A reflectarray Using a Dielectric Discretized Concave Mirror Based on Electromagnetic Band Gap

Abstract

This paper presents a reflectarray antenna with an innovative dielectric mirror in the form of a discretized concave reflector. The mirror, manufactured via 3D printing, combines dielectric and air layers, forming an Electromagnetic Band Gap (EBG) that reflects signals to the reflectarray feed antenna within its operating frequency band. A transmission line model was used for EBG parametric analysis, resulting in a simple, fast, and efficient design tool implemented in Octave. A design technique was developed to optimize the position and tilt of each mirror element, aligning reflected signal phases for constructive addition in the antenna's main beam direction. An Octave code implemented this design technique. Additionally, a Python program automated the generation of the dielectric reflector simulation model for Ansys HFSS. A reflectarray antenna is designed to operate in the 10.7 GHz to 12.7 GHz band, using a Yagi-Uda feed and a dielectric reflector made of PLA and air layers. The reflectarray antenna was manufactured and characterized, demonstrating a gain of 19.56 dBi and a half-power beam width of 8.04 degrees at 11.7 GHz at 〖θ〗_0=23° and 〖φ〗_0=0°. Good agreement was obtained between simulated and measured results, validating the design procedure.

Index Terms
Antenna; bandgap; reflectarray; transmission-line model.

I. INTRODUCTION

The Reflectarray Antenna (RA) is defined by the IEEE as "An antenna consisting of a feed and an array of reflecting elements arranged on a surface and adjusted so that the reflected waves from the individual elements combine to produce a prescribed secondary radiation pattern” [¹]. Among its advantages compared to traditional antenna arrays are ease of installation, low cost, and reduced weight [²].

Various topologies have been proposed for the fabrication of the reflectarray antenna (RA), employing planar reflectors with metallic elements such as square-ring [³] [⁴] and Jerusalem cross [⁵], manufactured on the surface of dielectric substrates. The high gain of the reflectarray antenna (RA) is achieved by designing the reflective elements that form the reflector so that the signals reflected by them add up in phase in the direction specified in the design. The design of reflectarray antennas has been impacted by advances in 3D printing technology, as described in [⁶], which discusses the application of new materials and geometries in the development of antennas and metamaterials for radio frequency applications. A dual-band circularly polarized reflectarray antenna operating in the K and Ka bands, using a fully metal reflector, was developed using 3D printing techniques [⁷]. A dual-polarized Ka-band RA using a 3D-printed reflector composed of a dielectric resonator lattice is presented in [⁸]. In [⁹], a low-cost dielectric reflectarray using 3D printing technology, operating at 100 GHz and scalable to terahertz frequencies, is proposed.

Alternatively, a multilayer dielectric reflector is proposed by J. Zhu et al. [¹⁰], fabricated using a 3D printer. The RA presented in [¹⁰] operates in the K and V bands, combining two superimposed reflectors. Each of these reflectors alternates layers of air with layers of dielectric formed by small square dielectric patches positioned at different heights, but all with top faces parallel to the same plane.

This paper presents an improvement in this type of dielectric reflector, suggesting an individual inclination of each element of the dielectric layers of the reflector to increase the RA's gain. To the best of our knowledge, the proposed reflector geometry has not been previously reported. We also present a transmission line model to obtain the frequency response of the multilayer dielectric reflector, allowing for the analysis of its operation as an EBG. This model can be easily implemented in math CAD scripts, such as Matlab or Octave, and used as a fast tool to aid in the design of the reflector. Section II shows the structure of the reflectarray antenna using a multilayer dielectric reflector, details a two-step procedure developed to design the dielectric reflector surface, and presents its application to the design of a Ku-band reflectarray employing a concave dielectric reflector interleaving air and PLA layers, envisaging fabrication using 3D printing. Section III covers the fabrication of the designed reflectarray antenna using 3D printing technology, and presents the antenna characterization in a semi-anechoic chamber, comparing simulated and experimental results of radiation pattern and gain across the operating frequency band. Section IV discusses simulated and measured results, validating the reflectarray antenna design and 3D printing manufacturing process of the concave dielectric reflector. It highlights antenna performance, including gain and radiation patterns across the 10.7 GHz to 12.7 GHz operating band. Finally, Section V summarizes the design procedure and the experimental results of the reflectarray antenna, validating the proposed reflector structure and the two-step procedure developed to design the reflector. The viability of the project was confirmed through simulations and laboratory measurements.

