A design of a directive antenna based on a Fabry-Pérot cavity is described, using a single metallic partially reflecting surface (PRS) in front of a coaxial-fed patch antenna. The main features of this type of antennas are their low profile and single feeding point. The design is initially carried out following an approximate ray model analysis using the extracted PRS characteristics from electromagnetic simulations. The antenna performance is also simulated, obtaining a directivity of 20.6 dBi for 15.25 GHz, and verifying its predicted behaviour. Furthermore, a prototype is manufactured at the group premises and some preliminary measurements are presented.The development of this research project is being possible thanks to the Initiation to Research Grant of the I Plan
Propio de Investigaci´on y Transferencia of the Universidadnde Málaga. This project has also received funding from
the Spanish MCIU/AEI/FEDER (Programa Estatal de I+D+i Orientada a los Retos de la Sociedad) under grant RTI2018-
097098-J-I00.

Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Abdo-Sánchez, Elena

Camacho-Peñalosa, Carlos

Hernández-Escobar, Alberto

Mateos-Ruíz, Pablo

English

Mateos-Ruiz, Pablo

Abdo-Sánchez, María Elena

Repositorio Institucional Universidad de Málaga

Design and Fabrication of a Fabry-Pérot CavityAntenna for the Ku-bandPablo Mateos-Ruiz, Alberto Hernández-Escobar, Elena Abdo-Sánchez, Carlos Camacho-Peñalosa{pablomr, ahe, elenaabdo, ccp}@ic.uma.esDpto. de Ingenierı́a de Comunicaciones, Universidad de Málaga – Andalucı́a Tech,E.T.S. de Ingenierı́a de Telecomunicación, Bulevar Louis Pasteur 35, 29010 Málaga, Spain.Abstract—A design of a directive antenna based on a Fabry-Pérot cavity is described, using a single metallic partiallyreflecting surface (PRS) in front of a coaxial-fed patch antenna.The main features of this type of antennas are their low profileand single feeding point. The design is initially carried outfollowing an approximate ray model analysis using the extractedPRS characteristics from electromagnetic simulations. The an-tenna performance is also simulated, obtaining a directivity of20.6dBi for 15.25GHz, and verifying its predicted behaviour.Furthermore, a prototype is manufactured at the group premisesand some measurements are presented.I. INTRODUCTIONFabry-Pérot Cavity Antennas (FPCAs) have gained popu-larity over the last few years as a compact low-cost solutionfor designing very directive antennas in the microwave andmillimetre-wave regions. FPCAs have a single feeding point,decreasing their complexity compared to feeding networksused in conventional array antennas. This solution was firstproposed by G. V. Trentini in [1], and it has been furtherstudied to this day. This technique is based on the operatingprinciple of Fabry-Pérot resonators, using a passive partiallyreflecting surface in front of a ground plane. Thereby, a leaky-wave and beamforming effect is introduced, which increasesthe directivity of the primary source inside the resulting cavity.The antenna bandwidth and the frequency for which themain resonance occurs strongly depend on the characteris-tics of the PRS and its separation from the ground plane.Therefore, the PRS design is crucial. In this case, its partialreflection is obtained from a frequency selective surface (FSS)made of apertures on a conducting plane. FSSs are arrays ofelements commonly used for filtering electromagnetic waveswhich are partially reflecting near their resonance frequency.Moreover, they are planar structures easy to model and man-ufacture, making them convenient for building a prototype.In this paper, an analytical and numerical study on thedesign process of this type of FPCA is presented. The simpleray theory from [1] has been used for obtaining the maindesign expressions and theoretical radiation patterns. It isbased on multiple reflections between the ground plane andthe PRS, which are both assumed to be infinite. In practice,however, the finite size of the antenna must be taken intoaccount to achieve a high gain and good efficiency. Besides,the radiation pattern will be affected by the diffracted fields atthe antenna edges. All these effects are accounted for throughelectromagnetic simulations using Ansys® HFSS software.This antenna is designed to operate in the Ku-band (12–18GHz), mainly used in satellite communications. The purposeis to study the directivity that can be achieved with this type oftechnique and its limitations. Also, a prototype of this antennahas been manufactured at our premises at the University ofMálaga with low-cost materials, which is also shown alongwith the explanation of the fabrication process taken and somepreliminary measurements.II. SIMPLIFIED