A novel technique to design Fabry-Pérot antennas with non-homogeneous PRS is described. It takes advantage of a transmission line circuit model to efficiently obtain all necessary unit cell designs that satisfy the cavity resonance condition. This approach allows an increase in directivity for a given footprint without decreasing the bandwidth. Some design examples are presented, showing the evolution from a simple single-layer PRS to a non-homogeneous two-layers one. Through electromagnetic simulations, the latter one achieves an increase of about 3 dB in directivity while maintaining the bandwidth. This way, the gain-bandwidth product is improved from a value of 5 to almost 9, effectively raising the antenna efficiency.This work has been supported by the Spanish Ministerio de Ciencia, Innovación y Universidades (MCIU) (Contrato Juan de la Cierva-Incorporación) under Grant IJC2018-038440-I and by the 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

Mateos-Ruiz, Pablo

English

Abdo-Sánchez, María Elena

Repositorio Institucional Universidad de Málaga

Non-homogeneous Fabry-Pérot AntennaDesign at Ku-bandPablo Mateos-Ruiz, Elena Abdo-Sánchez, Carlos Camacho-Peñalosa{pablomr, elenaabdo, ccp}@ic.uma.esInstituto Universitario de Investigación en Telecomunicación, E.T.S. de Ingenierı́a de Telecomunicación,Universidad de Málaga, Andalucı́a Tech, 29010 Málaga, SpainAbstract—A novel technique to design Fabry-Pérot antennaswith non-homogeneous PRS is described. It takes advantage of atransmission line circuit model to efficiently obtain all necessaryunit cell designs that satisfy the cavity resonance condition. Thisapproach allows an increase in directivity for a given footprintwithout decreasing the bandwidth. Some design examples arepresented, showing the evolution from a simple single-layer PRSto a non-homogeneous two-layers one. Through electromagneticsimulations, the latter one achieves an increase of about 3dBin directivity while maintaining the bandwidth. This way, thegain-bandwidth product is improved from a value of 5 to almost9, effectively raising the antenna efficiency.I. INTRODUCTIONIn recent years, Fabry-Pérot Cavity Antennas (FPCAs) havebeen greatly studied as an effective technique to increase thedirectivity of a primary radiation source. This source is placedbetween two parallel surfaces, one being a ground plane andthe other a Partially Reflective Surface (PRS). Trentini [1] wasthe first to prove the capabilities of these structures, basedon Fabry-Pérot resonators and ray theory. These antennashave the advantages of having a low profile, being passiveand offering a high directivity with a single feeding point,in contrast to array antennas which require complex feedingnetworks. However, one of their main drawbacks is theirnarrow bandwidth, which has attracted a lot of attention in aneffort to find ways to solve this problem [2]–[4]. In addition,some works have also focused on dual-band solutions [5], [6],polarization reconfigurability [4] or RCS reduction [7], [8].The lateral size and how much field is diffracted at the cav-ity edges are also factors which require further development.Typically, the maximum antenna size has been limited eitherby available space or computational limitations at simulations.Moreover, as the PRS is more reflective, a larger antenna iscommonly needed for the electromagnetic field to be mostlytransmitted through the PRS and reduce the lateral radiation.Once the antenna lateral size is fixed, the PRS characteris-tics can be varied throughout its length in order to betteradequate its properties to the field density underneath it, andconsequently increasing the antenna efficiency. For example,in [8], a certain degree of heterogeneity is introduced in thePRS design, combining two unit cells with slightly differentresponses to obtain a more desirable overall performance.In this article, the PRS non-homogeneity is explored ingreater depth as a means of both increasing the bandwidthand directivity. This way, the aim is to better exploit the usedspace and accomplish a higher antenna efficiency. First, a briefexplanation on wide-band PRS unit cell design and modellingis given. After that, a typical homogeneous PRS design iscarried out in order to contrast the procedure with a non-homogeneous (NH) design using a novel technique based onthe previously explained circuit model. Finally, these designsare simulated and compared to ascertain the improvement inthe last one.II. PRS DESIGNFrom the simplified ray model, it is derived that, essentially,for a FPCA to work at a desired frequency, the PRS reflectionphase φ must satisfy the resonance condition given by [1] atthat wavelength λ:φ+ π − 4πλD = 0 (1)being D the cavity height, and assuming that the otherreflective surface is a PEC. In addition, the PRS reflectionmagnitude governs the resonance intensity which, in turn, isproportional to the directivity of the antenna.On this basis, a simple design can be carried out by simplyparameterising any PRS design which allows the adjustmentof its reflection magnitude. Once the desired value is achieved,the obtained phase is introduced in (1), thus deriving thenecessary cavity height for the antenna to work at the designfrequency. This process was already explained in more detailin [9].However, the PRS design can be further optimised. Acommon way of doing it is better satisfying the resonancecondition around the design frequency, as described in [10].Rearranging (1), it can be seen that, in order to have maximumdirectivity within