Introduction
The Global Navigation Satellite Systems (GNSS) are nowadays an accurate and convenient solution for the navigation of a diversity of vehicles, from heavy to light ones and from huge to small ones, evolving in the sky [Reference Yinusa1], on the ground [Reference Zhong, Zhang, Liang, Han, Fan, Huang, Xu and Yuan2], or even under water [Reference Johannsen, Schulpen, Manders and Engel3]. Integration of a multi-band antenna on these carriers may be a hard task, especially when the geometry is complex and, above all, when the available space is limited. Planar antennas are well adapted to large structures, whereas conformal ones are required for small cylinder platforms [Reference Tinoco-S., Ribeiro-Filho, Heckler, Lacava and Pereira-Filho4].
Cavity-backed antennas are of interest for integration purposes, as they enable the radiating element to be isolated from its direct surrounding environment, but the cavity can create limitations in terms of impedance bandwidth, for example. Conformation of the antenna to a specific shape minimizes aerodynamic drag by being mounted on or embedded in the curved surface and provides superior radio frequency (RF) performance.
A ME antenna [Reference Luk and Wong5] is interesting for GNSS applications as it has very uniform radiation properties versus frequency close to a Huygens source and a relatively large impedance bandwidth. Moreover, for some specific case scenarios such as medium- or high-altitude Unmanned Aerial Vehicles (UAVs), where the environment can be considered as multipath-free, linearly polarized antennas can be used for GNSS applications although satellite signals are circularly polarized at the cost of 3 dB power loss in the link budget.
The ME dipole, introduced in 2006 [Reference Luk and Wong5], aims to combine an electric and a magnetic dipole to obtain both an impedance wideband behavior, due to the combination of two close resonances, and very stable radiation properties. However, the main drawback was its large electrical size, as the structure needs a large ground plane to work properly.
Evolutions were proposed to decrease the profile of the radiating element by meandering or tilting the magnetic dipole [Reference Ge and Luk6–Reference Luk and Wu8] or adding metamaterial to reduce the overall size [Reference Li, Luk, Ge and Zhang9]. In particular, many different structures with diverse polarizations designed for base station antennas are presented in the study by Luk and Wu [Reference Luk and Wu8]. Miniaturization was also achieved by creating multiple close resonances with the addition of parasitic elements [Reference Zhang, Jiao, Weng, Zhang and Feng10]. This leads to antennas combining a ME radiating element with other types of antennas. In the study by Tao et al. [Reference Tao, Feng and Liu11], the addition of parasitic element over the ME source creates a Yagi–Uda configuration and an impedance dual-band behavior. Modifications on the exciting probe were also investigated with, for example, a double Γ-probe [Reference Neetu, Tiwari and Marwah12], stair-shaped probe [Reference An, Lau, Li and Xue13], or fork shape probe [Reference Causse, Bernard, Sharaiha and Collardey14], which enables dual-band behavior and an antenna matched to 50 Ω for all GNSS bands and telemetry L and S bands (1.16–1.61 GHz and 2.2–2.4 GHz). These modifications change the radiating properties of the classical ME structure.
Cavity-backed configurations of the ME were also investigated, often with large dimensions for the cavity, which can be with different heights to increase the bandwidth of the antenna [Reference Chang, Zhang, Chen and Li15] or conformal with circular array configuration [Reference Feng, Chung, Lai and Zeng16]. Cavity-backed antenna in a smaller cavity is proposed in [Reference Causse, Rodriguez, Bernard, Sharaiha and Collardey17] by combining a specific placement of the probe outside the magnetic dipole and substrate to reduce the electrical size of the elements. For this last structure, three resonances are excited in the band of interest (instead of two for conventional ME antennas and cavity-backed ME antennas), presenting a wider bandwidth than conventional ME antennas of the same dimensions.