II. DESIGN METHODOLOGY

A. Reflectarray structure

Fig. 1 illustrates the structure of a reflectarray antenna using the proposed multilayer dielectric reflector and a Vivaldi feed antenna. The dielectric reflector is detailed in Fig. 2.

Fig. 1
Structure of the reflectarray antenna using a dielectric reflector and a Vivaldi feed antenna.

Fig. 2
Dielectric reflector with elements individually rotated and positioned for specular reflection of the electric field in the specified design direction.

The dielectric reflector consists of reflective stacks formed by alternating layers of air and dielectric material printed with a 3D printer. The use of alternating layers of dielectric materials with different electric permittivity allows for the design of an electromagnetic band gap (EBG) in the desired frequency band, reflecting the electromagnetic waves emitted by the feed antenna towards the specified direction of the antenna's main lobe. Thus, the dielectric reflector operates as a "reflector mirror" [¹⁰].

The main beam of the dielectric reflector presented in Fig. 2 is pointed at the elevation angle θ_0. The elements forming the layers of the dielectric reflector were individually positioned along the z-axis and rotated around the x and y axes to reflect the signal from the feed antenna constructively in the desired direction. Consequently, a discretized concave surface reflector was obtained. The angle between the direction of the incident signal I ⃗ and the normal direction N ⃗ to the central element of the reflector resulted in θ/2, causing specular reflection in the direction R ⃗ corresponding to θ=〖θ〗_0.

Initially, the layers of the dielectric reflector forming the multilayer structure were designed to create an EBG. Next, the procedure to determine the position and inclination of each element of the reflecting surface is outlined. The proposed design procedure is then applied to develop a Ku Band reflectarray antenna centered at 11.7 GHz, using a Yagi-Uda feed antenna.

B. Dielectric reflector layers design

The design of the dielectric reflector begins with the selection of the material to be used in its construction, considering parameters such as relative permittivity, loss tangent, and cost. Once the material is chosen, the initial thickness of the dielectric and air layers that make up the reflector, l_air and l_diel, are calculated as a quarter of the guided wavelength using

(1) $$l_{air}=\frac{{\lambda }_{\text{air}}}{4}=\frac{{\lambda }_0}{4}=\frac{c}{4f_c}$$

(2) $$l_{\text{diel}}=\frac{{\lambda }_{\text{diel}}}{4}=\frac{c}{4f_c\sqrt{{\epsilon }_r}}$$

where c is the speed of light in a vacuum, f_c is the central operating frequency of the RA, and ε_r is the relative permittivity of the dielectric material. In this way, the reflector operates as an electronic band gap at the RA's central frequency, reflecting the incident signal on its surface.

The number of layers comprising the dielectric reflector is then designed to maximize signal reflection within the RA's operating frequency band. This step requires computational optimization to find a compromise solution, as increasing the number of layers maximizes the EBG reflection but at the cost of narrowing the operational bandwidth and increasing the reflector's cost and weight. Additionally, parametric analyses must be conducted to verify the robustness of the designed reflector against dimensional variations that may occur during its fabrication. This step can be performed through computational simulations using Eigenmode Analysis [⁶], although these tend to be time-consuming.

This paper proposes estimating the performance of the stack of dielectric material plates more quickly by using transmission line equations in a cascading manner, as there is an analogy between the reflection of plane waves in perfect dielectrics and transmission lines. This procedure can be applied to the design of a uniform dielectric reflector by interleaving layers of dielectric material and air, but it also allows for efficiently exploring the performance of more complex dielectric reflectors.

Fig. 3 illustrates the transmission line model representing a reflector with four layers of dielectric material interleaved with three layers of air and surrounded by air on the outer layers. Considering that the n-th dielectric layer has a relative permittivity ε_rn, relative magnetic permeability µ_rn and thickness l_n, this layer is modeled by a transmission line segment with length l_n and characteristic impedance Z_{0_n}, which is equal to the wave impedance in the modeled medium. Neglecting the dielectric material losses and considering µ_rn = 1, Z_{0_n} is given by

Fig. 3
Transmission line model for the uniform stack of materials forming the reflective element.