RAY MODEL ANALYSISBeing the first analysis model derived for FPCAs in [1], itis the simplest one while providing key information for thedesign of these antennas. A brief outline of the ray modelanalysis is made below.The structure is composed of a radiation source on aconducting plane and a PRS at a distance D parallel to it.These surfaces are assumed to be infinite, thus the electro-magnetic field originated at the source will bounce betweenboth surfaces until completely transmitted through the PRS.The source generates an electric fieldEsource(θ) = E0f(θ)and the PRS is assumed to be lossless, homogeneous, isotropicand characterized by its reflection coefficient R = r ejφ,dependent on frequency and the angle of incidence θ.As derived in [1], each ray transmitted through the PRSwill have a complex amplitude An, being its sub-index thenumber of times it has bounced between the PRS and theground plane. Knowing the expression of the first transmittedrayA0 = E0f(θ)√1−R2 e−jk Dcos θ ,where k is the wavenumber, the amplitude of any ray at thesame wavefront as a function of it can be expressed asAn = A0(−Re−jk2D cos θ)nand the total electric field would be the sum of all these partialrays, being its intensity in the far-fieldET (ω, θ) =∞∑n=0An = E0f(θ)√1−R2 e−jk Dcos θ1 +Re−jk2D cos θ. (1)Consequently, the relation between the cavity radiatedpower and the source delivered power, called Transmissivity,can be obtained as|ET (ω, θ)|2|E0|2=(1− r2) f2(θ)1 + 2r cos(φ+ π − 4πλD cos θ)+ r2.(2)Note that the transmissivity and the antenna directivity arenot the same, although they are related by a scale factor de-pending on the radiation pattern for each frequency. MaximumdxdyLxLytDxyzFig. 1. Cavity with the selected PRS design.power at broadside direction (θ = 0°) is obtained whenφ+ π − 4πλD = 0 (3)and hence, the resonance distance Dr between the PRS andthe ground plane can be derived as followsDr =(φπ+ 1)λr4+Nλr2, N ∈ Z (4)where λr is the desired cavity resonance wavelength. Ad-ditionally, the maximum transmissivity for the resonancedistance can be obtained through the following expression [2]|ET (ω, 0°)|2|Esource(ω, 0°)|2=1− r2(1− r)2 =1 + r1− r (5)and making (2) to equal half of its maximum, an expressionfor the half-power fractional bandwidth is attainedFBW =∆λ−3dBλr=2φ+ πacos[1− 12(1− r)2r]. (6)From these expressions, the usual resonant structure be-haviour can be analysed. The more reflective the PRS is, thegreater the maximum transmissivity the cavity can offer at theexpense of narrower bandwidth.III. DESIGN OF THE FPCAThe design process of a simple FPCA with a resonancefrequency of around 15GHz is explained. First, the design ofthe PRS must be decided and, then, its reflection coefficientcharacterized in order to choose the exact parameters of thePRS for the desired maximum transmissivity. The radiationsource must be designed as well, taking into account that itneeds to be planar and easy to feed.A. PRSFollowing some initial design decisions in [3], the PRS iscomposed of a simple metallic sheet of thickness t = 300 µmand a matrix of square apertures in it (slots) with a periodicityof dx = dy = 5.8mm (0.29λ at 15GHz), as shown inFig. 1. The periodicity is smaller than the wavelength, whichis necessary for the PRS to be considered homogeneous.The size of the apertures sides L = Lx = Ly is obtainedfrom the reflection coefficient value through electromagneticsimulations.Assuming a desired maximum transmissivity of around18 dB, from (5) a reflection magnitude of r = 0.97 isobtained. Through electromagnetic simulations in HFSS us-ing periodic boundary conditions and Floquet ports, the S-parameters of an infinitely long PRS can be calculated fromFig. 2. PRS reflection for normal incidence as a function of the slot sidesize obtained from electromagnetic simulations.-20 -10 0 10 2000.20.40.60.81Fig. 3. PRS transmission characteristics as a function of the incidence anglefor different frequencies obtained from electromagnetic simulations.a single periodic cell. As a matter of fact, the unit cell issimulated with rounded corners of radius 1mm to account forthe size of the drill used in the manufacturing stage, as will beexplained in Section V. A parametric analysis is performedunder plane wave normal incidence condition and electricfield linearly polarised in x-direction (which is equivalent toy-direction due to the PRS symmetry). The magnitude andphase of the reflection coefficient for different side sizes Land f = 15GHz are shown in Fig. 2.From these results, it can be extracted that for L =4.1mm the PRS has s11 = 0.9704 ej163.82° and, from (4),Dr = 9.55mm is achieved for this particular configuration.Furthermore, it is also verified