Cylindrically conformed patch antennas are also used in linear polarization for positioning L-band applications in single- and dual-band configurations [Reference Chen and Zheng18, Reference Sahoo and Vakula19]. These antennas exhibit a low profile but cannot be used in GNSS multiple constellation application cases because their bandwidth remains very narrow. Besides, considering a printed antenna on a cylinder with a radius smaller than half of a wavelength, higher-order modes appear and become not anymore negligible, shifting the patch resonance frequency and affecting radiation characteristics [Reference Yinusa1, Reference Kellomäki20].
Whereas the concept of ME antenna and its design are well known in planar configuration, to the authors’ knowledge, cylindrical ME antenna was not reported before the recent publication of Feng et al. [Reference Feng, Chung, Lai and Zeng16]. In this last article, a conformal ME dipole is presented within a cylinder radius corresponding to 0.49λ0, whereas the ground plane is of 0.71λ × 0.70λ at the central frequency.
In this article, we show the impact of the conformation on small cylinders (with radius from 0.46λ to 0.18λ) of a wideband linearly polarized cavity-backed ME antenna with a Γ-shape probe located outside of the magnetic dipole [Reference Causse, Rodriguez, Bernard, Sharaiha and Collardey17] and on the performance and the importance of the size of the cavity and of the walls. The coupling between the ME dipole and the cavity walls is demonstrated to be the key phenomenon to keep three resonances with an impedance close to 50 Ω, and finally, the cavity size reduction has proven to be an effective solution to maintain this coupling over a wide band. Well-integrated antennas presenting a cylindrical shape, compact and with good performances are obtained. The conformation enables the proposed antennas to be flush mounted on cylindrical carriers having small radius compared to the wavelength. In section “Planar antenna,” the planar reference antenna dimensions and performances are presented. In section “Study of conformation,” a study of the impact of conformation is proposed. First, the influence of cavity wall height on the input impedance of a planar antenna is shown, and then the conformal case is studied. It is shown that the evolutions of behavior due to the conformation on small cylinders (from 0.46 λ to 0.18 λ) lead to a miniaturization of the ground plane of the antenna while keeping close impedance bandwidth. In section “Optimized antenna and measurement results,” an optimized conformal antenna (radius 44 mm) is presented, and simulation results are compared to measurements. Finally, a conclusion of this work is proposed in section “Conclusion.” This article is an extension of the work [Reference Causse, Bernard, Collardey and Sharaiha21] already proposed by the same authors.
Planar antenna
The reference planar antenna is a ME dipole antenna with a Γ-shaped probe placed outside of the magnetic dipole, as can be seen in Fig. 1. This specific location enables the enhancement of the antenna bandwidth by inducing a third well-controlled resonance in the band of interest of the antenna, as described in the study by Feng et al. [Reference Feng, Chung, Lai and Zeng16], thus enhancing the bandwidth in comparison to conventional ME antennas of the same dimensions. All dimensions are shown in Table 1. The cavity is fulfilled by a dielectric material fabricated using 3D printer filament Preperm ABS300 (εr = 3 and tan δ = 4.6
$\, \times \,{10^{ - 3}}$). The electric dipole resonates in λg/2 (where λg is the guided wavelength in the substrate) at 1.12 GHz, as the excitation probe placement combined with the cavity makes the resonant length equal to (2 × Ldip + Wdip/2) and reduces the length 
${L_{dip}}$ of the electric dipole compared to that obtained in the study by Luk and Wu [Reference Luk and Wong5]. The magnetic dipole resonates in 
${\lambda _g}$/4 at 1.45 GHz, and the probe resonates in 
${\lambda _g}$/4 at 1.7 GHz. The input impedance and the 
${S_{11}}$ parameter magnitude are shown in Fig. 2. The simulations are performed using Ansys HFSS [22]. The E-plane is the YoZ one according to the coordinate system shown in Fig. 1. The cavity walls are made of copper, as are the radiating elements, and they present a height HE on XoZ plane and HH in YoZ plane.
Top view (a), side view (b), and 3-D view (c) of the reference magnetoelectric dipole antenna.
Dimensions of the reference antenna
Simulated Z11 (a) (real part in continuous line and imaginary part in dashed line) and S11 (b) of the reference antenna.