(3) $$Z_{0\_n}=\sqrt{\frac{\mu }{\epsilon }}=\sqrt{\frac{{\mu }_0{\mu }_{rn}}{{\epsilon }_0{\epsilon }_{rn}}}=\frac{{\eta }_0}{\sqrt{{\epsilon }_{rn}}}$$

where ε₀, µ₀ and η₀ are, respectively, the electric permittivity, the magnetic permeability, and the wave impedance of in a vacuum.

The reflection coefficient S₁₁ of the dielectric reflector is given by

(4) $$S_{11}=\frac{Z_{in}-{\eta }_0}{Z_{in}+{\eta }_0}$$

and depends on Z_in, the impedance seen by the wave incident on the top surface of the reflector, where Z_in = Z_{in_7} in the example of Fig. 3. The reflection coefficient is given by

The impedance Z_in is a function of the characteristic impedances Z_{0_n} and the physical lengths l_n of the layers forming the reflective stack, considering that the n-th layer of the dielectric stack is terminated by the impedance Z_{in_n-1)} of the preceding layer. In the example of Fig. 3, the first layer is terminated by η₀, the second layer by Z_{in_1}, the third layer by Z_{in_2}, and so on. In this way Z_{in_1}, Z_{in_2}, up to Z_{in_7} are sequentially calculated using

(5) $$Z_{in\_\left(n\right)}=Z_{0\_\text{n}}\frac{Z_{in\_\left(n-1\right)}+j{Z}_{0\_\text{n}}\tan \left({\text{β}}_n{l}_n\right)}{Z_{0\_\text{n}}+j{Z}_{in\_\left(n-1\right)}\tan \left({\text{β}}_n{l}_n\right)}$$

given

(6) $${\text{β}}_n=\frac{2\pi \text{π}}{{\text{λ}}_n}$$

with the wavelength in the n-th layer of dielectric given by

(7) $${\text{λ}}_n=\frac{{\text{λ}}_0}{\sqrt{{\epsilon }_{rn}}}$$

where λ₀ is the wavelength in a vacuum and ε_rn is the relative permittivity of the n-th layer.

Table I presents the characteristics of commercially available materials that can be used for fabricating the dielectric reflector using a 3D printer. These materials exhibit low dielectric losses, justifying their representation by ideal transmission lines. The dielectric reflector of the RA presented in this paper was fabricated using PLA.

TABLE I
RELATIVE PERMITTIVITY AND LOSS TANGENT OF MATERIALS USED FOR 3D PRINTING.

Material	Relative permittivity at 10 GHz	Loss tangent at 10 GHz
Radix [11]	2.8	0.0043
ABS [12]	2.6	0.0031
PLA [12]	2.71	0.0063

The transmission line model was employed to design a dielectric reflector with a central frequency of 11.7 GHz, covering the 10.7 to 12.7 GHz band for satellite TV signal reception. The thickness of the PLA and air layers was set to 3.9 mm and 6.4 mm, respectively, corresponding to a quarter wavelength at 11.7 GHz in each material.

Fig. 4 presents the reflection coefficient of dielectric reflectors using 2, 3, 4, and 5 layers of PLA interleaved with air. The reflection coefficient is reduced by increasing the number of PLA layers, and reflection coefficients of -0.32 dB and -0.12 dB were obtained for reflectors using 4 and 5 layers of PLA, respectively. Considering that a higher number of PLA layers increases the weight and fabrication cost of the reflector, a structure using 4 PLA layers interleaved with air was chosen as a cost-performance compromise. The results presented in Fig. 4 were confirmed by simulating the layers using Ansys HFSS, with the curves being nearly identical, showing excellent agreement with the results from the transmission line model.

Fig. 4
Reflection coefficient of dielectric reflectors with 2, 3, 4, and 5 PLA layers interleaved with air.

The designed reflector consists of four layers of PLA with a thickness of 3.9 mm, interleaved with air layers of 6.4 mm, corresponding to a quarter-wavelength at 11.7 GHz.

Fig. 5 presents the results of the parametric analysis of the designed dielectric reflector, considering a manufacturing tolerance of ±200 µm in the thickness of the PLA layers using the 3D printing process. It was observed that the EBG behavior was minimally affected by the manufacturing tolerance within the design frequency range, as highlighted in Fig. 5.

