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)”

References

[1] R. C. Hansen, Phased Array Antennas, Wiley Series in Microwave

and Optical Engineering. New York: Wiley, 1998. [2] A. Yu, F. Yang, A. Z. Elsherbeni, and J. Huang, “Transmitarray

antennas: An overview,” In USNC/URSI Radio Science Meeting, Jul.

2011. [3] H. X. Xu, T. Cai, Y. Q. Zhuang, Q. Peng, G. Wang, and J. G. Liang,

“Dual-Mode transmissive metasurface and its applications in

multibeam transmitarray,” IEEE Transactions on Antennas Propagation, vol. 65, no. 4, pp.1797-1806, 2017.

[4] W. L. Stutzman, and G. A. Thiele, Antenna theory and design. John Wiley & Sons, 2012.

[5] M. Li, and N. Behdad, “Wideband true-time-delay microwave lenses

based on metallo-dielectric and all-dielectric lowpass frequency selective surfaces,” IEEE Transactions on Antennas Propagation, vol.

61, no. 8, pp.4109-4119, 2013. [6] P. Nayeri, F. Yang, A. Z. Elsherbeni, "Design and experiment of a

single-feed quad-beam reflectarray antenna", IEEE Transactions on

Antennas Propagation, vol. 60, no. 2, pp. 1166-1171, Feb. 2012.

2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

752