 𝜇𝑟(𝑓𝑖
′
) (6)
It is clear from (5) and (6) that in order to identify probe reflection coefficients at two neighbor frequencies fi
and fi
'
, an appropriate frequency interval should be with a value to produce enough change between these two
reflection coefficients so that they can be distinguished by network analyzer. Also, it should be selected as
small as possible to obtain improvement in the accuracy of the measurement. It is to be noted that the
frequency interval with appropriate value can be determined using rule-of-thumb or by the analysis of
sensitivity and numerical simulation.
3. REFLECTION COEFFICIUENT FORMULTION
3.1. Using analytical methods
It is apparent in (4) that the accuracy of εr and µr extraction depends on how accurately the
theoretical reflection coefficient is formulated. For rectangular waveguide probe, the formulations of
reflection coefficient are analytically developed using different analytical approaches under the assumption
of infinite size of probe flange. The probe reflection coefficient using the existing spectral-domain analysis
(SDA) [22] developed to extract complex relative permittivity (εr) of materials is considered for this purpose.
The problem geometry using this analytical approach is shown in Figure 1, where a radar absorbing coating
characterized by both εr and µr is to be tested using rectangular waveguide probe whose open end, in this
case, is cut into a metal flange with size assumed to be infinitely large. Considering only TE10 mode, the
probe aperture normalized input admittance Yn is given by:
𝑌𝑛 =
𝑌𝑎
𝑌𝑜
=
𝑗
(2𝜋)2𝜇√1−(
𝜆𝑜
2𝑎
)
2
[∫ ∫ ℑ{(𝜀𝜇 − 𝑅2
𝑐𝑜𝑠2
𝜃
2𝜋
𝜃=0
∞
𝑅=0
) (2𝐶𝜑 +
𝐽ℑ
𝑥𝑧
)}𝑅𝑑𝜃𝑑𝑅] (7)
where Ya is probe aperture admittance and Yo is the unbounded medium admittance, d is the coating material
thickness, ε and µ are EM properties of test material and a and b are the dimensions of the probe. The
reflection coefficient (Γ) seen by the aperture of the probe can be calculated using (8):
𝛤 =
1−𝑌𝑛
1+𝑌𝑛
(8)
The theoretical complex reflection coefficient of the probe is calculated using (7) and (8) respectively.
3.2. Using FDTD method
For the problem under study using probe with a flange of finite size, numerical modelling based on
FDTD method was adopted to calculate probe reflection coefficient since using of analytical method, in this
case, is quite difficult. The problem FDTD computational domain is illustrated in Figure 2. It consists of two
regions, the interior of waveguide which is air-filled region and exterior region represented by the test
material backed by metal plate. The medium of each region is characterized by constitutive parameters ε and
µ, which is assumed to be isotropic, linear, homogenous, and source-free (J=0). The interior walls and the
flange of the probe are assumed to be made from a perfect conducting material with its center chosen as the
origin of the 3D Cartesian coordinates. It is also assumed that only the TE10 dominant mode signal is used to
excite the waveguide propagating in the positive z- direction from the excitation plane. The interaction of the
near field at the probe aperture with the test material is described by the time domain set of Maxwell’s curl
equations using (9) and (10):
𝜇
𝑑𝐻
𝑑𝑡
= −𝛻𝑥𝐸 (9)
𝜀
𝑑𝐸
𝑑𝑡
= 𝛻𝑥𝐻 (10)

3831
where E and H denote the electromagnetic field vectors components. Following the standard FDTD
procedure developed by Yee [23], the FDTD computational domain is divided into spatial grids of 3D
orthogonal cubic shape with a unit cell of Δx, Δy, and Δz positioned at (i, j, k) respectively. The condition for
stability in FDTD algorithm for 3D should satisfy courant condition using (11):
𝑣𝛥𝑡 ≤ [
1
𝛥𝑥2 +
1
𝛥𝑦2 +
1
𝛥𝑧2]−1/2
(11)
where v is the medium light velocity and Δt is time increment. In this work, for time-marching system to be
stable and to avoid aliasing, both spatial and time intervals have been chosen to satisfy (11). In order to
increase FDTD method efficiency, the open boundary of the problem simulation is truncated using absorbing
boundary conditions (ABCs). For the problem under study, Mur absorbing boundary conditions [24] are
adequate to be employed to truncate the radial boundary of the computational domain because the radiation
from the probe is limited. A Gaussian pulse was used as excitation source to illuminate the computational
domain with the envelope given by:
𝐺(𝑡) = 𝐸𝑥𝑝 {−[
(𝑛𝑐𝛥𝑡−𝑇𝑜
𝑤
]2} (12)
where To is the time offset and w is the pulse width parameter. The sampling point of the fields is chosen to
be located a way from the probe open end to avoid the modes of high order, which may exist due to
discontinues between the different interfaces. The constitutive parameters values of different media are
averaged at the boundary of the interface between test material and the probe region. The reflection
coefficient of the probe (Γ) seen by the probe aperture is calculated using (8) when the fields steady-state
condition is reached.