that the PRS characteristics donot change rapidly neither in frequency nor for angles closeto normal incidence.In addition, an approximation of the cavity transmissioncharacteristics can be accomplished through a Defect CavityModel usually used to analyse more complex partially re-flecting structures [4] [5], which is based on the resonanceprinciple of Fabry-Pérot. This way, simulating by periodicboundary conditions two parallel unit cells separated a dis-tance 2Dr, the results in Fig. 3 are obtained. It can beobserved that the maximum transmission for normal incidenceoccurs at f = 14.99GHz with a half-power beamwidth of∆θ = 10.7°, giving an approximate geometrical directivity ofaround 25.5 dBi. It is also noticed the usual FPCA frequency-dependent patterns [3]: for lower frequencies than the res-onance one, the transmission decreases, while for greaterfrequencies, a beam split behaviour is produced. Finally, atransmission bandwidth of 0.97% is obtained, which corre-lates with the theoretical value of FBW = 1% (6) for theachieved PRS reflection.B. Radiation sourceA rectangular patch antenna is selected as the radiationsource because of its convenience, simple analysis, low pro-file, and easy feeding through a coaxial cable from belowthe ground plane. In order to ensure the analytical modelassumption that the cavity is filled with air, the dielectric of thepatch antenna is supposed to be air too. Due to the materialsavailable, the substrate thickness is h = 2mm and so, thewidth (x-axis) and length (y-axis) of the patch to resonate at15GHz will be W = 9.1mm and L = 8.9mm, respectively[6].The feeding point of the patch is off-centered along they-axis (Fig. 1). Therefore, the electric field will be mainlylinearly polarized in the YZ plane. To find the exact feeding-point position, electromagnetic simulations are carried outincluding a typical 50Ω coaxial connector into the model.Thereby, it is found that feeding the patch a distance d =3.8mm from the center, a return loss above 30 dB is achievedfor 15GHz with an antenna gain of 8.7 dBi.IV. SIMULATIONSFirst, the finite size of the antenna needs to be accountedfor. The amount of field transmitted through the PRS isproportional to the size of the antenna, the rest being scatteredat the edges. This way, a smaller antenna will have biggersidelobes at the expense of lower directivity. Conversely, if theantenna is too big, the directivity will be more similar to thetheoretical case, but almost no field will reach the edges of thePRS, decreasing the antenna efficiency. Due to computationallimitations, a PRS size of 20x20 slots (11.6x11.6 cm2) isselected.A simulation of the whole antenna (Fig. 1) is carriedout in HFSS with the previously designed parameters anda frequency sweep around the resonance. Fig. 4 shows theantenna gain for both the FPCA and the patch antenna withoutthe PRS, in order to compare the increase in directivitybetween them. These patterns are obtained for f = 15.2GHz,obtaining a FPCA gain of 20.6 dBi, an increase of 11.8 dBrespect to the gain of the patch. The sidelobe level remainsbelow −11 dB with respect to the main lobe level for the E-plane and below −13 dB for the H-plane. However, the side-lobe level increases for higher frequencies (beam split effectrelated) while decreasing for lower ones. Cross-polarizationlevels are below −30 dB in both planes.The frequency of these radiation patterns is the one forwhich the FPCA achieves maximum gain, as can be noticedin Fig. 5. In addition, a theoretical estimation for the broadsidegain is computed from the designed PRS reflection andradiation patterns obtained from (2). A qualitative agreementis verified between the simple ray theory and simulations,with a slightly higher resonance frequency (f = 15.25GHz)than the one predicted, giving a 1.6% relative error. This iscaused by analytical model assumptions that are not satisfiedin practice, such as the infinite PRS size or the plane waveincidence condition. In any case, the resonance frequency can030609012015018021024027030033001020(a)030609012015018021024027030033001020(b)Fig. 4. Simulated gain comparison between designed FPCA and patch-onlyantenna for f = 15.2GHz in (a) the E-plane and (b) the H-plane.13 13.5 14 14.5 15 15.5 16-100102030Fig. 5. FPCA gain in broadside direction as a function of frequency.be easily corrected slightly changing the distance betweenboth sheets. Furthermore, the maximum gain is some decibelsbelow the theoretical asymptotic value due to the sidelobesproduced by diffracted fields at the antenna edges and thepatch antenna performance inside the cavity.Fig. 6. Antenna Prototype.V. FABRICATIONA prototype of the antenna is built to verify the previouswork, explaining