Fig. 5
Parametric analysis of the reflection coefficient of the dielectric reflector for PLA layer thickness of 3.9 ± 0.2 mm.

Table II presents the reflection coefficient of the dielectric reflector the design bandwidth, obtained using the transmission line model. The performance of the designed reflector was compared to results obtained from full-wave simulation of the 3D model using Ansys HFSS [¹³] showing excellent agreement between both.

TABLE II
SIMULATED REFLECTION COEFFICIENT OF THE DESIGNED DIELECTRIC REFLECTOR.

Frequency (GHz)	S11(dB)	Phase S11
10.7	-0,442	-156°
11.7	-0,326	-180°
12.7	-0,442	-203º

C. Dielectric reflector surface design procedure

Once the layer stack structure of the dielectric reflector has been designed, the surface of the layers is discretized, resulting in an arrangement of small square patches. The reflector design proceeds by determining the positioning of each element to achieve constructive interference of signals in the direction of maximum gain. The design procedure follows the steps described below and was implemented in specially developed Octave script.

The design begins with the selection of the main beam pointing direction of the antenna, defining the elevation angle θ = θ₀ and the azimuth angle φ = φ₀, as illustrated in Fig. 6. The reflective elements of the dielectric reflector are then positioned side by side on a circular flat surface with diameter D, perpendicular to the z-axis. The feed antenna is placed on the z-axis at the center of the reflecting surface at a distance f from it. The larger the diameter D of the reflector, the greater the antenna gain. However, D is limited by the characteristics of the 3D printer used in its fabrication. The distance f of the feed antenna from the reflector was chosen to ensure that it operates in the far-field region.

Fig. 6
Representation of a Reflectarray Antenna, detailing the angles θ₀ and φ₀ of the desired radiation pattern direction. The origin of the coordinate system is situated at the central axis of the Reflectarray plate.

Additionally, it is necessary to choose the side of the square patches forming the discretized surface of the dielectric reflector. This side should be small enough to create a smooth surface but not so small as to generate an excessive number of elements, which would result in prohibitive simulation and fabrication times.

Once these parameters are defined, the design of the positioning of each square patch of the dielectric reflector layers begins, aiming for constructive interference of reflected signals in the direction defined by the angles θ₀ and φ₀, applying a two-step procedure.

In the first step, each element of the reflector is displaced along the z-axis to reflect the incident signal from the feed antenna towards the direction (θ₀, φ₀) specified in the design. The i-th element of the dielectric reflector, initially centered at (x_i, y_i, 0) is shifted to (x_i, y_i, z_i), with z_i calculated such that ϕ_i, the phase of the signal reflected by the i-th element [¹⁴], satisfies

(8) $${\varphi }_i=k_0{R}_i-k_0\left(x_i\sin {\theta }_0\cos {\phi }_0+y_i\sin {\theta }_0\sin {\phi }_0\right)$$

The term k₀R_i in (8) compensates for the spatial phase delay from the feed phase center to the i-th element, given by

(9) $${\varphi }_{spd}=-k_0{R}_i$$

where R_i is the distance from the center of the i-th element to the phase center of the feed antenna, and k₀ is the propagation constant in a vacuum at the center frequency.

Additionally, the term $-k_0\left(x_i\sin {\theta }_0\cos {\phi }_0+y_i\sin {\theta }_0\sin {\phi }_0\right)$ in (8), is added to the phase value of the signal reflected by the i-th element, creating a collimated beam in the direction of maximum gain of the reflectarray antenna at the center operating frequency.

A script in Octave was developed to calculate the phase ϕ_i for each element of the dielectric reflector using (8). Fig. 7 illustrates the distribution of the ϕ_i values along the dielectric reflector, calculated for the antenna presented in this paper, designed to operate at 11.7 GHz, with θ₀ = 25° and φ₀ = 90°. The calculated phase ϕ_i values are indicated on the sidebar to the right, showing the relative phase differences between the reflective elements.

Fig. 7
Phase ∅_i of the signal reflected by the i-th element along the reflector surface for θ₀ = 25° and φ₀ = 90°.