Figure 2. The problem FDTD computational domain
4. NUMERICAL ANALYSIS
The FDTD formulation of the probe complex reflection coefficient performed in the previous
section is numerically calculated using a developed code with 3D. The obtained results are to be validated
and verified by comparing with the data obtained experimentally and analytically. The complex reflection
coefficient (Γ=|Γ|eϕΓ
) results of FDTD simulation using X-band waveguide radiating into a radar absorbing
coating is compared first with the experiment results and then with the results obtained analytically
developed based on spectral-domain analysis model using (7) and (8) respectively. The test material used was
GEC-9052 radar absorbing coatings with complex permittivity of (18.18-j0.418) and complex permeability
of (1.55-j1.984) and 1.22 mm thickness. The obtained results in polar format are shown in Figure 3. It shows
that the FDTD simulation results agree well with the measured data validating the computational tool. On the
other hand, the spectral domain model results show a discrepancy with both FDTD simulations results and

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the measured data. The reason for this discrepancy may be due to the way by which the spectral domain
analysis model formulation was developed. Practically, the probe flange used is with finite size of 50 mm
dimension [25], thusly a computational error can be introduced in the probe reflection coefficient results
compared to the results of measured ones. This error contributes to the overall error of εr and µr extraction
process.
Figure 3. Comparison of the complex reflection coefficients calculated using FDTD method and spectral
domain analysis model results versus measured results
An analysis was accomplished to numerically evaluate the flange size of the probe influence on
reflection coefficient measurement for two cases. The first case considered is the variation of measurement
frequency while the second case considered is the variation of both εr and µr of lossy material under test.
Figure 4 illustrates the reflection coefficient magnitude variation of the probe loaded by high loss material as
the size of the flange varies from minimal value (30 mm) to the largest considered value (70 mm) calculated
at two different frequencies of 9 GHz and 12 GHz, respectively. From the figure, it is clear that the reflection
coefficient magnitude shows variation at 12 GHz less than the variation obtained at 9 GHz. This is due to
increasing of the losses of radiation at high frequencies. Also, it is obvious that the magnitude variation of the
reflection coefficient becomes duller for flange size greater than 50 mm (for the case of 9 GHz frequency).
Figure 4. Reflection coefficient magnitude variation with size of probe flange
Figure 5 shows the deviation in percentage in the calculated magnitude of reflection coefficient
(relative to that calculated for the case when infinite flange probe is used) due to variation of normalized
probe flange size to the wavelength inside the test material. In this analysis, two different lossy materials
were considered. They are generally lossy material and high loss material. The simulation was performed at
-0.5
-0.4
-0.3
-0.2
-0.45 -0.4 -0.35 -0.3
Imaginary
Part
Real Part
FDTD Method
SDA Method
Measured

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frequency of 10 GHz using 1.2 mm thickness for each sample. It is obvious from the figure that the reflection
coefficient deviation decreases for material of high loss as compared to that for the generally lossy material.