The reference antenna exhibits an impedance bandwidth (|S11| < −10 dB) of 39.0% from 1.13 to 1.67 GHz and external dimensions of 85 × 85 × 35 mm3 (0.39 × 0.39 × 0.16λ03 at the center frequency of 1.38 GHz). The broadside gain of the reference antenna and the 3-dB beamwidth versus frequency are shown in Fig. 3.
Broadside realized gain (a) and 3-dB beamwidth in E- and H-planes (b).
The obtained results are in adequation with the behavior of classical ME antenna with a very steady realized gain of around 5.2 dBi and 3-dB beamwidth over 90° with close values in E- and H-planes of the antenna (respectively, XoZ and YoZ planes). This planar antenna will be compared with conformal evolutions in terms of matching and radiation properties.
Study of conformation
This study aims to characterize the impact of cylindrical conformation on the input impedance and radiation properties of cavity-backed ME antenna. Starting from the optimized planar antenna presented in section “Planar antenna,” first, the impact of the modification of wall height is investigated based on the study by Feng et al. [Reference Feng, Chung, Lai and Zeng16]. This will be helpful to apprehend in a second time the case of a conformal antenna for which the cavity height is lower along the longitudinal axis; the approach is applied to fully conformal structures in the second part of this section.
Planar case
The variation of cavity height for a planar antenna with fixed ground plane dimensions was proposed by Causse et al. [Reference Kellomäki20] (for a similar antenna filled with polypropylene and of dimensions 75 × 75 × 40 mm3). From this study, it can be concluded that the variation of height for the cavity walls parallel to the exciting probe (HH) is the most beneficial for impedance bandwidth enlargement of the antenna considering a relatively small cavity width.
Considering the antenna described in section “Planar antenna,” the cavity width L is varied from 85 to 70 mm in a first time; the other parameters are identical to the ones in Table 1 (optimized for L = 85 mm). The simulated impedance and reflection coefficient are given in Fig. 4. When this width is reduced, the magnitudes of the first and second resonances increase, unmatching the structure for the lowest frequencies and reducing the bandwdith (BW). This is due to the coupling between the ME dipole and the cavity walls parallel to the exciting probe. In fact, when the width L is reduced, these walls are closer to the elements and the coupling increases. We also note a frequency shift of the second resonance (magnetic dipole), as well as, more slightly, of the third resonance.
Simulated (a) input impedance (real part in continuous line and imaginary part in dashed line) and (b) reflection coefficient for various width L (HH = 35 mm).
In a second time, starting from the cavity wall height HH = 35 mm, this parameter is reduced for various cavity width L between 85 and 60 mm. The simulated reflection coefficients are represented in Fig. 5. For L = 85 mm, reducing HH of a few millimeters improves the matching and the BW is similar; in this case, there is no benefit in reducing HH. For L = 80 and 75 mm, the antenna with HH = 35 mm is not matched, whereas it becomes matched for a lower value of HH (33 mm for L = 80 and 31 mm for L = 75 mm). For L = 70 mm, a wide BW is achieved for HH = 28 mm; finally, for L = 65 mm, even by reducing HH, a wide BW could not be achieved. The results are summarized in Table 2. By reducing the cavity height HH, the coupling between the walls and the ME dipole is minimized, and finally, an optimal value of HH could be found for each L value, corresponding to a wide BW. Furthermore, it could be observed from Table 2 that an even wider BW could be achieved with a weaker value of L (down to 70 mm). This phenomenon will be advantageously used in the section Conformal case for conformal antennas.
Simulated reflection coefficients for various HH and L between 85 and 65 mm.
BW of the planar antenna after optimization of the cavity height HH for various cavity width L (reference central frequency of 1.38 GHz)
Conformal case
The cylindrical conformation of the antenna is close to the cavity wall height modification proposed previously. In fact, this conformation is made in the direction orthogonal to the electric dipole (corresponding to the Y axis) as this configuration is the most beneficial for the wideband behavior of the antenna [Reference Kellomäki20]. A schematic of the conformation can be seen in Fig. 6. The cavity walls in E-plane become rounded on top, whereas the cavity walls in H-plane become smaller than those in the planar case. The cavity-backed antenna can be integrated into a cylindrical or partially cylindrical carrier made from conductor material, non-conductor material, or both.