The elements of the discretized reflector need to be tunable to generate the ϕ_i values obtained from (8). Common techniques in planar reflectors use elements with phase/time delay lines, variable sizes, or variable rotation angles. In the case of the antenna in this paper, this phase ϕ_i is obtained by shifting each i-th element along the z-axis by a distance z_i calculated using

(10) $${\varphi }_i=2\cdot \frac{{360}^0}{{\lambda }_0}\cdot z_i$$

In a second step, each reflective element is rotated around the x and y axes to focus the antenna beam, keeping the center of its surface at the coordinate (x_i, y_i, z_i). The rotation of the i-th element is calculated considering the antenna's pointing direction, θ₀, φ₀ and its coordinates. The reflector results in a discretized concave surface, smoothed by the individual inclinations of each of its elements. This step allowed for a 1 dB increase in the maximum gain of the reflectarray antenna using the designed dielectric reflector and a horn feed antenna, as shown by electromagnetic simulations.

Fig. 8 illustrates the positioning of the reflector elements after the first and second design steps, and the final structure of the reflectarray. As a result of this procedure, the normal direction $\overrightarrow{N}$ to the surface of the central reflector element was rotated by θ₀/2 around the x-axis, as required for specular reflection in the direction θ₀. The inclination of the other elements is affected by their position along the reflector.

Fig. 8
Dielectric reflector with each of its elements inclined to produce specular reflection of the electric field in the specified reflectarray main lobe direction.

D. Ku band reflectarray design

The design procedure presented here was implemented in a computer program developed in Octave and applied to the design of a reflectarray antenna operating in the Ku band. Table III and Table IV present, respectively, the specifications of the antenna and the characteristics of the designed dielectric reflector.

TABLE III
REFLECTARRAY ANTENNA DESIGN SPECIFICATIONS.

Parameter	Value
Frequency band	10.7 to 12.7 GHz
Main beam direction	θ0 = 25° and φ0 = 90°
Dielectric Reflector	Air and PLA layers
Fabrication technology	3D printer

TABLE IV
CHARACTERISTICS OF THE DESIGNED DIELECTRIC REFLECTOR.

Parameter	Value
Diameter	188.5 mm
PLA layers	4 layers 3.9 mm thick
Air layers	3 layers 6.5 mm thick
PLA square patches	505 patches, 7.5 x 7.5 mm2 each

To analyze the performance improvement of the designed reflector throughout the design steps, a RA fed by a horn antenna was designed at 11.7 GHz, considering three dielectric reflector geometries. The horn fed was positioned at a distance of 260 mm from the center of the dielectric reflector, and main lobe direction was set to θ₀ = 25° and φ₀ = 90°.

Fig. 9 presents the simulated results of this reflectarray antenna with three geometries of the dielectric reflector. Considering the reflector obtained after the first design step, with all elements displaced by z_i and with the face parallel to the xy-plane, a gain of 21.3 dB was achieved. By inclining the face of all elements by θ₀/2 = 12.5 °, the gain improved by approximately 0.3 dB. Finally, applying the second design step, each reflector element underwent an individual rotation around the x and y axes, creating a discretized concave surface and producing a 1 dB increase in antenna gain compared to that achieved using the reflector obtained from the first design step.

Fig. 9
Radiation pattern of the reflectarray with different reflector geometries - (a) reflector obtained after design step one, (b) reflector obtained applying design step one and rotating all elements by 12.5° only around y-axes, and (c) reflector obtained applying the proposed two-step design.

The surface of the reflector designed using the proposed two-step procedure was compared to a parabolic surface with a focal length of 260 mm. For a reflector with a diameter of 180 mm, as used in the present study, the deviation between the reflector surface and the parabolic surface ranged from 0% at the center to 0.5% at the edge of the reflector. However, when the reflector's diameter is doubled, it exhibits a more pronounced concavity, deviating by 5% from the parabolic surface at its edges. Therefore, the reflector designed in this study does not correspond to a parabolic surface, an effect that becomes more noticeable as the reflector diameter increases.

A planar Yagi-Uda feed antenna was chosen for the RA because it is lighter, causes less shadowing on the reflector, and is easier to manufacture compared to the horn antenna. For this purpose, a Yagi-Uda antenna was designed on RT/duroid® 5880 laminates, demonstrating a gain of 8.7 dBi at 11.7 GHz, and a -10 dB bandwidth from 11.35 GHz to 11.96 GHz. The feed antenna was positioned above the dielectric reflector at a distance of 260 mm, in the far field, resulting in an f/D ratio of 1.38.