The analysis results obtained show that for generally lossy material, the dimension of the flange at least
chosen to the distance as large as possible at which the field has negligible decay. For high loss materials,
due to the fact that the electromagnetic field is greatly depressed and distributed over a limited distance
around the waveguide aperture consequently, a probe flange with adequate dimensions can be practically
used. In fact, both the flange of the probe in conjunction with backing metal plate guide the wave inside the
test material toward its edges acting as parallel transmission line. For thin or low loss material, using finite
size of probe flange may cause a significant inaccuracy in the measurement due to the spurious reflection at
the test material edges. However, for high loss materials the finite size of flange influence on measurement is
less because the distribution of EM fields is with a limited distance around the aperture of the probe
consequently. A definite dimension of the flange can practically be used. The results of FDTD analysis
showed that the probe can be designed with flange size adequate to obtain the desired measurement accuracy
of both εr and µr depending on the nature characteristics of the material to be tested and the frequency of
measurement.
Figure 5. The reflection coefficient magnitude variation with flange size for different materials
5. EM-PARAMETER EXTRACTION
The extraction process is used to retrieve or estimate both complex εr and µr of a test material by
inverse problem. This is necessary since the forward theoretical formulations developed for probe reflection
coefficients are noninvertible directly in a straightforward fashion. Thus, numerical search algorithms are
iteratively used to extract them by fitting the measured reflection coefficients to the theoretically calculated.
To determine both εr and µr simultaneously, it makes the problem of 2-parameter extraction (εr and µr).
Mathematically, the truth associated with the multi-parameter measurement states that if there are n
parameters to be determined, it needs to measure n reflection coefficients even though only one of these
parameters is needed to be determined. Hence, in order to extract both εr and µr, at least two complex
reflection coefficients are needed independently measured under two conditions of testing. Using the
proposed technique, the two reflection coefficients for a given frequency point fi are measured at two
different frequencies fi and fi
'
by varying the frequency of measurement in one step for all selected frequency
points (i=1, 2, 3, …, N) over the given range of frequency. It is to be noted that the selection of fi and fi
'
should satisfy (5) and (6) respectively. The extraction of both εr and µr is numerically performed by fitting
the measured reflection coefficients (Γmeas) to the calculated ones (Γcalc), for two conditions of testing using
(13) and (14).
𝛤
𝑚𝑒𝑎𝑠(𝑓𝑖, 𝜀𝑟, 𝜇𝑟, 𝑑) = 𝛤
𝑐𝑎𝑙𝑐(𝑓𝑖, 𝜀𝑟, 𝜇𝑟, 𝑑) + 𝛾𝑖 (13)
𝛤
𝑚𝑒𝑎𝑠(𝑓𝑖
′
, 𝜀𝑟, 𝜇𝑟, 𝑑) = 𝛤
𝑐𝑎𝑙𝑐(𝑓𝑖
′
, 𝜀𝑟, 𝜇𝑟, 𝑑) + 𝛾𝑖
′
(14)
Consequently, for given Г, εr and µr are computed from (13) and (14) using two-dimensional search
algorithms such as the Evenberg-Marquardt or Newton-Raphson algorithms. The solutions of (13) and (14)
suffer from the possibility of obtaining to the local minima convergence. In order for the solution to be

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converged with global minima using the available search algorithms, the difference between the measured
and the calculated reflection coefficient of the optimum cost function (F) should be minimized using (15):
𝐹 =
1
𝑁
∑ |𝛤
𝑚𝑒𝑎𝑠(𝑎, 𝑏, 𝜀𝑟, 𝜇𝑟, 𝑓, 𝑑) − 𝛤
𝑐𝑎𝑙𝑐(𝑎, 𝑏, 𝜀𝑟, 𝜇𝑟, 𝑓, 𝑑)|
𝑁
𝑖=1
2
(15)
For both (13) and (14) over a given frequency band of interest. In this work, Newton-Raphson method was
employed to extract both εr and µr of radar absorbing coatings.
