3-D-Printed Spiral Leaky Wave Antenna With Circular Polarization

This article presents the design, manufacturing and measurement of a fully dielectric leaky wave antenna operating at 18 GHz. The antenna is composed of a grounded dielectric substrate with a top dielectric Archimedean spiral corrugation, which allows obtaining a directive pencil-beam in broadside direction with circular polarization depending on the turning sense of the spiral. The 3D-printing implementation allows having two new degrees of freedom for the spiral when compared to other previous implementations based on metals, which are the relative permittivity and the height of the spiral. A study about the effect of these two parameters is presented and one proposed antenna is manufactured using low-loss and low-cost ABS filaments. Measurement results show good agreement with simulations, validating the implementation of this kind of antennas using low-cost 3D-printing.


I. INTRODUCTION
T HE RECENT advances in additive manufacturing have allowed implementing prototypes or topologies that before were either too expensive or not possible to manufacture by using traditional techniques [1], [2]. In particular, high-frequency topologies have gotten special interest due to the appearance of low-cost and low-loss dielectric filaments suitable for this technology. Among others, in recent implementations we can find lenses [3], [4], dielectric resonator antennas [5], [6] or polarizers [7], [8].
One particular topology that can have benefits from its implementation using dielectric 3D-printing are leaky waves antennas (LWA). Most of these antennas uses periodic structures to generate the leaky wave modes. Their implementation can be difficult depending on the shape or frequency band of the antenna. In a previous work, a Bull-Eye LWA [9] was done using dielectric 3D-printing, by replacing the typically metallic periodic surface with highpermittivity dielectric materials. This allows the generation and control of equivalent surface wave modes as in the original models. This hypothesis has been presented for the first time with a fully 3D printed model denominated DLWA Bull-Eye [10].
Other interesting structures that are candidate for 3Dprinting implementation are the antennas based on a periodically modulated surface wave to generate a controlled radiation pattern [11], [12]. They have potential to be used for space applications due to their versatile radiation patterns with high gain and circular polarization if required [13]. Within these structures, we can find the denominated Spiral LWA [14], [15]. This kind of antenna can generate directive broadside radiation patterns with circular polarization depending on the spiral's sense, LHCP if the spiral is clockwise, RHCP if the spiral sense is counterclockwise [16], [17], [18]. The interest of implementing these antennas using 3D-printing is that we can add additional degrees of freedom to the implementation, which are the permittivity and thickness of the corrugations.
In this work we propose a parametric study of the new degrees of freedom given by the use of 3D-printing, and the implementation and measurement of a 3D-printed Archimedean spiral leaky wave antenna at 18 GHz, using low-loss and low-cost dielectric filaments. In addition, the importance of the presented antenna is to validate the fabrication process at the chosen frequency, using the advantages of 3D printing to generate periodically modulated surfaces with a simple cost-effective solution.

II. ANTENNA DESIGN
The proposed antenna consists of a dielectric LWA operating at a central frequency of 18 GHz, composed of an Archimedean spiral based on the work presented in [19]. The main difference with respect to the referred work is that first, the introduction of a rectangular dielectric corrugation used to replace the metallic spiral that is composed of a different material than the substrate. In addition, the use of 3D-printing gives new degrees of freedom in the design as now, apart from the thickness, we can also modify the relative permittivity of the corrugation with the spiral shape. The frequency band used in this design was selected considering different factors, namely, to have a reasonable size of the structure, the fabrication tolerances with the available 3D printer, and the possibility to be fed using a basic coaxial connector.
The designed antenna is presented in Fig. 1. It consists of a grounded dielectric substrate with relative permittivity ε r1 = 3, a thickness of h = 2 mm, and a diameter of d = 180 mm. On top of the substrate, a dielectric Archimedean spiral is printed using a higher relative permittivity ε r2 with thickness t. The period between corrugations is set to p = 10 mm whilst its width is set to w = 3 mm. Finally, the central circular surface of the antenna as shown in Fig. 1 has a diameter c = 11 mm.
This particular antenna operates by exciting a TM 0 cylindrical surface wave mode using a coaxial probe at the center [20], [21]. When using this feeding and the Archimedean spiral shape, the antenna support cylindrical leaky wave mode (CLW) radiating with circular polarization depending on the turning sense of the spiral, with a high-gain broadside radiation pattern [19]. As demonstrated in [10] we can replace the metallic strips with dielectric corrugations to achieve a behavior similar to that of the metallic equivalent.

III. PARAMETRIC STUDY OF THE DIELECTRIC ARCHIMEDEAN SPIRAL CONSTITUTIVE PARAMETERS
The way this antenna is designed gives us two new degrees of freedom on its implementation, which are the thickness t of the corrugations of the spiral and its relative permittivity ε r2 . The influence of these parameters will be assessed as a function of the performance of the antenna, in terms of matching, axial ratio, and radiation pattern. All studies will be carried out using the right-handed circular polarization (RHCP) implementation, as both cases are identical in terms of geometry.