The designed reflectarray antenna was simulated using the ANSYS-HFSS full-wave simulator, resulting in a maximum gain of 19.02 dBi in the direction θ₀ = 23.5° and φ₀ = 0° at 11.7 GHz. Fig. 10 presents the simulated 3D radiation pattern of the reflectarray antenna.

Fig. 10
Simulated 3D radiation pattern of the reflectarray antenna at 11.7 GHz.

It was observed an 1.5° error between the specified elevation angle of the main lobe (25°) and the one obtained in the simulation. This error can be minimized through iterative design and simulation steps of the RA.

The simulated radiation pattern of the designed reflectarray antenna is presented in Fig. 11, considering dielectric reflectors employing 2, 3 and 4 PLA layers interleaved with air. As expected, the RA gain increases with the number of PLA layers, and the higher reflection from the 4 PLA layers reflector also affects the side lobes.

Fig. 11
Simulated gain of the reflectarray antenna using reflectors with 2, 3 and 4 PLA layers interleaved with air.

Simulated and measured results of gain and 2D radiation pattern of the reflectarray antenna using the reflector with 4 PLA layers are presented in the next section.

III. FABRICATION AND MEASUREMENTS

The designed dielectric reflector was manufactured as a single block using a 3D printer, with PLA dielectric layers interleaved with air layers. The Yagi-Uda feed antenna was fabricated on RT/duroid® 5880 laminates using the micromilling technique. A support structure was designed to position the feed antenna 260 mm above the dielectric reflector and was constructed using PLA and 3D printing technique.

The RA prototype was characterized in a semi-anechoic chamber at LIT/INPE - the Integration and Testing Laboratory of the National Institute for Space Research. Fig. 12 (a) presents photographs of the RA using the Yagi-Uda feed antenna and Fig. 12 (b) the setup used for its characterization.

Fig. 12
(a) Reflectarray antenna prototype and (b) antenna measurement setup.

Fig. 13 presents the measured and simulated RA radiation patterns at 11.7 GHz for φ = 90°. Table V summarizes the simulated and measured RA parameters at 11.7 GHz, demonstrating a very good agreement between the antenna gain and the shape of the main lobe of the radiation pattern. The measured gain was 19.56 dBi, closely matching the simulated gain of 19.02 dBi. The measured main beam pointing direction was θ₀ = 23.0°, deviating by 0.5° from the value predicted by computational simulation. The measured half-power beamwidth was 8.04°, differing by 0.2° or 2.55% from the simulated value.

TABLE V
SIMULATION AND MEASURED RESULTS OF THE RA AT 11.7 GHZ

	Gain	Angle of Maximum Signal	1 dB beamwidth	3 dB beamwidth	10 dB beamwidth
Simulated	19.02 [dBi]	23.5 [deg]	4.52 [deg]	7.84 [deg]	13.56 [deg]
Measured	19.56 [dBi]	23.0 [deg]	4.68 [deg]	8.04 [deg]	13.39 [deg]

Fig. 13
Measured and simulated elevation radiation pattern curves for φ₀ = 90° of the Reflectarray Antenna fed by a Yagi-Uda antenna at 11.7 GHz.

The support structure of the feed antenna was not accounted in the simulation of the reflectarray. The measured results indicate that the support structure had no significant effect on the main lobe of the radiation pattern but may have affected the secondary lobes of the RA. Notice that the measured back lobe of the reflectarray antenna resulted smaller than the one predicted by simulation results. The structure used to attach the RA to the measurement system contains a metal plate covered by an electromagnetic absorber with dimensions larger than those of the RA. This plate partially blocked the electromagnetic signal coming from the source antenna during the back lobe measurements, affecting the measured values.

Fig. 14 presents the gain of the reflectarray antenna across the band from 10.7 GHz to 12.7 GHz. The maximum antenna gain occurred at 11.7 GHz for both measured and simulated results, 19.56 dBi and 19.02 dBi, respectively, showing good agreement. At 12.7 GHz, the simulated antenna’s gain decreases to 9.15 dBi, while the measured gain drops to 10.7 dBi. The gain reduction observed as the frequency deviates from 11.7 GHz is attributed to the performance of the Yagi-Uda antenna used to illuminate the reflector, which -10 dB bandwidth is from 11.35 GHz to 11.96 GHz.

