Simple Frequency Characteristic Evaluation of
Shaped-Beam Design for Reflectarray Antenna
Yoshimi Sunaga/Kento Takeshima/Shigeru Makino

Hiromasa Nakajima/Michio Takikawa

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

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

Abstract— The analysis of the reflectarray antenna’s frequency
characteristics is a time consuming task. This is owing to the designof the size of the phasing elements, and the analysis of the reflection
phase of the phasing elements. We propose a method forestimating the frequency characteristics of a reflectarray antenna
by introducing aberration theory. The frequency characteristics
can be estimated without the design consideration to phasing
element size, and by the analysis of the reflection phase of phasing
elements by the conditions of aberration theory. Therefore, in thispaper, we propose a simple method to estimate the frequency
characteristics of the reflectarray antenna that does not requireelement design estimates the frequency characteristics by using thedesired reflection phase of our proposed design frequency.

In this case, since the frequency characterisitic of theelement’s reflection phase is always negative, Φ0 must also benegative to satisfy Eq.1. Generally, in the case of a single layer
reflectarray antenna, the range of the achievable reflection phaseΦ0 is limited to about 360° and the reflection phase Φ0 includes
a positive value such as, −π ≤ Φ0 ≤ π . Therefore, therealizable ideal frequency characteristics Φ(𝑓) is constant withrespect to frequency, as follows:

Keywords—

Reflectarray antenna, aberration theory,

shaped beam design

I. INTRODUCTION
The procedure for evaluating the frequency characteristics ofthe reflectarray antenna is as follows. First, the reflection phaseof each phasing element is analyzed, and the size of phasing
elements is determined to realize the desired reflection phase.
Next, the radiation characteristics of the reflectarray antenna are
determined by analyzing the reflection phase frequency
characteristics of the element. Since the reflectarray antenna has
a very large number of elements, it takes a very long time todesign the size of phasing elements, and to analyze the frequency
characteristics of the reflection phase. Consequently, a large
amount of time required to design a shaped beam for a desired
service area. We propose a simple method to evaluate thefrequency characteristics of a reflectarray antenna with a pencil
beam design by using aberration theory [1]. In this paper, we
present this simple method to estimate the frequency
characteristics of the reflectarray antenna of shaped beam designby using the desired reflection phase of our proposed design
frequency.

II. EVALUATION OF FREQUENCY CHARACTERISTICS BY
APPLYING ABERRATION THEORY

The frequency characteristics of the reflection phasewere assumed to be Φ(𝑓) and the reflection phase at thedesign frequency 𝑓0 was defined as Φ0 = Φ(𝑓0 ) . The
conditions under which the phase error of the reflectarray
antenna does not occur are as follows.
Φ(𝑓) =𝑓Φ𝑓0 0

978-1-5386-7102-3/18/$31.00 ©2018 IEEE(1)

Φ(𝑓) = Φ0(2)

The realizable wavefront can be estimated by using the desiredreflection phase Φ0 at the design frequency for the analysis ofother frequencies. Therefore, the frequency characteristics of
the wavefront can be estimated without designing the phasing
element size. Figure 1 shows the frequency characteristics ofthe phase error on the aperture (XZ plane). The broken line
indicates the phase error on the aperture that was calculated byusing Eq. 2 (hereinafter, simple design), the solid line shows thephase error calculated by a was performed with a reflectarray
antenna with pencil beam design, a design frequency of 12.0
GHz, and aperture diameter of 1,000 mm. Figure 1 shows thatthe phase error on the aperture in the detailed design and simple
design are generally in agreement. Therefore, it was concluded
that the simple design could estimate the frequencycharacteristics of the reflectarray antenna.
III. SHAPED BEAM DESIGN
Figure 2 shows the geometrical configuration of thereflectarray antenna. A primary radiator was located at F. The
aperture diameter D = 2,000 mm. O was the center point of thereflectarray antenna with diameter D, and the distance frompoint F to point O was R = 2,000 mm. The clearance to avoid
the blocking of a primary radiator was c = 300 mm. The
inclination angle of the reflectarray antenna’s mirror surface wasθd = 20.27°. The design frequency was 12.5 GHz. Figure 3
shows the radiation pattern that used the evaluation function of
5 blue points determined such that the coverage area becomes
the shape of the Japanese archipelago, where (a) is the analysis
result of detailed design; (b) is the analysis result of the simple
design. The detailed design is the analysis result of design thesize of phasing element to realize the desired reflection phaseΦ0 , and calculate the frequency characteristic of the phasing
element. The simple design is the analysis result applying
desired reflection phase Φ0 at design frequency to each freq-1187

AP-S 2018

uency. Detailed design values and simple design values
generally agree, and it became clear that the radiation pattern notmuch difference between the detailed design and the simple
design at design frequency. To optimize the phase distribution
on the aperture, we optimized the defined evaluation function byusing the steepest descent method.

(b)

(a)

IV. ANALYSIS RESULT
Table 1 lists the analysis time of the detailed design andsimple design. Figure 4 and 5 show the analysis results of theradiation pattern the outside design frequency of the detailed
design (a) and simple design (b), where Figure 4 shows theresults in the case of 12.1 GHz, while Figure 5 shows the resultsin the case of 12.9 GHz. Table 2 shows the gain differences
radiated to the three cities under normal design shorter analysis
time was entailed in the simple design, in comparison to thedetailed design. Figures 4 and 5 show that the radiation patternof the detailed design is roughly in agreement with that of thesimple design. Table 2 shows that only a small gain difference
existed between the radiation pattern of the normal design andthat of the simple design.

(a)

(b)
Fig. 3. Radiation pattern of 12.5 GHz.

V. CONCLUSION
In this paper, the simple frequency characteristic evaluation
method of shaped-beam design for reflectarray antenna wasproposed. The validity of the simple design was verified basedon the fact that the difference between gain value of detailed
design, and gain value of simple design is very small. It was
shown that the simple design is more efficient than detailed
design. It was shown that the simple evaluation method iseffective for judging the adequacy of the frequency characteristics of shaped beam design for the reflectarray antenna.

(a)

(b)

Fig. 4. Radiation pattern of 12.1 GHz.

(b)

(a)

Fig. 5. Radiation pattern of 12.9 GHz.
Table 1. Review time

Fig. 1. Phase error on aperture (XZ plane).

RingDesignFrequencyCharacteristics

Total

detailed

15 h10 h25 h

simple

0h

5 min

5min

Table 2. City gains
12.1 GHz

12.5 GHz12.9 GHzTokyo

0.20 dB

0.15 dB

0.13 dB

Osaka

0.12 dB

0.05 dB

0.01 dB

Sappro0.40 dB

0.32 dB

0.24 dB

REFERENCES[1]

Fig. 2. Geometrical configuration of reflectarray antenna.

1188

S. Makino, “Estimation of Frequency Characteristics of Reflectarray byIntroducing Aberration Theory” EUCAP. Paris. France. March 2017