Multi-beam Transmitarray Antenna Design
Using Principle of Superposition
Chang-Hyun Lee1, Sang Wook Chi
1, Jae-Gon Lee
2, and Jeong-Hae Lee
1
1Department of Electronic and Electrical Engineering, Hongik University, Seoul 04066, Korea
2Metamaterial Electronic Device Research Center, Hongik University, Seoul 04066, Korea
Abstract –This paper introduces a multiple beamforming
method using the principle of superposition. Using the principle of superposition, it is possible not only to form multiple beams
very simply, but also to suppress side lobes or to separate two adjacent beams. In this paper, the realization of those mentioned above using the principle of superposition is
explained using an array factor theory, and a dual beam transmitarray antenna with a superstrate consisting of unit cells arranged in 11x11 is designed using the principle of
superposition. The gains of antenna was simulated to be 14.22 dBic and 15.64 dBic at =0o and 180o when =20o.
Index Terms — Transmitting antenna, metasurface, multi-
beam antenna, multiple beamforming, circular polarization.
1. Introduction
Multi-beam antennas have numerous applications such as
electronic countermeasures, satellite communications,
microwave power transfer (MPT), and multiple-target radar
systems [1]. Recently, multi-beam antenna using a
transmitarray has attracted a growing interest in the area of
high-gain antennas due to their numerous advantages [2].
In this paper, a multi-beam transmitarray antenna based on
metasurface is designed using principle of superposition.
This method can form multi-beams with a simpler process
than the conventional methods using an optimization
algorithm [3] or the Fourier series [4]. Using the
superposition principle, a phase set for multiple
beamforming can be easily obtained through the sum of
phase sets for single beam steering. In addition, it is possible
to suppress side lobes and separate adjacent beams by giving
a specific phase difference between phase sets for single-
beam steering. Finally, a beamforming method using the
principle of superposition is described through the array
factor theory, and a transmitarray antenna dual beam at =0o
and 180o when =20
o is designed.
2. Multi-beam Forming Method Using Principle of
Superposition
When the array distances are dx in x-axis and dy in y-axis,
the array factor of the array is expressed as
(1)
where M and N are the number of arrays in the x and y
direction, respectively, and βx and βy are the phase difference
between adjacent units in x and y direction, respectively.
0.00
0.25
0.50
0.75
1.00
020
40
60
80
100
120
140
160180
200
220
240
260
280
300
320
340
0.00
0.25
0.50
0.75
1.00
=0
o
=180
o
Fig. 1.Nomalized array factor for dual beamforming
at =0o and 180
o when =10
o
Therefore, in order to steer the beam at θ0 and ϕ0, the phase
differences have to be set as
(2).
When M and N are odd and the m-th element on the x-axis
and the n-th element on the y-axis are denoted as m and n,
respectively, the phase of the m by n element for single beam
forming is expressed as
(3).
The phase of the center element was set to 0o and used as a
reference. In order to calculate the phase set for dual beam,
the principle of superposition is used. Using the principle,
the phase set for dual beam forming can be easily obtained
by adding the phase sets for single beam steering calculated
from (3). The applied source set for dual beam at {ϕ1,θ1} and
{ϕ2,θ2}is expressed as
1 2, , ,
,
st nd dualm n m n m nj j jj dual
m ne e e A e
(4)
1
,
st
m n and
2
,
nd
m n are the phase of m by n element for single
beam steering at {ϕ1,θ1} and {ϕ2,θ2}, respectively. ϕ∆ is a
phase that is added collectively to the phase set for forming
the second beam, and this value can be used to form null or
improve the gain in a specific angle. Fig. 1 shows the array
factor for dual beamforming at =0o and 180
o when =10
o.
When ϕ∆ is 0o, the two beams are too close to each other, so
that the beam patterns are combined and cannot serve as a
double beam. However, if ϕ∆ is set to 180o for the destructive
interference at the center of the two beams, a null is
2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea
[ThP-43]
751
220mm
(a)
62mm(=1.2l0)
12.8mm
(b)
Fig. 2. The structure of the designed transmitarray antenna
(a) Top view (b) Side view
generated between the two beams and two beams are
separated as shown in Fig.1. Side-lobe suppression is also
possible using this principle. It is also applicable to the
formation of more than three beams.
In order to confirm the multiple beamforming method, a
dual-beam transmitarray antenna is designed. The superstrate
of the transmitarray antenna consists of five metallic layers
separated by four substrates to cover full transmission phase
variation of 2 and the metallic layers [5] are designed to
circular patches with the same dimension to operate as
circular polarized transmitarray antenna. The superstrate is
11 x 11 array of unit cells of size 0.387λ0 x 0.387λ0 at the
operation frequency of 5.8GHz. The unit edge etched patch
CP antenna of 0.5l0 x 0.5l0 at 5.8GHz is chosen as a feed
antenna, and it feeds at 1.2l0 away from the superstrate as
shown in Fig. 2. The gains at two beams are simulated to be
14.22 dBic and 15.64 dBic, respectively. The aperture
efficiency is confirmed to be 29.5% which is relatively high.
The aperture efficiency was calculated using the following
equation [6].
(5)
where N represents the number of beams and Gi, i, and A
are the gain and steering angle of each beam, and aperture
(superstrate) area. The full-wave simulated radiation pattern
of designed circular polarized transmitarray antenna is
shown in Fig 3.
3. Conclusion
This paper presents a multiple beamforming method using
the principle of superposition. It is confirmed through
-20
-10
0
10
20
020
40
60
80
100
120
140
160180
200
220
240
260
280
300
320
340
-20
-10
0
10
20
Fig. 3. Full-wave simulated radiation pattern of the designed
transmitarray antenna with dual-beam at =0o and 180
o when
=20o
the array factor theory that the side lobe suppression and the
adjacent beam separation are also possible in addition to the
simple formation of multiple beams by employing the
principle of superposition for multiple beamforming. Finally,
it is shown that the proposed multiple beamforming method
can be applied very simply by designing a dual-beam
transmitarray antenna. The proposed multiple beamforming
method is expected to open the way for simply designing
functional devices with multi-beam. More details will be
mentioned at the presentation.
Acknowledgment
This research was supported in part by Basic Science
Research Program through the National Research Foundation
of Korea (NRF) funded by the Ministry of Education (No.
2015R1A6A1A03031833) and in part by the MSIT(Ministry
of Science and ICT), Korea, under the ITRC(Information
Technology Research Center) support program(IITP-2018-
2016-0-00291) supervised by the IITP(Institute for
Information & communications Technology Promotion)”
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2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea
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