Cut-views of antenna conformation in (a) H-plane and (b) E-plane; (c) 3D view.
The electric dipole is conformed to a cylinder of radius R, and the cavity walls follow the cylinder shape. 
${H_E}$ is fixed to 
${\lambda _g}$/4 with respect to the ME magnetic dipole resonance constraint. 
${H_H}$ can vary within the range [0,
${H_E}$] depending on the radius R.
In this configuration, the length 
${H_H}$ and the width L are directly linked to the conformation radius R according to the following formulas:
\begin{equation}{H_H} = {H_E} - R.\left( {1 - \cos \left( {{{\sin }^{ - 1}}\left( {{L \over {2R}}} \right)} \right)} \right)\end{equation}
\begin{equation}L = 2 \times \sqrt {{R^2} - {{\left( {R - {H_E} + {H_H}} \right)}^2}} \end{equation}These two equations impose that for a given radius R, a unique value of HH corresponds to one value of L; in the optimization step (below), only L is tuned, as HH depends on this parameter. The criteria is to cover the whole GNSS band, but not more, and ideally with an antenna as small as possible. In other terms, if for a given conformation radius R and a given width L, the achieved bandwidth is larger than the GNSS band from 1.16 to 1.61 GHz, then the width L can be optimized to a value corresponding to a bandwidth covering only the GNSS band (the value of HH being affected by the variation of L).
The variation of 
$L$ impacts both the height 
${H_H}$ and the distance between the ME dipole and the cavity. Figure 7 shows, for a chosen value of R = 44 mm, the evolution of the behavior of the antenna input impedance for different values of 
$L$.
Variation of input impedance versus L for R = 44 mm and HE = 35 mm (real part in continuous line and imaginary part in dashed line).
We can observe a very similar behavior compared to the planar case, except that the effects of size reduction are stronger. When 
$L$ is large and 
${H_H}$ is smaller than 20 mm, the electric dipole resonance is shifted out of the band of interest as it behaves like a free space ME dipole (no coupling between cavity and radiating element).
In Table 3 are summarized some values of external dimensions for optimized conformal antennas ; these results are found through numerical simulations. The criteria were impedance bandwidth and working frequencies for fixed cylindrical conformation radii. During the optimization process, the width L was varied in a first time, and other parameters were optimized in a second time to reach a good impedance matching on the GNSS frequency band (mainly the lengths c and Ldip). All the presented results are with HE = 35 mm for the reasons exposed previously. We note that Lmin is the smallest width L, allowing to cover all GNSS bands with a wideband behavior (for a given conformation radius R).
Dimensions of the optimized conformal antennas for different values of conformation radius
We can see that the values Lmin and HH decrease when the radius of conformation R decreases. In fact, the coupling between the radiating element and the cavity becomes weaker if the conformation radius R is decreased, which can be compensated by reducing the cavity width L (because the height HH is higher for a smaller width, and the cavity wall then comes closer to the radiating element). Although other parameters are optimized for each conformation radius R, the optimization of the width L is the key parameter in this process. The results presented in Table 3 lead to conclude that decreasing the radius of conformation brings miniaturization of the antenna without significantly impacting the impedance behavior of the antenna. It has to be noted that without compensating for the coupling reduction due to the conformation by optimizing the cavity width, wideband behavior cannot be achieved. As can be seen from Table 3, the 3-dB beamwidth is affected mainly in the H-plane with a wider beamwidth, which is an advantage for the targeted application. It is to be noted that in comparison to the planar case, the enlargement of the 3 dB beamwidth in E- and H-planes is obtained with an antenna size decrease and a decrease of the cavity walls in H-plane HH. A ground plane area reduction of 53.3% is obtained for a 40-mm radius cylindrical conformation compared to the reference planar antenna. This size reduction is only imputed to the conformation as the dielectric material inside the cavity remains the same. It is to be noted that in comparison to the planar case of discussed in section “Planar antenna” (results given in Fig. 3), the 3 dB beamwidth is more symmetric in E- and H-planes, especially within the small radius R.