Fig. 14
Simulated and measured antenna gain versus frequency.

IV. DISCUSSIONS

Laboratory measurements of the radiation pattern and gain of the Reflectarray Antenna fed with the Yagi-Uda antenna showed good agreement with the simulations concerning to the main beam direction and half-power beam width, validating the proposed topology as well as the design and manufacturing procedures used. The maximum measured gain of the antenna was 19.6 dBi at θ₀ = 23.5° and φ₀ = 90° at the frequency of 11.7 GHz, meeting the design specifications with an error of 1.5° in θ₀.

Comparing the measured and simulated radiation patterns, partial agreement is observed in the RA side lobes. It is worth noting that the RA simulation did not include the support arm of the feed antenna, which particularly affects the measured results of the secondary lobes of the radiation pattern.

A significant decrease in RA gain was observed below 11.35 GHz and above 11.96 GHz, as predicted by the simulations. This effect is due to the characteristics of the feed antenna used, which has lower gain and higher reflection losses at those frequency bands.

As shown in Fig. 13, the measured antenna gain closely matches the simulated values for the front part of the radiation pattern, for θ from -90 to 90 degrees. However, when moving to the backside of the reflector, the blockage caused by the mounting support of the measurement setup reduces reception, resulting in lower measured values. As a result, the measured front-to-back ratio was smaller than the simulated one.

A reflectarray with more uniform gain across the operating band can be achieved by using a feed antenna with a wider operating band. The RA performance may also be improved using a feed antenna with a radiation pattern that offers the best compromise between gain, signal spillover reduction, and illumination across the reflector.

The 3D printer’s ability to print arbitrary shapes allowed the fabrication of a reflectarray antenna using a concave dielectric reflector. This technology can be extended to the fabrication of the feed antenna, resulting in a reflectarray entirely manufactured by 3D printing.

V. CONCLUSIONS

A reflectarray antenna using a dielectric reflector with EBG behavior, interleaving air and dielectric layers, was proposed. A transmission line model was applied to simulate the reflection coefficient of the multilayer dielectric reflector, resulting in a fast design tool to optimize the thickness of the reflector layers. The proposed design procedure can be applied to predict the performance of non-uniform dielectric reflectors, combining layers of materials with varying thickness, permittivity, and magnetic permeability.

The shape of the reflector layers was designed using a two-step procedure aimed at optimizing the RA's gain. As a consequence, a concave reflector was created by individually setting the position and inclination of each element that constitutes the discretized reflector surface. The central part of the designed reflector approximates a parabolic surface. However, the reflector surface gradually deviates from the parabola towards its edges, providing signal reflection with the phases required in the RA design.

An RA antenna operating at 11.7 GHz was designed using a Yagi-Uda feed antenna and a dielectric reflector created using the proposed procedure. The antenna reflector was fabricated by 3D printing, interleaving air and PLA layers.

The designed RA demonstrated a gain of 19.6 dB in the direction θ₀ = 23.5° and φ₀ = 90°, with a 3 dB beamwidth of 8 degrees, validating the design procedure.

ACKNOWLEDGMENTS

The authors thank INPE - National Institute for Space Research for providing the facilities of LIT - Laboratory of Integration and Tests for the antenna characterization, engineer Guilherme Nader Kawassaki for conducting the antenna measurements, and Rogers for providing the RT/duroid® 5880 laminates used to manufacture the Yagi-Uda antenna.

