This paper deals with the design of a microstrip line feed toppled T shaped microstrip patch antenna that gives dualband characteristics at 4 GHz and 6.73 GHz respectively. The simulation of proposed antenna geometry has been performed using method of moment based IE3D simulation software. A radial basis function neural network (RBFNN) is used for the estimation of bandwidth for dualband at 4 GHz and 6.73 GHz respectively. In RBFNN model, antenna parameters such as dielectric constant, height of substrate, and width are used as input and bandwidth of first and second band is considered as output of the network. To validate the RBFNN output, an antenna has been physically fabricated on glass epoxy substrate. The fabricated antenna can be utilized in
S
and
C
bands applications. RBFNN results are found in close agreement with simulated and experimental results.
1. Introduction
Microstrip patch antennas (MSAs) have gained attention of researchers due to the topical development in the field of wireless communication. These antennas are in mammoth demand due to their wide range of applications such as mobile, satellite, terrestrial cellular, personal communication systems
[1

3]
etc. Microstrip antennas plays vital role in efficient reception and transmitting of signals in wireless communications. These antennas become more abundant when single antenna can be used for both transmission and reception of the signals, i.e., for dualband operation has two or more than two bands of frequencies. This provoked the researchers to design microstrip patch antenna for dualband operation.
Dualband MSA was first reported by Wang and Lo
[4]
in 1984. Subsequently, plethora of dualband microstrip antennas have been reported
[5

20]
. In dualband microstrip antenna design, determination of bandwidth is a fundamental point because the bandwidth is important parameter of microstrip patch antenna
[21

27]
. Two types of analysis are mostly reported in the literature
[21

27]
for calculating the bandwidth of these antennas. These analysis techniques are numerical and analytical methods. Both these methods have its own limitations. Analytical methods are applicable for few specific shapes of the patch geometry whereas a numerical method is applicable for all shapes of the patch geometry and requires much time for solving the differential equations. Another drawback is that for any minor change in geometry it requires new solution for geometry and thus it becomes time consuming method. To avoid all these difficulties, a novel method is suggested in this paper, which is the application of artificial neural network (ANN) model.
ANNs are suitable models for parameter optimization of microstrip patch antenna. ANN models are computationally much more efficient than EM models (analytical and numerical methods). The ANN provides fast and accurate models for MSA modeling, simulation, and optimization. ANN is computational tools and based on learning strategies. The application of ANN on the field of microstrip patch antenna is very recent. A number of papers
[28

