Origami Fresnel Zone Plate Lens Reflector Antennas for Satellite Applications

Abstract

This work presents a methodology for designing deployable reflector antennas that combine origami structures and the Fresnel zone plate lens to obtain a compact antenna structure. In particular, Miura and Yoshimura’s origami patterns have been considered for the design of the Fresnel reflector mirror and the conical horn antenna feeder, respectively. A set of memory-form alloy (MFA) actuators have been used to deploy the antenna. The MFA actuators are activated by a direct current aimed at increasing the temperature and activating the memorized shape. The combination of these techniques provides light, inexpensive, and very compact antennas, particularly suitable for satellite applications. A numerical and experimental assessment campaign has been carried out on antenna prototypes operating in the $K_u$ band at 15 GHz. The obtained experimental results are quite promising.

1. Introduction

In recent years, there has been a significant advance in telecommunication systems for satellites, airborne, and terrestrial applications. Antennas play a key role in every communication system. In particular, satellite communications require light, compact, high-gain antennas and a well-focused beam pattern [1]. Time modulation arrays [2,3] and self-powered absorptive reconfigurable intelligent surfaces are recent solutions for the design of satellite antennas [4].Reflector antennas are widely used and typically consist of a small feed positioned at the focal point of a shaped metallic mirror designed to reflect electromagnetic waves [5]. A valid alternative is the use of electromagnetic lens antennas fabricated with dielectric materials [6]. The radiation pattern of dielectric or metallic lens antennas is mainly controlled by the reflector or lens shapes. Although reflector and lens antennas offer high performance, they are often bulky, mechanically fragile, and typically too large to be compatible with a small satellite. To overcome the problems of dielectric lens antennas, promising electromagnetic radiators called Fresnel zone antennas, demonstrated their effectiveness in different communications scenarios [6,7]. Fresnel zone antennas belong to the family of lens and reflector antennas. Their beam pattern and focusing effects are controlled through suitable phase shifts by acting on the lens surfaces and alternating shadows and reflecting zones [8]. There are numerous advantages of Fresnel antennas over conventional reflector or lens antennas. These antennas, beyond the high gain, focused main beam, and low side lobe levels (SSL), are cheaper, mechanically robust, easy to install, flat, and easily printable on a flexible dielectric substrate [9,10,11].

Despite the advantages introduced by lens antennas, their fabrication is still complicated and requires materials with particular dielectric characteristics [12] or techniques able to simulate it [13,14]. Recently, the ancient technique of origami folding has been used to develop structures that are efficiently packable, easily deployable, and operationally multifunctional engineering structures [15,16,17]. The application of origami folding has also been applied to antennas [18,19,20,21], thereby creating a new class of physically reconfigurable electromagnetic (EM) structures [22]. Origami-based structures have the unique ability to transform themselves from 2D manifolds, not necessarily flat structures, into a continuous range of 2D or 3D shapes with controlled deterministic mechanisms that permit the development of rigid foldable systems. Therefore, origami antenna technologies are expected to provide new capabilities to various systems that require compact radiating structures, deployable reflectors, and expandable reconfigurable surfaces, such as drones, airborne and small satellites (cubesats and nanosats). An origami antenna can be folded and stowed in small satellite compartments and launched into space. When the satellite reaches orbit, the antenna is deployed into a large-aperture configuration and is ready to communicate with ground stations on Earth. Origami technologies offer an important alternative to traditional antennas, which are heavy, bulky, and static, enabling the development of compact, easy-to-deploy, collapsible, lightweight, and reconfigurable antennas that can enhance the capabilities of communication systems. In this work, we propose a deployable origami reflector antenna operating in the $K_u$ frequency band that combines the advantages of planar Fresnel reflectors and origami folding techniques. In particular, the reflector is a planar Fresnel-zone metallic lens printed on a flexible Kapton dielectric substrate. The reflector is designed following a Moriyama origami-based design [20] that can transform itself from a non-flat compressed shape into a continuous flat 2D large surface. The feeder is realized with a Yoshimura origami [23,24,25] conical horn antenna, capable of collapsing from a 3D to a compact structure. The antenna structure deployment is obtained with linear actuators realized with metallic memory form alloy (the Nitiniol) activated by the heat generated by a current. An antenna prototype working in the $K_u$ band at 15 GHz was designed, fabricated, numerically, and experimentally assessed. The obtained results are quite satisfactory and demonstrate the capability of origami antenna technology to develop compact/collapsible, easy-to-deploy, lightweight, and reconfigurable antennas, particularly suitable for satellite applications. To the best of the authors’ knowledge, this is one of the first attempts to combine different types of origami structures to obtain a complete compact deployable antenna reflector antenna feeder enclosed. Also, the use of a linear actuator fabricated with a memory form alloy, electronically activated without a bulky and complex mechanical structure. Thanks to the robustness and simplicity of the considered antenna structure, it is particularly suitable for the design of radiative systems for satellites, in particular for very small satellites such as CubeSats that require very light and compact antennas due to the limited amount of available payload. The work is organized as follows: in Section 2, the antenna structure and the mathematical formulation are presented. Section 3 is devoted to the numerical and experimental assessment of the prototype, and finally, in Section 4, conclusions and ideas for future work are drawn.