A. THICKNESS VARIATION OF THE DIELECTRIC SPIRAL
For this study, the thickness t will vary taking values between t = 1.0 mm and t = 3.0 mm with steps of 1.0 mm, while the relative permittivity is set to ε r2 = 10. Fig. 2 contains the simulated results for the reflection coefficient |S 11 |, maximum gain, and axial ratio as a function of the frequency. First, we can see that the antennas are matched between 16 GHz and 20 GHz independently of the thickness value, while the maximum gain changes in frequency depending on the height of the spiral. Concerning the axial ratio we can observe how it is degraded when the thickness is 3.0 mm.
Finally, the simulated gain radiation patterns at different frequencies are shown in Fig. 3. From the results, we can see how the Archimedean spiral produces a high-gain pencilbeam with a half power beam-width (HPBW) of around ≈ 6 • . We can confirm the dependence of the radiation pattern with the thickness value and the frequency where the broadside CP radiation pattern is obtained as previously demonstrated in [10].

B. RELATIVE PERMITTIVITY OF THE DIELECTRIC SPIRAL
The other degree of freedom available in this design is the relative permittivity ε r2 of the spiral. Three values have been chosen for this analysis, two of them correspond to the minimum and maximum relative permittivities available for low-loss dielectric materials for 3D-printing (ε r2 = 3 to ε r2 = 15), while the highest value of ε r2 = 30 is used to observe the effect on the structure of a higher permittivity. For all the simulations, the thickness of the spiral is set to t = 2 mm.
The simulated results for the reflection coefficient, maximum gain, and axial ratio as a function of the frequency are shown in Fig. 4. From the results, we can see that the matching is affected by the values of the relative permittivity, being the case with the lower permittivity the one who exhibits the larger mismatch in the assessed band probably because for this permittivity, much of the energy of the cylindrical wave has not been radiated when it reaches the end of the antenna and this produces reflections. Regarding the maximum gain and axial ratio, we can see that the permittivity affects the bandwidth where we can consider that the antenna is circularly polarized, and also the frequency where the maximum gain in broadside is obtained. Those shifts in frequency can be explained as the electrical length of the thickness of the spiral-shaped corrugation is more affected VOLUME 4, 2023 429 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. by a drastic change in the permittivity, rather than by a small variation in the thickness. Finally, the simulated axial ratio and reflection coefficient gain radiation patterns at different frequencies are shown in Fig. 5. We can confirm that the broadside behavior is altered in frequency depending on the permittivity of the spiral as this parameter affects the propagation constant β g and therefore the guided wavelength. The relation between the wavelength and the periodicity of the corrugations (which is kept constant) determines the shape of the radiation pattern. This can be a useful parameter when designing this kind of antennas. From the parametric study, we can get one combination of height and relative permittivity of the spiral that maximizes the gain while keeping a low axial ratio. For that, we choose ε r2 = 10 and t = 2mm and a RHCP implementation. In Figure 6 the simulated axial ratio and reflection coefficient are shown. Figure 7 contains the simulated radiation patterns using the chosen parameters in four different frequencies within the bandwidth of circular polarization (AR ≤ 3 dB), all of them using the chosen parameters.

IV. 3D-PRINTING MANUFACTURING PROCESS
To manufacture the proposed antenna, we used a Creality CP-01 3D-printer [22] and ABS dielectric filaments provided by AVIENT [23]. For the permittivity values, we chose a relative permittivity of ε r1 = 3 for the grounded substrate, which is manufactured with the PREPERM ABS300, while for the spiral we choose a relative permittivity of ε r2 = 10, implemented using the filament ABS1000 from the same provider. The thickness of the spiral is set to t = 2 mm, while all the other dimensions are set to the nominal ones presented in Section II. A summary of the 3D-printing parameters used for the deposition of the filaments used in the implementation is shown in Table 1.
The manufactured Archimedean Spiral DLWA is presented in Fig. 8 and corresponds to the RHCP design. For the ground plane we use an aluminium sheet and for the feeding a SMA connector Pasternack PE4111, that operates up to 26.5 GHz [24]. As the antenna has circular polarization, the alignment between both layers is important. As this design uses two different materials and is printed using a single extruder 3D-printer, we need to change filaments. To avoid any gluing of separate pieces, and ensure a successful alignment between the substrate and the spiral, the spiral and the substrate were manufactured in a single 3D-Printing process, using an offset setting that corresponds to the height h of the grounded substrate to change the filament used for the spiral deposition.

V. MEASUREMENT RESULTS
The measured reflection coefficient, maximum gain and axial ratio of the 3D-printed antenna are presented in Fig. 9. The measured |S 11 | exhibits a good matching in the whole Finally, the measured gain radiation pattern at four different frequencies is presented in Fig. 10. Here, the measured cross-polarization (LHCP) level is also presented at the same elevation plane. We can see how the measurement results agree well with the simulation results, having a HPBW of  around ≈ 6 • , and sidelobe levels of ≈ −20 dB. In addition, the values of the measured co-polarization are similar to the ones obtained in the simulations.

VI. CONCLUSION
A parametric study about the new degrees of freedom given by implementing dielectric corrugated leaky wave antennas using 3D-printing has been presented. The results show that this technology can give options to antenna designers in terms of the behavior of the antenna by just varying simple parameters on the construction, namely the height and material of the corrugation. The possibility to change the frequency band where the broadside CP beam is obtained, by keeping the same antenna dimensions can be useful especially when size and integration can be an issue, and also to have better control of the aperture efficiency. In addition, this technology gives a low-cost alternative for antenna topologies that have difficult shapes, and they are costly to manufacture using traditional methods and materials with the required permittivity values.