44]
are present in the literature that signifies the importance of ANN in the field of microstrip patch antenna.
This work aims to design a microstrip line feed toppled T shaped MSA for dual frequency operation using radial basis function neural network. In this work RBFNN is used for the optimizing the bandwidth of proposed antenna with respect to used dielectric material. The proposed antenna is physically fabricated for the verification of RBFNN results. The beauty of the proposed work is the combination of simulated, experimental, and ANN results. This paper is organized as follows, section 1 deals with the introduction, and section 2 deals with antenna geometry. Section 3 demonstrates the neural modeling and generation of data. Finally section 4 and 5 hold the results and conclusion of entire study respectively.
2. Antenna Design and Data Generation
In
Fig. 1(a)
, the proposed antenna geometry is shown. A very low loss dielectric substrate glass epoxy with 1.58 mm height,
tan∂
= 0.002, and dielectric constant of
ε_{r}
= 4.7 is used as the substrate for proposed antenna. The patch and ground plane are printed on the top and bottom of the dielectric substrate respectively. The dimension of the ground plane is
L_{g}
×
W_{g}
. The radiating patch is designed and its dimensions are selected so as to achieve dualband characteristics. All the respective values of designing parameters mentioned in
Fig. 1(a)
are given in
Table 1
. The proposed antenna geometry is simulated using IE3D software
[45]
.
Fig. 1(b)
shows the physically fabricated microstrip antenna with ground plane on glass epoxy substrate. Microstrip line feeding is used here for the excitation of antenna geometry.
Design specifications for proposed antenna geometry
Design specifications for proposed antenna geometry
(a) Proposed antenna design; (b) Fabricated antenna
Fig. 2(a)  (b)
shows the current distribution of the proposed antenna at frequencies 4 GHz and 6.73 GHz respectively. From the
Fig. 2(a)
, it is observed that a good amount of current with different length appears on the upper patch and ground plane of the proposed geometry. This different length of currents is responsible for generating dualband resonance frequencies.
Fig. 2(b)
depicted the current distribution at 6.73 GHz and found that, current flowing in two direction on the upper patch and ground plane due to which antenna characteristics improves in good radiation mode.
Current distribution at frequency: (a) 4GHz; (b) 6.73GHz
3. ANN Implementation
The implementation of ANN on above proposed geometry is mainly characterized in two steps; these are generation of data for training and testing, and selection of ANN topology.
 3.1 Data generation
The bandwidth of microstrip patch antenna is mainly depending on the length (
L
), width (
W
), height (
h
), and dielectric constant (
ε_{r}
) of the substrate. Here, three parameters of the antenna are considered as an input for ANN model. In ANN model simulated, theoretical, and measured data can be used for training and testing. The simulated data of the proposed antenna geometry is obtained from method of moment based IE3D simulation software and used in RBF neural network model. Here 55 samples (34 training and 21 testing samples) are generated with the variation of dielectric constant from the range of 2 ≤
ε_{r}
≤ 4.7 and antenna geometry is simulated using IE3D software. Simulated reflection coefficient (S
_{11}
) of the proposed antenna geometry is recorded and their respective bandwidths for dualband are calculated. Whereas the other two parameters
h
and
W
are kept constant.
 3.2 Model selection of artificial neural network
Artificial neural network uses several topologies. The most used topology of ANN are RBF and multilayer perceptron (MLP) neural network because the process of learning in this model (topology) has two stages and both of the stages are made more efficient by using appropriate learning algorithm. So, this is the leading reason of using RBFNN instead of MLPNN in the present work. A three layered radial basis neural network is selected for the estimation of bandwidth of proposed antenna geometry.
Fig. 3
shows the structure of RBFNN model which have three layers. First one is the input layer consist of three source nodes with
ε_{r}
,
h
,
w
as an input function. Another is the output layer which consisting of two computational units with parameters bandwidth of first and second band respectively. Middle one is the hidden layer, which consists of N = 60 numbers of computation units as the size of the training samples and each unit of hidden layer is mathematically described by radial basis function
[46]
.
where
j_{th}
input data point
x_{j}
defines the center of radial basis function and
x
is the dimension of input vector (
x
= 3). Gaussian function is implemented in each hidden layer of the network as shown in
Fig. 3
and defined by
Radial basis function neural network model
where
σ_{j}
is measure of the width of
j_{th}
Gaussian function with center
x_{j}
. In this model, all the Gaussian hidden units are assigned a common width (
σ
).
Fig. 4
shows the number of epochs to achieve minimum mean square errors (MSE) in case of RBF neural network. From the results of
Fig. 4
, it is observed that the level of mean square error is found minimum with 188 numbers of epochs during the training of RBF neural network model.
Number of epochs to achieve minimum mean square errors
4. Results and Discussion
Radial basis function neural network is tested with 21 sets of training data.
Figs. 5