Optimized antenna and measurement results
Based on the previous analysis of the impact of conformation on antenna behavior, an optimized ME antenna conformed to a 44-mm radius cylinder is proposed. The prototype of this antenna is shown in Fig. 8, surrounded by a holding frame fabricated using classical 3D printing material Acrylonitrile Butadiene Styrene (ABS) material with 60% material filling. The optimized dimensions shown in Table 3 take into account the small influence of the holding frame. This holding frame has the function to keep the metallic cavity surrounding the antenna closed, as it would be if integrated into a carrier. It is used only for the characterization of the antenna. The integration of this antenna on a metallic carrier would require a slight modification of the proposed dimensions and thus is not shown here as the presented prototype validates the principle.
Prototype of the optimized conformal ME antenna (R = 44 mm).
This structure exhibits external dimensions of 62 × 62 × 35 mm3. The substrate was fabricated with Preperm ABS300 material (εr = 3, tan δ = 4.6 × 10−3) using Ultimaker S5 3-D printer. It was measured using Agilent E8363C network analyzer for S parameters and MVG SG24 anechoic chamber for radiation properties. Measured and simulated S11 are visible in Fig. 9. We can note a good agreement with a small shift of 30 MHz (2,2%) between simulated and measured S11, with 1.16–1.69 GHz for the simulation and 1.20–1.81 GHz (40,5%) for the prototype. The difference is mainly due to the fabrication process and its uncertainties; this shift is attributed to the gaps between the substrate pieces, which is required for the assembly; the repartition of these gaps is not homogeneous, depending on how the manufactured elements (by 3D printing technology) interlock. However, the measurement validates the principle and the considered substrate’s electromagnetic properties.
Simulated and measured |S11| of the conformal optimized antenna.
Measured and simulated realized broadside gain and simulated 3 dB beamwidth in E- and H-planes versus frequency are shown in Fig. 10. Measured 3 dB beamwidth is 106° and 113° for E- and H-planes, respectively, at 1.2 GHz and 116° and 122° for E- and H-planes at 1.61 GHz, corresponding to a maximum of 6° compared to simulation.
Measured gain has a maximum difference of 1.1 dBi with simulation in the 1.2–1.61 GHz frequency band and a mean gain value of 4.2 dBi.
Simulated and measured realized gain (a) and simulated 3 dB beamwidth (b) of the conformal antenna.
These gain values and the radiation patterns observed in Fig. 11 show smaller front to back ratio when compared to classical ME antennas. This is explained by the small dimensions of the ground plane compared to the wavelength (0.285 × 0.285λ02) [Reference Idayachandran and Nakkeeran23, Reference Liu, Li, Zhang, Wu and Xia24], but a good agreement is obtained with simulations. Out of the working bandwidth, the gain drops drastically, which can be an advantage for sensitive applications such as GNSS applications. Radiation efficiency is around 90% between 1.2 and 1.61 GHz. The measured gain variations are attributed to the measurement system uncertainties, which are given by the supplier up to 1 dB. The achieved 3 dB beamwidth values are closer in E- and H-planes for conformal case than for planar antenna of section 2; this can be explained because the configuration is closer to a free space ME antenna. We also note a good symmetry of the radiation pattern, which is typical of ME antennas.
Simulated and measured normalized radiation pattern in E- and H-planes (a and b) at 1.20 GHz and (c and d) at 1.61 GHz.