2. Antenna Structure and Mathematical Formulation

The antenna structure is reported in Figure 1. It consists of a primary planar metallic Fresnel zone reflector mirror, and it works like a prime focus parabolic reflector antenna. The metallization is applied on a flexible dielectric substrate (Kapton, ${\epsilon }_r=3.5$, thickness $t_c=75$ μm). A flexible material was chosen to apply the Ori Moriyama origami pattern [20] and make it possible to fold and deploy it with a simple linear actuator realized with a Nitiniol alloy (a memory form material). The planar Fresnel zone mirror consists of two layers. The first layer features a planar arrangement of alternating concentric metallic and transparent regions, which correspond, respectively, to the odd and even Fresnel plate zones, to the position of a focal point [26]. The second layer is a metallic ground plane placed at $D={\displaystyle \frac{\lambda }{4}}$ from the first layer. The following equation provides the outer diameter for a planar lens with M full-wave circular zones [11]:

$$D_M=2\sqrt{2m{\lambda }_{0}F+{\left(m{\lambda }_0\right)}^2}1\le m\ge M$$

(1)

where ${\lambda }_0$ is the wavelength, F is the focal length of the lens, and M is the number of considered full-wave circular zones. If there are mechanical constraints concerning the lens diameter D, the following relation [13] can be used to estimate the number of full-wave circular zones M:

$$M={\displaystyle \frac{\sqrt{F^2+\frac{{D_m}^2}{4}}-F}{{\lambda }_0}}$$

(2)

Each m-th full-wave zone of the lens is divided into N subzones, where N is an even number $N=2,4,6,8,\dots .$ which represents the phase correction. In particular, the phase at every n-th subzone differs from the adjacent sub-zone phase by $\pm {\displaystyle \frac{2\pi }{N}}$ radians. For $N=2$, the subzones are equal to the half-wave Fresnel zones, for $N=4$ the lens becomes a quarter-wave phase correcting lens, and so on for $N=6,8$, etc. The outer radius of the n-th subzone is provided from the following relation [10]:

$$S_h=\sqrt{{\displaystyle \frac{2hF{\lambda }_0}{N}}+{\left({\displaystyle \frac{h\lambda }{N}}\right)}^2}$$

(3)

where $h=1,2,3\dots ,H$, and $H=M·N$. The considered Fresnel reflector is developed considering an operative frequency $f_w=15.0$ GHz, a phase correction $N=16$, a maximum diameter $D_m=0.10$ m (compatible with the dimensions of a cube satellite), and a focal point $F=0.05$ m. The choice of the N = 16 subzones is a compromise between the accurate phase correction and the limited available physical dimension, typical of a small cube satellite. The considered dielectric substrate is a flexible sheet of Kapton with thickness $t=75$ μm, and ${\epsilon }_r=3.5$, $tan\left(\delta \right)=0.002$. Another sheet of Kapton, completely metallized, is used as a background and placed at a distance $D=\lambda /4$ from the mirror. The geometry of the Fresnel reflector and the summary of the geometrical parameters are reported in Figure 2 and

Table 1. Fresnel lens geometrical parameters.