6. EXPERIMENATAL RESULTS
The numerical analysis based on FDTD method was experimentally verified using the measurement
system shown in Figure 6. A thru-reflect-line calibration method was used to calibrate X-band rectangular
waveguide [26]. Different samples of radar absorbing coatings were tested by employing the proposed
technique to extract both εr and µr using vector network analyzer (HP8510B). To verify the probe flange size
influence on εr and μr measurement, probe with different flange sizes were used. Table 1 shows the measured
values of εr and μr of X1 sample radar absorbing coating with 2.08 mm thickness. The results were obtained
using both spectral domain analysis model for the case of infinite extend of the probe flange and FDTD
modeling for probe with 40 mm and 50 mm flange sizes respectively. The measurement was performed at
frequency of 10 GHz. As expected, it is clear that the discrepancy in the measured values of εr and μr
obtained using spectral-domain model are higher compared to the published data [13]. This discrepancy in
the measured results is reasonable due to that analysis model and FDTD method for different probe flange
sizes at f=10 GHz (Δf=0.3 GHz) the assumption of an infinite extension of the probe flange was made in the
formulation of the reflection coefficient. For FDTD modeling of the problem, the results of 50 mm flange
size agree well with the published data while for 40 mm flange, the FDTD results show a small discrepancy
with published data. This discrepancy is produced due to the influence of using small size of probe flange
(less than the required size) resulting in presence of more scattering at the edges of the probe aperture by
which the reflection coefficient is highly affected.
Figure 6. Measurement system
Table 1. The measured results of εr and µr of X1 radar absorbing coating obtained using spectral domain
Flange size (mm) Method ε'
40 FDTD 10.74 -0.006 1.29 0.65
50 FDTD 10.63 -0.005 1.33 0.64
Infinite SDA 11.53 -0.016 1.24 0.83
Reference (13) 10.40 -0.005 1.35 0.64
Another set of experiments were carried out using the proposed technique to study the frequency
dependence of both εr and μr of radar absorbing coatings over given frequency range. The results of the
extracted εr and μr values of MF-116 radar absorbing coating with 1.4 mm thickness are presented in
Figure 7. The real parts variations of both εr and μr with frequency are shown in Figure 7(a) while the
variations of their loss tangents are shown in Figure 7(b). A good agreement can be observed between the
results of measurement and the data provided by Eccosorb® MF technical bulletin. Another important
parameter that should be taken into consideration when performing testing of radar absorbing coating is test
material thickness. To achieve this purpose, three thicknesses of X2 sample radar absorbing coating of
1.22 mm, 3.66 mm and 6.10 mm were selected for this test performed over a given frequency range and the
results are illustrated in Figure 8. The variations of the extracted real part of both εr and μr with the frequency
are shown in Figure 8(a) whiles Figure 8(b) shows the variations of the extracted their loss tangent. It shows

3835
that the extracted values of the real and imaginary parts of both εr and μr of the test material with 1.22 mm
and 3.66 mm thicknesses agree well with the data provided by manufacture especially for real parts, although
the results show a tendency of differences between them especially real part of εr. This is due to thin sample
since the test material is backed by a conductor, a strong interrogation between the magnetic field and test
material is produced resulting a relatively accurate measured result of μr while a weak interrogation between
the electric field and test material is produced resulting a relatively inaccurate measured result of εr. Also, it
can be observed that the test material thickness affects the accuracy measurement of εr and μr especially loss
tangent of εr. A relatively large deviation in tanδε of 6.10 mm thickness sample results was obtained; whose
values become the minus compared with 1.22 mm and 3.66 mm thicknesses samples results. It is to be noted
that the test material used in the measurement has 𝑡𝑎𝑛𝛿𝜀 = 0.06. The obtained results from this study show
that the tested material loss factor value and its thickness are the dominant reasons that influencing the
accuracy of measurement such that obtaining a reasonable accuracy in the measurement becomes difficult for
thick sample whose 𝑡𝑎𝑛𝛿𝜀 ≤ 0.1. For high loss material, this is because of decreasing of reflections as the
test material thickness increases. In general, for high loss materials, it is the inherent limitation of reflection-
only method that it suffers poor accuracy in the measurement for low values of their loss factor. Also, the
thickness measurement of radar absorbing coatings becomes poorer for thick samples. Hence, it becomes
necessary that the test material thickness is properly chosen to obtain the required accuracy in the
measurement using the proposed technique.