Conclusion
In this article, a study of the impact of the cylindrical conformation of linear polarisation (LP) cavity-backed ME antenna with a feeding probe located outside of the magnetic dipole was proposed. This study shows the key role of the coupling between the radiating element and the cavity in the wideband response of such structure; as the conformation radius becomes small, the cavity wall height decreases and the coupling is attenuated, and this phenomenon can be compensated by reducing the cavity size. In this case, the wall will be closer to the radiating element without being at the same level. Moreover, wideband behavior is maintained. The level of miniaturization directly depends on the conformation radius considered and increases when the radius decreases. An optimized version of conformal antenna (R = 44 mm) was fabricated to be integrated into a cylindrical carrier using low-cost additive manufacturing. A footprint area reduction of 46% was observed compared to the planar optimized antenna using the same substrate to fill the cavity. The antenna exhibits 37.2% bandwidth, covering all GNSS bands, and a stable gain with a mean value of 4.5 dBi.
Funding statement
This work was funded by the French-German Research Institute of Saint-Louis (ISL), France.
Competing interests
The authors report no conflict of interest.
Alexandre Causse received the engineer degree in electronics from the Ecole Supérieure d’Ingénieurs en Electronique et Electrotechnique (ESIEE), Paris, France, and M.S. in RF communication systems from Gustave Eiffel University, Paris, France, both in 2019. In 2022, he achieved a PhD in antenna design focusing on small cavity-backed wideband antennas for GNSS applications with the French-German Research Institute of Saint-Louis (ISL), Saint-Louis, France, and the Institut d’Electronique et des Technologies du numeRique (IETR), University of Rennes, France. He then joined the Direction Générale de l’Armement (DGA), Rennes, France, as an RF engineer focusing on electronic warfare systems.
Loïc Bernard graduated in Electronics and Communication Systems from the National Institute of Applied Sciences (INSA) of Rennes, France, in 2000. After this engineer degree, he received the PhD degree in electrical engineering from INSA of Rennes, France, in 2003. Then, he joined the French-German Research Institute of Saint-Louis (ISL), France, in May 2004 as a research scientist. He received the “Habilitation à Diriger des Recherches” degree from the University of Rennes 1, Rennes, France, in 2017. In 2021, he also became an associate member of the Institute of Electronic Telecommunication of Rennes (IETR). He is involved in the electronics instrumentation of flying systems with very high dynamics for aerodynamic and ballistic research; his research interests include antennas, antenna arrays, microwave circuits, and metamaterials.
Sylvain Collardey received his PhD degree in telecommunication from the University of Rennes 1, France, in 2002. He graduated in Electronics and Telecommunication Engineering from the University of Rennes 1 in 1998. Currently, he is an associate professor at the University of Rennes and is involved as a researcher in the Department of Antenna and Microwave Devices, IETR. His research interests include characterization and development of small antennas, superdirective antennas, numerical modeling, periodic and non-periodic structures (EBG, metasurfaces, etc.), and RFID technology. He has published more than 100 revue papers and conference communications.
Ala Sharaiha received the PhD and Habilitation à Diriger la Recherche (HDR) degrees in telecommunication from the University of Rennes 1, France, in 1990 and 2001, respectively. Currently, he is a full professor at the University of Rennes 1 and the Co-Head of the Antennas and Microwave Devices Department at the IETR research laboratory (Institute of Electronics and Telecommunications in Rennes). He has graduated/mentored more than 42 PhD students/postdocs and co-authored with them. He has authored or co-authored more than 500 journal and conference papers, concerning antenna theory, analysis, designs, and measurements. He holds 14 patents. His published works have been cited over 2500 times in Google Scholar. His current research interests include small antennas, broadband and UWB antennas, reconfigurable antennas, printed spiral and helical antennas, and antennas for mobile communications. He is presently a French delegate member of the European Association on Antennas and Propagation (EuRAAP) and a member of the small antennas working group of EuRAAP. He is a senior member of the IEEE and is a reviewer for the IEEE APS, IEEE AWPL, the IET Letters, and the IET Microwave Antennas Propagation. He was the conference Chairman of the 11th International Canadian Conference Antenna Technology and Applied Electro-Magnetics (ANTEM), held at Saint-Malo in France, 2005.