6
show the ANN output for estimated bandwidth with respect to several dielectric constant of the material for first and second band. The values of obtained bandwidth with respect to the dielectric constant have been evaluated at
me
(numbers of neurons in hidden layer) = 25, where all the other parameters, such as
eg
(error goal) = 0.0001,
sc
(spread constant) = 0.01 are kept constant for both of the cases. From these Figs. it is observed that at 25 neurons are in the hidden layer, error is minimized and RBFNN outputs are found in good agreement with the target bandwidth (%).
Bandwidth of first band at 25 neurons
Bandwidth of second band at 25 neurons
To validate the ANN results a tested sample of data is used for fabricating the antenna design as shown in
Fig. 1(b)
. The reflection coefficient and radiation pattern of the fabricated antenna are measured using Agilent N5230 network analyzer and in anechoic chamber respectively.
 4.1 Proposed antenna results
Fig. 7
shows the variation in reflection coefficients with frequency for several heights of the used substrate glass epoxy.
Fig. 7
demonstrates that the reflection coefficients for upper and lower resonance frequencies are shifted towards higher resonance side with decreasing the height from 1.58 mm to 0.25 mm. This change occurs as the substrate height is inversely proportional to the resonant frequency of patch antenna. Characteristics of proposed antenna are summarized in
Table 2
with respect to the variation of different heights.
Antenna characteristics with the variation of substrate height (h)
Antenna characteristics with the variation of substrate height (h)
Reflection coefficient variation for several heights of the substrate
Fig. 8
shows the variation in reflection coefficient with frequency for several dielectric materials. It is observed that the lower resonance frequency is shifted towards higher resonance side with decreasing the value of dielectric constant from glass epoxy to foam whereas higher resonance frequency is shifted towards higher resonance side. From the
Fig. 8
, it is clear that the obtained bandwidth is wider for Bakelite (
ε_{r}
= 3.3) and RT Duroid (
ε_{r}
= 2.32) substrate than the comparison of glass epoxy substrate. In this work, substrate used is glass epoxy and the reason behind selecting this substrate because it is easily available and less costly than the other substrates.
Table 3
shows the summarized data of proposed antenna characteristics with the variation in dielectric constant (
ε_{r}
) of substrate. This data is used for the testing of RBF neural network model and star sign in
Table 3
shows that glass epoxy (
ε_{r}
= 4.7) substrate is used to validate ANN results.
Reflection coefficient variation for several dielectric materials
Antenna characteristics with the variation in dielectric constant (εr) of substrate
Antenna characteristics with the variation in dielectric constant (ε_{r}) of substrate
The reflection coefficient spectrum of proposed antenna is shown in
Fig. 9
. It is evident that the simulated and measured results of reflection coefficient are in good agreement. In measurement, the reflection coefficient for S
_{11}
≤ 10 dB covers dualband at 4 GHz and 6.73 GHz. A nonnoticeable difference occurs between the measured and simulated values of reflection coefficient due to the oddity in fabrication and soldering joint losses which was not included during the simulation. The characteristics of proposed antenna with ground plane and without ground plane are measured and their responses are summarized in
Table 4
.
Fig. 10
shows the plot of gain and efficiency of the proposed antenna.
Reflection coefficient with and without ground plane
Antenna characteristics
Plot of gain and efficiency with frequency
The radiation patterns for
EH
plane with resonant frequencies 4 GHz and 6.73 GHz are represented in
Fig. 11
(a)(b) respectively. The 3dB beamwidth is 56.3° for
Etheta
,
phi
=0° and 67.4° for
Etheta
,
phi
=90° at frequency 4 GHz. The 3 dB beamwidth is 44.6° for
Etheta
,
phi
=0° and 70.1° for
Etheta
,
phi
=90° at frequency 6.73 GHz.
E
plane is measured in
xz
axis and
H
plane is measured in
xy
axis. Comparison of simulated, ANN, and measured results are summarized in
Table 5
.
Radiation pattern at (a) 4 GHz (b) 6.73 GHz
Comparison of simulated, ANN, and measured results for bandwidth
Comparison of simulated, ANN, and measured results for bandwidth
5. Conclusion
In this paper, microstrip line feed toppled T shaped MSA is successfully analyzed using RBF neural network. The antenna operates in dual frequency bands at 4 GHz and 6.73 GHz respectively. The achievement of dualband with substrate glass epoxy is the focus of attention with etched toppled T shaped as a radiator. An RBF algorithm has been successfully developed for the estimation of bandwidth for first and second bands respectively. RBF neural network model results are found quite satisfactory with high accuracy for bandwidth estimation. The reflection coefficient and radiation pattern results obtained are in closed agreement with simulated and experimental results.
BIO
Mohammad Aneesh He received B.Tech degree in Electrical and Electronics Engineering from Uttar Pradesh Technical University Lucknow, India in 2007 and completed his M.Tech degree in Advance Communications System form Sam Higginbottom Institute of Agriculture, Technology & Sciences Allahabad India in 2009. He is presently pursuing Ph.D from Dept. of Electronics & Communication University of Allahabad, Allahabad, India.
Anil Kumar He received B.Tech degree in Electronics and Communication from Gorakhpur University, India in 1999, M.Tech degree in Micro Electronics from Institute of Technology, Banaras Hindu University (BHU), Varanasi, India in 2005, and Ph.D degree from Sam Higginbottom Institute of Agriculture, Technology & Sciences, Allahabad, India in 2013. He is presently working as Associate Professor with the Department of Electronics and Communication, Shiats, Allahabad.
Ashish Singh He received B.Tech degree from B.B.S. College of Engineering and Technology, U.P. Technical University, M. Tech (Electronics Engg.) & pursuing Ph.D. from Dept. of Electronics & Communication, University of Allahabad.
Kamakshi She received B.Tech degree in Electronics Engineering from the Institute of Engineering and Rural Technology Allahabad, U.P., India 2007. She completed her M.Tech degree in Communication Technology from Department of Electronics and Communication, Allahabad University in 2009 and now days she is working as a research scholar with the same Department.
J. A Ansari He received B.Sc and B.Tech degree from University of Allahabad, India, the M.Tech degree in communication systems from the Institute of Technology, Banaras Hindu University (BHU), Varanasi, India, in 1991, and the Ph.D degree from Mahatma Gandhi Chitrakoot Gramodaya Vishvavidyalaya, Chitrakoot (Satna), India, in 2000. He has published more than 110 papers in different national and international journals and conference proceedings. His current area of research is microstrip antenna, millimeter wave, and fiber optics. He is presently working as professor with the Department of Electronics and Communication, University of Allahabad.
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