Parameters	Value [cm]
$R_1$	1.12
$R_2$	1.60
$R_3$	1.97
$R_4$	2.30
$R_5$	2.57
$R_6$	2.83
$R_7$	3.08
$R_8$	3.31
$R_9$	3.53
$R_{1}0$	3.74
$R_{1}1$	3.95
$R_{1}2$	4.15
$R_{1}3$	4.34
$R_{1}4$	4.53
$R_{1}5$	4.71
$R_{1}6$	4.90

, respectively. As can be noticed, the planar Fresnel zone reflector consists of alternating circular zones of metal and air. In the metal zones, the electromagnetic (EM) waves that impinge on the lens surface are 180° out of phase with the aperture center. The metallized zones block the out-of-phase waves while the transparent zones (air) diffract and combine constructively the electromagnetic wave to collimate into a beam in the focus [26,27]. An Ori Moriyama origami pattern is applied to the planar 2D structure [20]. In particular, the 2D geometry is divided into $H\times H$ small squares, with straight horizontal lines and vertical lines with alternating segments of length $D/H$ inclinated with alternating angles of 98° and 82° as shown in Figure 3. The origami pattern considered transforms the 2D structure of dimensions $(D,D)$ into a compact 2D structure of dimensions $(D/H,D/H)$. Concerning the feeder, a conical horn with a circular waveguide interface (the LB-CNH-C13.97-15Ghz model from Pasternack company) was considered as a reference [28]. The reference conical horn was transformed considering the modified Yoshimura conical origami structure reported in Figure 4. The Yoshimura feeder was realized with six segments to produce a hexagonal section for the aperture and circular waveguide interface. In the synthesis process, the geometrical parameters of the modified Yoshimura origami pattern were optimized to operate in the $K_u$ frequency band at 15 GHz. In more detail, an evolutionary optimizer, the particle swarm algorithm (PSO) [29,30], was adopted to minimize a suitable cost function and make the synthesis of the origami antenna feeder. The goals of the cost function are to minimize the $S_{11}$, the secondary (SSL), and the half power beam width (HPBW), and maximize the Gain. In particular, the cost function, reported in the following, receives as input the origami pattern geometrical parameters defined in Figure 3 (namely $L_1$, $L_2$, $L_3$,$D_1$, $D_2$, and $D_3$) and provides as output an estimation of the antenna radiating properties.

$$\begin{array}{c}\hfill F\left(\mathit{X}\right)={\alpha }_1·min\left\{S_{11}\left(\mathit{X}\right)\right\}+{\alpha }_2·min\left\{SSL\left(\mathit{X}\right)\right\}\\ \hfill +{\alpha }_3·min\left\{HPBW\left(\mathit{X}\right)\right\}+{\alpha }_4·min\left\{{\displaystyle \frac{1}{Gain\left(\mathit{X}\right)}}\right\}\end{array}$$

(4)

where ${\alpha }_1=0.4$, ${\alpha }_2={\alpha }_3={\alpha }_4=0.2$ are four weights empirically chosen, and $\mathit{X}=\left\{L_1,L_2,L_3,D_1,D_2,D_3\right\}$ is the vector of geometrical parameters to optimize. Then, the PSO optimizer was used in conjunction with a commercial electromagnetic simulator able to simulate the antenna with a high degree of accuracy. The PSO generates a set of trial solutions changing the geometrical parameters of the origami pattern, and the electromagnetic simulator estimates the performances of the corresponding trial origami feeder used to estimate the cost function and guidingguide the evolution of the algorithm toward the optimal solution. After the synthesis procedure, the following geometrical parameters are summarized in

Table 2. Yoshimura origami pattern geometrical parameters.