(a) (b)
Figure 7. Frequency dependence of complex permittivity and complex permeability of MF-116 radar
absorbing coating ∆f=0.250 GHz (a) real parts and (b) imaginary parts
(a) (b)
Figure 8. Frequency dependence of complex permittivity and complex permeability of X2 radar absorbing
coating for different sample thicknesses, ∆f=0.250 GHz (a) real parts and (b) Imaginary parts

 ISSN: 2088-8708
3836
7. CONCLUSION
In this paper, a new technique of swept-frequency with interpolation approximation is introduced for
simultaneously broadband in-situ εr and μr of radar absorbing coatings determination using open-ended
rectangular waveguide probe. The goal is to develop a technique to achieve this purpose in a convenient way,
where using the existing methods becomes impossible or quite difficult. Also, the probe reflection
coefficients of finite dimensions of the flange directly placed on the material to be tested is successfully
calculated and analyzed for different test conditions using FDTD method, where it becomes difficult to be
analytically formulated. The successful results of experiments validated by the published data and
corresponding data provided by companies illustrate good prospects and feasibility of the proposed technique
for in-situ EM-properties characterizing and testing of radar absorbing coatings. Also, the obtained results
showed that both flange size and thickness of coated material are the limiting factors in the accuracy of
measurement. The main feature of the proposed technique is that it needs only one frequency sweep of
reflection coefficients measurement data set over a given band of interest, and thus, speeds up and simplifies
the process of measurement. Furthermore, this technique improves the measurement accuracy and its
repeatability compared to the other methods currently employed for testing radar absorbing coatings. The
proposed technique can be extended to perform measurement of multi-parameter such as simultaneously
determination of εr, μr and thickness of radar absorbing coatings, which will be considered in the near future.
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BIOGRAPHIES OF AUTHORS
Abdulkadhim Ameen Hassan received the B.S. Engineering degree in 1980
in Electrical Engineering (Electronics and Communications) from Mosul University, Iraq,
in 1980. He then obtained his M. Engineering degree (Electronics) from University of
Technology Iraq, from 1981 to 1983 and Ph.D. degree (Communications and Information
Engineering) from Shanghai University of Science and Technology China in 2000. From
2000-2002, he was a visiting professor at United Arab Emirates University and at Ajman
University of Science and Technology for the period from 2003 to 2006. He worked as a
lecturer at the Institute of Applied Technology, United Arab Emirates for the period from
2007 to 2010. From 2011 to 2013, he was a lecture at Electronics and Communications
Engineering Department, College of Engineering, Kufa University, Iraq. From 2014 to
2018 he was the Head of Electrical Engineering Department, College of Engineering, Kufa
University, Iraq. Since 2015, he has been an Assistant Professor in Kufa University. He is
currently a professor in the Department of Electrical Engineering, Faculty of Engineering,
Kufa University Iraq. His research interest includes the areas of Microwave Theory and
Techniques and Microwave Measurement Techniques. He can be contacted at email:
Email: abdulkadhim.shlash@uokufa.edu.iq.
Janan Hameed Saadie received B.Sc. degree in 1994 from the University of
Technology, Iraq, in materials science. In 2003 received the M.Sc. degree in materials
science, thin films, from the same University, Iraq. She is currently an Assistant Professor
at the Department of Materials Engineering at Kufa University, Iraq. Her research interests
includes the areas of thin films, composite materials and nanomaterials. She can be
contacted at email: jenan.saadie @uokufa.edu.iq.

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