Reﬂectarray Antenna with High Efﬁciency
and Low Side Lobe
Shota Takino/Sanshiro Shigemitsu/Shigeru Makino

Hiromasa Nakajima/Michio Takikawa

Kanazawa Institute of Technology
7-1 Ohgigaoka, Nonoichi, Ishikawa, Japan.

Mitsubishi Electric Corporation
5-1-1 Ofuna, Kamakura, Kanagawa, Japan.

Abstract—The design of a reﬂectarray antenna(hereinafterreferred to as a reﬂectarray), is generally based on the resonant
element spacing to suppress the grating lobes in free space.
However, considering that this condition is not sufﬁcient, we
designed a resonant element spacing to suppress the grating lobe
in the dielectric. This paper compares the radiation pattern andgain designed with the resonant element spacing obtained underthese two conditions, and evaluates the efﬁciency and side-lobecharacteristics.
Index Terms—frequency selective reﬂector(FSR), side lobe,
grating lobe, efﬁciency

The conventional reﬂectarray exhibits a low efﬁciency andhigh side-lobe characteristics at the resonant element spacing
d obtained using (1). This is because (1) does not consider thegeneration of the grating lobe in the dielectric body, although
the grating lobe is generated with a low efﬁciency and highside-lobe characteristics. Fig. 1 shows a detailed diagram of
the grating lobe generation in the dielectric. The incident

I. I NTRODUCTION
In a metal-plate-loaded FSR, wherein the metal plate isloaded into an FSR via a dielectric, the reﬂection phaseof an incident electromagnetic wave can be controlled byappropriately selecting the radius and shape of the resonant
element. A reﬂectarray applies the reﬂection phase control
function of the metal-plate-loaded FSR to the reﬂector. It
consists of a ﬂat mirror surface and a primary radiator, andit can form a plane wave by controlling the reﬂection phaseof a spherical wave fed from the primary radiator - [1]. In
the conventional design of the reﬂectarray, the propagation of
the grating lobe, generated from the resonant element, into
the dielectric body causes a low efﬁciency and a high sidelobe. In contrast, in the proposed design, the grating lobe
does not propagate into the dielectric body or free space.
The resonant element spacing conditions in existing prototype
reﬂectarrays, wherein grating lobes do not propagate in thedielectric, have achieved efﬁciencies of over 60% and low
side lobe characteristics with side lobe levels of 30 dB orless in a certain frequency band fL -fH in the Ku band [2].
In this study, we analyzed reﬂectarrays designed with six
patterns wherein the resonant element spacing was 0.9, 1,and 1.1 times the resonant element spacing obtained by theconditional equation for the dielectric substrate and for freespace. We then determined the allowable resonant element
spacing for fabricating the actual reﬂectarray. These analyses
only consider the center frequency f0 .
II. DESIGN OF REFLECTARRAYS WITH HIGHEFFICIENCY AND LOW SIDELOBEFirst, the conditions under which the grating lobes do not
propagate in free space are shown in (1).
d1
<λ1 + sin θ

978-1-7281-4670-6/21/$31.00 ©2021 IEEE

(1)

Fig. 1. Detailed diagram of grating lobe generation

radio waves are divided into components that are reﬂectedby the resonant element and the transmitted component. The
reﬂected component is reﬂected at the same angle as theangle of incidence. In contrast, the transmitted component
propagates between the metal plate and the dielectric, andis ﬁnally reﬂected at the same angle as the incident angle.
Herein, when the grating lobe component propagates in thetransmitting component, it radiates in an unintended direction.
Accordingly, we proposed a design that considers the grating
lobe in the dielectric [3]. Each resonant element controls
the reﬂection and transmission; thus, the spacing between
the resonant elements is considered. Equation (2) shows theelement spacing conditions for preventing the grating lobes
from propagating into the dielectric.
d1<√(2)λ0
ϵr + sin θ0Here, we use a dielectric with relative permittivity ϵr =2.59
and the wavelength condition λ can be determined at a certain
frequency f0 in the Ku band. In addition, θ is set to 25◦ . Using(1) and (2), the resonant element spacing d is calculated for0.9times, 1 time, and 1.1times the element spacing. The six

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APS 2021

patterns considered are 0.4392λ, 0.4961λ, 0.5409λ, 0.6303λ,0.6995λ, and 0.7727λ. The radiation patterns and the efﬁciencies of these six patterns were compared to determine theoptimum resonant element spacing of the actual reﬂectarrayand to conﬁrm the validity of (2).
III. RESULT AND COMPARISON
The parameters of the reﬂectarray designed in this study
are shown in Fig.2. Five design parameters are considered: dielectric substrate thickness t, relative permittivity ϵr , resonant
element spacing d, ring width w, and ring radius r. Results ofFig. 4. Radiation pattern of V-polarization at an interval of six resonant
elements

resonator in (2) exceed 60%, which is the optimum interval forthe resonators. Therefore, it can be concluded that the optimum
element spacing is obtained by (2).

Fig. 2. Design parameters

the full-wave analysis of the high frequency structure simulator
using ANSYS are depicted in Fig.3, and those of the H andV-polarization radiation patterns for 0.9, 1, and 1.1 times
the resonant element spacing using (1) and (2) are depictedin Fig. 4. These radiation patterns are obtained at a certain
frequency f0 in the Ku band. From Figs. 3 and 4, it canbe observed that the sidelobes in the radiation pattern at
0.9times and 1 time the resonant element spacing of (2) are
low sidelobes at approximately 30 dB for both H- and Vpolarization. Consequently, the optimum resonator spacing in
the radiation pattern is determined using (2). Fig. 5 depicts theFig. 5. Efﬁciency/gain of H- and V-polarization

IV. CONCLUSION
In this study, the antenna efﬁciency and radiation patterns ofa reﬂectarray were compared using resonant element encoding
in six cases. Consequently, the resonant element spacing determined by (2) was considered to be optimum for designing theelements of the reﬂectarray antenna. This report was supported
by JSPS (20K04491).
R EFERENCES[1] S.Makino. et al., EUCAP2017, Mar, 2017.
[2] K.Takeshima. et al., ISAP2017, Oct,2017[3] Y.Fujii. et al., ISAP2014 , Dec, 2014.

Fig. 3. Radiation pattern of H-polarization at an interval of six resonant
elements

graphs of the efﬁciency and gain of the H- and V-polarizations.
From Fig. 5, it can be seen that the efﬁciency of the H- andV-polarizations at 0.9 times and 1 time the intervals of the1920