Parameters	Value [cm]
$L_1$	1.90
$L_2$	2.12
$L_3$	2.51
$D_1$	4.50
$D_2$	6.51
$D_3$	10.6

. The CAD model of the reference antenna and the Yoshimura origami feeder are reported in Figure 5. The length of the circular waveguide interface and the conical aperture of the Yoshimura feeder are slightly different from the reference conical horn antenna, after the optimization process.

3. Numerical and Experimental Assessment

In this section, two prototypes of reflector lens antennas are numerically and experimentally assessed. In particular, starting from the geometrical parameters reported in Table 1 and Table 2, a standard and an origami prototype are developed, fabricated, and assessed. In the first set of measures, the return loss of the standard conical and the modified Yoshimura origami feeders is compared. The two feeders were inserted into an anechoic chamber, the $S_{11}$ was measured with a vectorial network analyzer, and then the beam pattern was collected along the E-plane, and H-plane with an angular step of 1 degree. The measurements are reported in Figure 6 and Figure 7. In particular, Figure 6 reports the comparisons of measured and simulated $S_{11}$ of the two feeders without the Fresnel reflector. As expected, the $S_{11}$ Yoshimura origami feeder results in a higher value than the standard conical horn. In particular, the measured $S_{11}$ of the Yoshimura feeder is about five dB above the standard conical feeder for all the considered frequency range. However, at 15 GHz, the operative frequency of the considered prototypes, the return loss results are satisfactory with a value of −18 dB for the Yoshimura feeder and −25 dB for the standard conical feeder. Figure 7a reports the comparisons of measured and simulated beam patterns of the conical feeder without the Fresnel reflector. The agreement between numerical and simulated data is quite good. The feeder presents a main beam aperture of about 30° and a gain of about 15.1 dBi in the E-plane (confirmed by the antenna datasheet). The comparisons of measured and simulated beam patterns of the Yoshimura origami feeder without the Fresnel reflector are reported in Figure 7b. Also, in this case, the agreement between numerical and experimental data is very good. The main beam aperture of the Yoshimura is about 31° and has a gain of about 13.5 dBi in the E-plane. As can be noticed from the data reported in Figure 7a,b the Yoshimura beam pattern measured on the H-plane presents a main beam width higher for the conical feeder, with a difference of about 20°. Finally, in Figure 7c, the standard conical and the Yoshimura feeder beam patterns along the E-plane are compared. The gain, beam width, aperture, and SSL level are comparable. Figure 8, reports the measured and simulated $S_{11}$ of the standard conical feeder, with the planar Fresnel reflector and the deployed Moriyama Fresnel reflector. The plane phase of the feeder was placed in the Fresnel reflector focus. This measure was used to evaluate the performance decrease due to the introduction of the Moriyama origami pattern on the Fresnel reflector. As can be noticed from the data reported in Figure 8, the difference between planar Fresnel and Moriyama origami Fresnel reflectors is negligible. The comparisons between numerical and simulated data are quite in agreement, with only a difference of about 3 dB observed in the considered frequency range. However, for the frequency of 15 GHz, the $S_{11}$ is quite good, with a value of about −25 dB. To complete the $S_{11}$ assessment, a set of measurements was carried out considering the whole antenna structure, feeder, and reflector. In particular, the comparisons between simulated and measured data concerning the prototype with a standard conical horn and planar Fresnel reflector, as well as the deployed Yoshimura horn and the Moriyama Fresnel reflector, were carried out. The results are summarized in Figure 9. In both cases, the agreement between numerical and experimental results is quite satisfactory, with differences of fewer than 2 dB in the whole frequency range. As expected, the introduction of the Yoshimura feeder presents non-negligible effects, causing an $S_{11}$ increase of about 6 dB. However, it is worth noticing that at 15 GHz the $S_{11}$ of the Yoshimura, Moriyama antenna, it is still satisfactory, with a value of about −15 dB.

