Shaped-Beam Reflectarray Antenna Optimized atMultiple Frequency
Sanshiro Shigemitsu /Syota Takino/Shigeru Makino

Hiromasa Nakajima/Michio Takikawa

Kanazawa Institute of Technology
7-1 Ohgigaoka, Nonoichi, Ishikawa, Japan.
Mail:b1600502@planet.kanazawa-it.ac.jp

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

Abstract— In previous research, only the center frequency wasoptimized when designing a reflectarray antenna that radiates ashaped beam. In this study, we designed a shaped beamreflectarray antenna by optimizing the center frequency as wellas multiple frequencies, in addition to using the conventional
design method.
Keywords—reflectarray antenna; shaped-beam antenna; simple
evaluation method; multi-frequency optimization

I. INTRODUCTION
In shaped-beam antennas, it is difficult to geometrically obtain
the reflection phase because the shaped beam is radiated invarious directions. Therefore, the reflection phase of all resonant
elements should be determined using a nonlinear optimization
technique such that the required gain in the beam’s radiation
direction can be satisfied. In previous studies [1], aberration
theory was used to reflectarray antenna design using a simple
evaluation method that can evaluate the ideal reflection phase.
This technique applies the desired reflection phase at the center
frequency to other frequencies and can be evaluated without any
device design or frequency-response analysis of the reflection
phase. The conventional shaped-beam design is created byapplying conditions where the reflection phase of the resonant
elements is frequency-independent without phase error.
However, the conventional shaped-beam reflectarray antenna isoptimized only at the center frequency and has a drawback inthat the frequency characteristics deteriorate unless a goodevaluation point is selected. In this study, we improve theformula of the conventional evaluation function to be optimized
at other frequencies. Furthermore, we design the shaped-beamreflectarray antenna optimized at three frequencies anddemonstrate its validity.

II. EVALUATION FUNCTION
In the past, the shaped beam was designed to be optimal at thecenter frequency f0; thus, frequencies other than the center
frequency f0 were not guaranteed. Let Φ(f) be the frequency
characteristic of the reflection phase, and Φ 0 be the reflectionphase at the design frequency f0. The conditional expressionthat the reflection phase of the resonant element does not causea phase error regardless of the frequency is as given in (1):Φ(𝑓) = Φ0(1)978-1-7281-4670-6/21/$31.00 ©2021 IEEE

By applying (1), if the desired reflection phase is obtained,
it can be evaluated without frequency characteristic analysisof the reflection phase or device design within a short
calculation time. Further, by using this condition,
optimization, including an arbitrary number of frequencies
becomes possible.
The formula of the evaluation function for optimizing anarbitrary number of frequencies is expressed by (2):𝑛𝑃
2F = ∑ ∑ 𝑊𝑖𝑝 (𝐺𝑖𝑝 − 𝐺0𝑝 )(2)

𝑖=1 𝑝=1

where n is the number of frequencies to be optimized, P is thenumber of evaluation points, and Wp is the weight of the gainat the frequency of i. Where I represents the frequency at which
optimization is performed. Gip is the gain function at thedirection point, and G0p is the required gain. The reflection
phase is determined using the steepest descent method in orderto minimize the evaluation function F.
III. SHAPED-BEAM DESIGN AND MEASUREMENT RESULTS
The design parameters used in this study are listed in Table 1.
Fig. 1 shows the design parameters used to design the mirror
surface. Figs. 2, 3, and 4 show the analysis results obtained byoptimizing only the conventional center frequency f0 and theanalysis results when optimized at three points: 0.957f0, center
frequency f0, and 1.043f0. Moreover, they show theconventional analysis results and the analysis results optimized
for three frequencies of the radiation pattern in the reflectarray
antenna with the ring design. Fig. 5 shows the locations of theevaluation points where differences in gain are observed
between the conventional and new designs. Fig. 6 shows thecorresponding gain frequency characteristics of each evaluation
point. In the designed reflectarray antenna, 11 evaluation points
were set using the analysis method [2]. From the analysis
results of the radiation pattern, no significant difference at f=f0
was observed; however, at f=0.957f0 and 1.043f0, there weredifferences near Hokkaido, Okinawa, and the Ogasawara
Islands. Fig. 6 shows that at points far from the mainland, suchas for Hokkaido and Okinawa, the low and high frequency side

1923

APS 2021

gains are more than 0.8 dB, which is higher than the value forthe conventional design.
IV. CONCLUSION
In this study, a shaped-beam reflectarray antenna was designed
and optimized at three frequencies. The analysis results
revealed that the shaped-beam reflectarray antenna optimized
at three frequencies showed frequency characteristics andhigher gain, compared to those optimized at one frequency. The
analysis of the radiation patterns at the low and high-frequency
sides shows that the radiation patterns are not disturbed, and it
can be observed that a wider bandwidth can be achieved
compared to the conventional design. Therefore, an evaluation
method that optimizes at frequencies other than the center one
is appropriate. In future, we will prototype and evaluate amulti-frequency-optimized reflectarray antenna. This work was
supported by JSPS20K04491.

Fig. 2

Radiation pattern (f=0.957f0)

Fig. 3

Radiation pattern (f=f0)

REFERENCES[1][2]

S.Makino, “Estimation of Frequency Characteristics of Reflectarray byIntroducing Aberration Theory” EUCAP.Paris.France.March 2017
Y.Sunaga, “Simple Frequency Characteristic Evaluation of Shaped-Beam
Design for Reflectarray Antenna”IEEE APS.Boston.USA.July.2018
TABLE 1. Desired reflection phase design parameters
Design Frequency band: f0Ka

Element shapeRing

Dielectric substrate thickness: t0.15λ

Dielectric constant of dielectric: εr

2.56

Mirror angle: θd[deg]25Center of opening surface: O(x,y,z)344.72, 0.0,
−289.26

Ring width: w0.096λRing radius: r0.14λ-1.77λOpening surface size: D

47.92λDistance from primary radiator tocenter of aperture: R

43.13λResonant element spacing: d0.383λ

Clearance: c9.077λFig. 4Radiation pattern (f=1.043f0)

Fig. 5 Location of the evaluation point away from the mainlandFig. 1

Design parameters for specular system
Fig. 61924

Gain frequency characteristics at the evaluation points