2022 IEEE International Workshop on Electromagnetics: Applications and Student Innovation Competition (iWEM), Narashino,Japan

Analysis Results of Single-Layered Reflectarray
Antenna with Split Rectangular Loop Elements
Masayoshi Takao
Kanazawa Institute of Technology
7-1 Ogigaoka, Nonoichishi,
Ishikawa, 921-8501 Japanb1833012@planet.kanazawa-it.ac.jp

Shigeru Makino
Kanazawa Institute of Technology
7-1 Ogigaoka, Nonoichishi,
Ishikawa, 921-8501 Japanmakino@neptune.kanazawa-it.ac.jp(a) Phase-coverage range of 360 [deg] for each polarization.

Abstract—The reflectarray antenna (hereinafter referred to as"reflectarray") applies the reflection phase control function offrequency selective reflector to a plane reflector. Various beam
shapes can be formed by appropriately selecting the mirror
surface configuration and the shape of the resonance elements.
In this study, a reflectarray that changes the beam direction
depending on the polarization is investigated.

(b) Independent phase control depending on polarization.
Therefore, we investigated a single-layer element thatsatisfies all of the above conditions.
B. Model Design
The design model is illustrated in Fig. 1. The design
parameters of the elements are listed in Table Ⅰ, where λ0 is
the wavelength corresponding to the design frequency f0.
Furthermore, the thickness of the dielectric substrate was hA.
Fig. 2 shows the order of changes in the element shapes using
the element for H-polarization as an example. The same is true
for the element for V-polarization if the entire element isrotated by 90 [deg].

Keywords—reflectarray antenna, polarization, grating lobe,element spacing, single layer antenna

I. INTRODUCTION
The reflectarray antenna [1] (hereinafter referred to as"reflectarray") has a plane reflector with resonant elements
periodically arranged at spacing d. It has been shown that areflectarray with low-side-lobe
and high-efficiency
characteristics can be designed using (1) for resonant element
spacing d, where the grating lobe does not propagate in the
dielectric material [2]:dλ≤1Yusuke Kaimori
Kanazawa Institute of Technology
7-1 Ogigaoka, Nonoichishi,Ishikawa, 921-8501 Japanb1714005@planet.kanazawa-it.ac.jp

ℓB1
ℓB2

SB

ℓB4(1)

ε r + sin θℓB3Here, λ is the wavelength corresponding to the maximum
frequency in the frequency band, εr is the dielectric constant,and θ is the maximum incident angle. Using resonant element
spacing that satisfies (1), a reflectarray that changes the beam
direction according to the polarization was studied [3].
However, in the study of the two-layer model [3], the gain wasreduced owing to the reflection loss caused by the multi-layerstructure. To improve this, a single-layer model study [4] wasconducted. A reduction in the number of layers reduced thereflection loss and improved the aperture efficiency.
However, the 360 [deg] reflection phase region could not besatisfied because the designable area for each polarization wasreduced by approximately half for each layer. Therefore, inour previous report [5], we proposed a split rectangular loop
element that can cover the reflection phase region byextending the element length by bending it.

ℓA4

ℓA1/2

PY

hA

ℓA3

PX

Fig. 1. Element Model
TABLE I.

In this study, we present the analytical results of areflective array designed using this split rectangular loop
element.
II. ELEMENT DESIGNDESIGN PARAMETERS OF ELEMENTBandKu

Line width w

0.004 λ0Thickness hA

0.127λ0Interval of line SB0.020 λ0Dielectric constant εr

2.59

Element length lA1 , lB10.004 λ0〜0.354 λ0tanδ

0.0028Element length lA2 , lB20〜0.235 λ0

Angle of incidence [deg]25Element length lA3 , lB30〜0.020 λ0

Element spacing PX , PY

0.394 λ0

Element length lA4 , lB40〜0.107 λ0①②③④Fig. 2. Variation of element shape

A. Element Requirements
In designing the elements, the frequency band was set tothe Ku band, as in a previous study [4]. Similarly, for theresonant element spacing d, (1) was used to prevent thepropagation of the grating lobes within the dielectric.

C. Reflection Phase Characteristic
The total elements ℓ A and ℓB are defined as ℓ A=ℓ A1+2ℓ+4ℓA2
A3+4ℓ A4, and ℓ B=ℓ B1+2ℓ B2+4ℓ B3+4ℓ B4, respectively,
where the total element length for the polarization orthogonal
to the co-polarization is fixed at a maximum value ℓ =1.33λ0
and the total element length for the main polarization ℓ wasvaried in the interval from 0.004λ0 to 1.33λ0. The angle ofincidence in the element analysis is 25 [deg]. The reflection

The requirements for the resonant elements to change thebeam direction according to the polarization are as follows:This study was supported by JSPS (20K04491), Japan.