In the next set of measurements, the antenna beam pattern and gain are estimated. For comparisons, numerical and experimental data, with standard and origami lenses and feeders, were analyzed. In particular, the beam pattern was collected in an anechoic chamber, along the E-plane with an angular step of 1°. The measurements are reported in Figure 10 with a comparisons of measured (dotted lines) and simulated (continuous lines) beam patterns of the standard conical feeder and Fresnel reflector (red lines), and the origami version (blue lines). As can be noticed, the agreement between numerical and simulated data are quite good. The antenna realized with the standard parts presents a main beam aperture of about 25° and a gain of about 19.0 dBi, while the origami version reports a main beam aperture of about 30° and a gain of about 17.5 dBi. The gain reduction is quite limited, and the impact of the gain degradation has limited effects on Ku-band satellite links. Concerning the deployment repeatability, it is worth noticing that the antenna structure was studied to be deployed after the satellite reaches the operational orbit, but it is not expected to recompact the antenna. Concerning the side lobe levels (SLL), there is only a dBi difference between the standard and origami versions. The electric field distribution along the YZ plane is reported in Figure 11a,b. In particular, Figure 11a reports the Electric field of the conical feeder and the planar Fresnel reflector, while Figure 11b reports the electric field of the Yoshimura feeder and the Moriyama Fresnel reflector. As noticed, in both cases, the spherical waves emitted from the two horns are correctly converted into a plane wave by the lens reflector.

For the sake of completeness, some details of the prototype are reported. The two versions of lens reflectors were obtained with a laser diode engraver, namely the Atomstack PRO 12W. The laser’s power was kept at 20% of the total power to avoid damaging the small-thickness dielectric substrate. At one of the two lenses, a planar Moriyama origami pattern was applied. A photo of the standard and Moriyama Fresnel reflector prototypes is reported on the left and right sides of Figure 12, respectively. Figure 13 shows the Moriyama Fresnel reflector before and after the activation. The realization of the Yoshimura origami feeder was a little bit more complicated. It was impossible to fold the Kapton sheet into a mechanically stable three-dimensional structure. To obtain a robust structure, a set of segments was realized with additive techniques (using a 3D printer, the Flashforge PRO). Then, the segments were metallized with a small layer of metallization and assembled with conductive flexible tape. The photo in Figure 14 shows the deployed origami compared with the standard conical feeder. Figure 15, shows the photos of the two prototypes ready for the experimental assessment are shown. In particular, Figure 15a,b refer to the standard and origami antenna prototypes, respectively. To obtain the deployment of two origami structures, the Moriyama and Yoshimura for the reflector and feeder, respectively. As can be noticed from Figure 15b, no PLA support was used to keep in place the reflector; the Nitiniol actuators also work as a pedestal, while the PLA support was used only for the circular waveguide to coaxial transition. The two linear actuators made with a commercial memory form alloy, the Nitiniol, are activated employing two small cables, aimed at providing a DC of about 500 mA. The current increases the temperature of the alloy up to 70° due to the Joule effect, causing its activation and the restoration of its original form. This current value guarantees to prevent overheating of the actuator and damage to the antenna structure. Figure 16 reports a photo of the Nitiniol actuator used to deploy the Moriyama Fresnel reflector before and after activation.

4. Conclusions

An innovative reflector antenna based on a Moriyama origami Fresnel reflector and a Yoshimura origami feeder has been presented. The antenna structure can be efficiently packable and then easily deployable, thanks to simple linear actuators based on a memory form material activated through a low intensity direct current. An antenna prototype has been designed, fabricated, numerically, and experimentally assessed. Moreover, it has been compared with the performance of a standard non-origami antenna. The obtained experimental results are quite satisfactory, and they demonstrated the potentialities of the combination of origami and Fresnel techniques.