the manufacturing process below. Clearly,some design parameters have been chosen depending on theavailable materials. Both the ground plane and the PRS arecopper sheets of 11.6 cm side (around 6λ side at 15GHz). Asthe cavity must be filled with air, the spacing between thesetwo sheets is achieved through some nylon screws and nuts inthe corners holding them separated a fixed distance. The PRSslots, the screw holes and the ground plane feeding point aredrilled using a LPKF ProtoMat S103 PCB milling machine.As aforementioned said, the drill used had a radius of 1mm,thus the PRS was designed considering it.The patch antenna is built using a Eccostock SH foamwith ǫr ≈ 1 and 2mm thickness as dielectric, mainly tosupport the patch on it. As this material is not metallized,a copper tape of width 9.1mm is used for making the patch.A 50Ω SMA coaxial connector with 4.1mm outer diameterand Teflon insulation is soldered to the ground plane and thepatch, sticking it to the foam. Before placing the PRS overit, its reflection coefficient is measured, accomplishing a goodreturn loss value around 14GHz.The whole antenna is assembled with four nuts on eachscrew between the sheets and another one to keep the PRSstill, resulting in the structure shown in Fig. 6. Some mea-surements have been carried out at the group premises witha network analyzer proving that the prototype works qualita-tively. The resonance frequency attained for this structure isaround 14.1GHz with a directivity of around 21 dBi (Figs.5, 7). The observed frequency shift is due to both the limitedprecision at adjusting the resonance distance in practice andthe attempt to align the resonances of the patch and the FPCA.VI. CONCLUSIONSFollowing a simple ray theory approach, the design of aFabry-Pérot cavity antenna consisting of a slotted metallicPRS and a primary patch antenna has been carried out. Theanalytical and numerical study has been presented, findinggood agreement between theoretical and simulated results.It is relevant that the ray model is a theoretical methodwhich, despite its simplicity, gives an easy way to design030609012015018021024027030033001020Fig. 7. Gain comparison between FPCA measurements and simulations fortheir resonance frequencies in the E-plane.FPCAs with a very acceptable outcome. The antenna hasbeen simulated obtaining a directivity of almost 21 dBi. Withregard to increasing the directivity and the bandwidth further,aperiodic PRSs or multiple layer structures would be required.In addition, a prototype has been built and has servedto illustrate the relatively easy and inexpensive process ofits fabrication. Also, qualitative agreement has been foundbetween measurements and simulations. For future work, theuse of a metallized-substrate patch should be considered forthe radiating element in order to decrease manufacturingtolerances. Although the use of a dielectric inside the cavityhas not been contemplated in the ray model, it can be easilyintroduced by characterizing the reflection of the dielectric-on-top-of-ground-plane structure.ACKNOWLEDGEMENTSThe development of this research project is being possiblethanks to the Initiation to Research Grant of the I PlanPropio de Investigación y Transferencia of the Universidadde Málaga. This project has also received funding fromthe Spanish MCIU/AEI/FEDER (Programa Estatal de I+D+iOrientada a los Retos de la Sociedad) under grant RTI2018-097098-J-I00.REFERENCES[1] G. V. Trentini, “Partially reflecting sheet arrays,” IRE Transactions onAntennas and Propagation, vol. 4, no. 4, pp. 666–671, October 1956.[2] Z. Liu, “Effect of primary source location on fabry-perot resonatorantenna,” in 2009 Asia Pacific Microwave Conference, Dec 2009, pp.1809–1812.[3] N. Guerin, S. Enoch, G. Tayeb, P. Sabouroux, P. Vincent, and H. Legay,“A metallic fabry-perot directive antenna,” IEEE Transactions on Anten-nas and Propagation, vol. 54, no. 1, pp. 220–224, Jan 2006.[4] M. T. Xu, L. Si, H. X. Jiang, and X. Lv, “An x-band high-gain low-profile dipole antenna based on electromagnetic band-gap,” in 2018International Conference on Microwave and Millimeter Wave Technology(ICMMT), May 2018, pp. 1–3.[5] C. Cheype, C. Serier, M. Thevenot, T. Monediere, A. Reineix, andB. Jecko, “An electromagnetic bandgap resonator antenna,” IEEE Trans-actions on Antennas and Propagation, vol. 50, no. 9, pp. 1285–1290,Sep. 2002.[6] C. A. Balanis, Antenna Theory: Analysis and Design. Wiley-Interscience, 2005.

Design and fabrication of a Fabry-Pérot cavity antenna for the Ku-band

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Design and fabrication of a Fabry-Pérot cavity antenna for the Ku-band

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