978-1-6654-3238-2/22/$31.00 ©2022 IEEE

ℓA2/2

11

2022 IEEE International Workshop on Electromagnetics: Applications and Student Innovation Competition (iWEM), Narashino,Japanphase characteristics of the H-and V-polarized elements areshown in Fig. 3 and 4, respectively. Areas ①–④, which aredivided by dotted lines in the graphs, correspond to thechanges in the element shape shown in Fig. 2. According toFig. 3 and 4, the phase changed significantly owing to thefolded element. Here, the phase change of the co-polarization
was 360 [deg] or more in both cases, thus covering the phaseregion when each polarization was the co-polarization.
Furthermore, the phase change of the polarization orthogonal
to the co-polarization is sufficiently small, less than 22 [deg]for each polarization, and it was confirmed that independent
phase control is possible for each polarization.

B. Radiation Pattern
A full-wave analysis using the finite element method wasperformed on the mirror surface designed with the proposed
split rectangular loop elements. ANSYS HFSS was used forthe analysis. Fig. 3 shows a comparison between thecalculated values of the radiation patterns for the H and V
polarizations at the center frequency of f0. Table III lists thebeam direction, gain, and aperture efficiency for eachpolarization. According to Fig. 5, the side lobe of the copolarization component is sufficiently suppressed, and thebeams swing in different directions for each polarization.
Furthermore, Table III shows that the analyzed values of thebeam direction agree with the design values.

Therefore, it can be said that the proposed element shapesatisfies both conditions (a) and (b) for changing the beam
direction depending on the polarization.
H-pol

V_Co-pol (Analysis Value)
H_Co-pol (Analysis Value)

V-pol

100

-10

0Amplitude [dB]

Reflection Phase [deg]V_Cr-pol (Analysis Value)
H_Cr-pol (Analysis Value)

0-100-200-300

①-400

②③

④-20-30-40-500-600
00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3-50Element length, ℓB [lambda]-60-40-200204060

Azimuth[deg]Fig. 3. Reflection phase characteristic of H-polarization
Fig. 5. Radiation pattern of V-pol and H-pol
H-polV-pol

TABLE III.

Reflection Phase [deg]1000Fre.

-100

f0-200-300①-400②③By using a split rectangular loop element, the amount ofreflection phase change was improved. As a result, we met all
requirements of the element. In addition, by using this element
shape to design the mirror surface of the reflectarray, wechanged the beam direction for each polarization.

-6000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

11.1

1.2

1.3

Element length, ℓA [lambda]

Fig. 4. Reflection phase characteristic of V-polarization

In the future, we plan to fabricate a prototype of thedesigned reflectarray and confirm its performance byperforming measurements.

III. ANALYSIS RESULT
A. Reflector Design
The reflectarray was designed based on the reflection
phase characteristics, as shown in Fig. 3 and 4. The design
parameters of the reflectarray are listed in Table II. Here, theposition of the primary radiator is F and the center of themirror surface is O. The beam directions were designed to be
separated from each other by one beam width (=3.04 [deg] ).
TABLE II.

REFERENCES
[1]
[2]
[3]

[4]

REFLECTARRAY DESIGN PARAMETERS

Tilt angle [deg]25

Beam direction [deg]±1.52

Diameter of opening surface D

19.92λ0Distance from F to O

17.93λ0

Clearrance c

3.77λ0Beam direction [deg] Gain [dBi] Efficiency [%]+1.55533.63
59-1.534
33.44
56

IV. CONCLUSIONS④-5000Pol.
H
V

BEAM DIRECTION AND GAIN ANALYSIS RESULTS[5]12J. Huang, J.A.Encinar, “Reflectarray Antennas,” Wiley, New Jersey,2007.
Y. Fuji, et al., “High-efficiency and Low-side-lobe Reflectarray
Antenna,” ISAP, December, 2014.
M. Fukaya, R. Obata, S. Makino, H. Nakajima, M. Takikawa, “A Dualpolarized Stacked Reflectarray Antenna with Changing Beamdirection,” AP-S, July, 2020．
S. Takino, S. Shigemitsu, Y. Kaimori, S. Makino, “A Dual-polarized
Single Layer Reflectarray Antenna with changing beam-direction,”
IEICE Technical Report A･P2021-138, January, 2022 (in Japanese).
M. Takao, et al., “A Single-Layered Reflectarray Antenna with Split
Rectangular Loop Elements,” IEEE AP-S, July, 2022.