REFERENCES

• ^[1] “IEEE Standard for Definitions of Terms for Antennas,” IEEE Std 145-2013 (Revision of IEEE Std 145-1993), pp. 1-50, 2014, doi: 10.1109/IEEESTD.2014.6758443.
  » https://doi.org/10.1109/IEEESTD.2014.6758443.
• ^[2] A. Z. Elsherbeni, P. Nayeri and F. Yang, "Reflectarray antennas for space applications," 2012 IEEE International Conference on Ultra-Wideband, pp. 362-365, 2012, doi: 10.1109/ICUWB.2012.6340389.
  » https://doi.org/10.1109/ICUWB.2012.6340389.
• ^[3] G. H. Dadashzadeh, M. H. Amini and A. R. Mallahzadeh, “Equivalent Circuit Model for Square Ring Slot Frequency Selective Surface,” Journal of Communication Engineering, vol. 3, no. 1, pp. 23-32, 2014.
• ^[4] F. Zhang and J. Zhang, “Design and Analysis of a Reflectarray Using Defected Double-Square Rings for Microwave Application,” 2015 8th International Symposium on Computational Intelligence and Design (ISCID), pp. 594-597, 2015, doi: 10.1109/ISCID.2015.102.
  » https://doi.org/10.1109/ISCID.2015.102.
• ^[5] H. V. H. Silva Filho et al., “Multiband FSS with Fractal Characteristic Based on Jerusalem Cross Geometry,” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, vol. 16, no. 4, pp. 932-941, 2017, doi: 10.1590/2179-10742017v16i4984.
  » https://doi.org/10.1590/2179-10742017v16i4984.
• ^[6] T. Whittaker, S. Zhang, A. Powell, C. J. Stevens, J. Y. C. Vardaxoglou and W. Whittow, “3D Printing Materials and Techniques for Antennas and Metamaterials: A survey of the latest advances,” IEEE Antennas and Propagation Magazine, vol. 65, no. 3, pp. 10-20, 2023, doi: 10.1109/MAP.2022.3229298.
  » https://doi.org/10.1109/MAP.2022.3229298.
• ^[7] J. Zhu, S. Liao and Q. Xue, “3-D Printed Millimeter-Wave Metal-Only Dual-Band Circularly Polarized Reflectarray,” IEEE Transactions on Antennas and Propagation, vol. 70, no. 10, pp. 9357-9364, 2022, doi: 10.1109/TAP.2022.3184483.
  » https://doi.org/10.1109/TAP.2022.3184483.
• ^[8] Y. -X. Sun, D. Wu and J. Ren, “Millimeter-Wave Dual-Polarized Dielectric Resonator Reflectarray Fabricated by 3D Printing With High Relative Permittivity Material,” IEEE Access, vol. 9, pp. 103795-103803, 2021, doi: 10.1109/ACCESS.2021.3098982.
  » https://doi.org/10.1109/ACCESS.2021.3098982.
• ^[9] P. Nayeri et al., “3D Printed Dielectric Reflectarrays: Low-Cost High-Gain Antennas at Sub-Millimeter Waves,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 4, pp. 2000-2008, 2014, doi: 10.1109/TAP.2014.2303195.
  » https://doi.org/10.1109/TAP.2014.2303195.
• ^[10] J. Zhu, Y. Yang, D. Mcgloin, S. Liao and Q. Xue, “3-D Printed All-Dielectric Dual-Band Broadband Reflectarray With a Large Frequency Ratio, ”IEEE Transactions on Antennas and Propagation, vol. 69, no. 10, pp. 7035-7040, 2021, doi: 10.1109/TAP.2021.3076528.
  » https://doi.org/10.1109/TAP.2021.3076528.
• ^[11] RadixTM Printable Dielectric 3D-Printable Dielectric Material for use on Fortify FLUX Series Printers. [Online]. Available: https://www.rogerscorp.com/-/media/project/rogerscorp/documents/advanced-electronics-solutions/english/data-sheets/radix-printable-dielectric-data-sheet.pdf
  » https://www.rogerscorp.com/-/media/project/rogerscorp/documents/advanced-electronics-solutions/english/data-sheets/radix-printable-dielectric-data-sheet.pdf
• ^[12] J. Zechmeister and J. Lacik, “Complex Relative Permittivity Measurement of Selected 3D-Printed Materials up to 10 GHz,” 2019 Conference on Microwave Techniques (COMITE), pp. 1-4, 2019. doi: 10.1109/COMITE.2019.8733590.
  » https://doi.org/10.1109/COMITE.2019.8733590.
• ^[13] ANSYS HFSS: High Frequency Electromagnetic Field Simulation Software. [Online]. Available: https://www.ansys.com/products/electronics/ansys-hfss
  » https://www.ansys.com/products/electronics/ansys-hfss
• ^[14] P. Nayeri, F. Yang and A. Z. Elsherbeni, Reflectarray Antennas: Theory, Designs, and Applications, Wiley, 2018.

Publication Dates

• Publication in this collection
  07 Apr 2025
• Date of issue
  2025

History

• Received
  19 June 2024
• Reviewed
  10 July 2024
• Accepted
  06 Jan 2025