a certain frequency range, the PRS reflectionphase must linearly increase with frequency:φ =4πDcf + (2k − 1)π, k ∈ Z. (2)Consequently, the importance of the PRS design has beena cornerstone around which most of the recent state of the artabout FPCAs has mainly focused on. In this way, achievinga positive-gradient reflection phase usually requires the PRSstructure to have a (partial) resonance around the design fre-quency. A more detailed Smith chart-based explanation aboutthe logic behind the positive gradient is given in [2]. From acircuit modelling perspective, at least two components wouldbe necessary for a resonance to be possible. Furthermore,the more degrees of freedom, the better the shaping of thereflection coefficient that can be obtained, but with a morecomplex design associated.In this case, a multi-layer approach has been chosen, as itlets the design of each layer to be simpler while facilitating acomprehensive transmission line modelling of the structure.ZinLsLsCpCpZtxθη0η0LtxLtxCtx(a)(b)Fig. 1. Transmission Line models: (a) complete and (b) simplified.III. TRANSMISSION LINE MODELIn order to synthesize the desired frequency response, awell-known transmission line (TX) model is used to modelthe multi-layer PRS. In it, each PRS layer is modelled asan impedance in parallel, while the spaces between themare modelled with transmission lines characterised by thelength of the gap between both layers and the permittivityof the dielectric used. The vacuum intrinsic impedance mustbe added after the last layer impedance to account for theair after it. This way, the total reflection coefficient can beobtained from the input impedance of the circuit.Although any number of layers can be used, only two areselected to illustrate the design procedure. The FPCA designis carried out around 14GHz, with a complementary designfor each of the layers: squared slots for the inner layer andsquared patches for the outer one. The periodicity of these unitcells is 5mm, which is less than λ/4 at the design frequency,as it must be smaller than the wavelength for them to be seenas homogeneous by the electromagnetic waves.The patches and slots can be modelled as a capacitance Cpand an inductance Ls in parallel, respectively [3]. Both layerscan be assembled from the two sides of a metallized dielectricsheet, making them easier to fabricate. In this design, aRO4350B substrate (εr = 3.66) with thickness hs = 60milsis chosen. This way, the circuit diagram is represented in Fig.1a, where θ = βtx hs and Ztx = 120π/εr.The analytical expression for the input impedance Zin istoo complex due to the transmission line. In this sense, asθ < 1, a short transmission line model can be used, which isrepresented in Fig. 1b. This simplifies the model and allowsa relatively compact input impedance expression:Zin =11jωLs+1jωLtx +1jωCtx +1jωLtx +1jωCp +1η0Γin =Zin − η0Zin + η0(3)where the expressions for the TX inductances and capacitance2 2.5 3 3.5 4 4.500.050.10.150.200.511.522.53Fig. 2. Equivalent capacitance (left) and inductance (right) values for differentside sizes of patch and slot unit cells, respectively, at 14GHz.1.51.41.31.21.110.90.80.70.60.50.950.90.830.740.640.53175172170168165160175180172 170 1681651602 2.5 3 3.5 4 4.522.533.544.5Fig. 3. Reflection magnitude and phase for a mesh of possible PRS designsat f0 = 14GHz.are, respectively,Ltx = Ztx√µεhs2, Ctx =√µεZtxhs. (4)As the dielectric length and permittivity are fixed, thetwo degrees of freedom left reside in the patches and slotsreactances. The range of synthesizable values can be obtainedvarying their sides dp and ds through electromagnetic simu-lations in Ansys HFSS using periodic boundary conditionsand Floquet ports. In addition, to account for the substratenext to the layer, the unit cell simulations are carried out withthe half-space from the cell to the first port filled with air,and the other one filled with the substrate. The results fromthese simulations are shown in Fig. 2. It can be seen thatboth layer unit cells have a very similar response, due to theircomplementarity.With these reactance values, all possible designs can beextracted simply using (3) along the desired frequency range.Taking the reflection coefficient (magnitude and phase) atthe desired frequency (14GHz), an isolines diagram can beplotted, as it effectively represents the key values obtainedfor each design, as can be seen in Fig. 3. In addition, foreach design, its normalized resonance frequency (minimumreflection coefficient) respect to the desired frequency is alsocomputed and represented as the third isolines set. This helps8 10 12 14 16 18 20 220.40.60.81(a) Magnitude.8 10 12 14 16 18 20 22150160170180(b) Phase.Fig. 4. Reflection coefficient for selected homogeneous PRS design.understanding how close to the positive phase gradient thedesign is.It is important to note that negligible coupling betweenthe layers must be ascertained for the model to be correct.This can be checked comparing the frequency response of anydesign extracted with the model and the simulation results ofits corresponding complete unit cell.IV. DESIGN PROCEDUREA. Homogeneous designIn order to select a particular design, the desired reflectionmagnitude is determined first. Afterwards, the design alongthe normalized resonance frequency isoline with unit valuewould be chosen, as it maximizes the bandwidth. There mustbe a compromise between how much directivity is wantedand how much the bandwidth can be widen. For this exampledesign, a PRS reflection magnitude of 0.611 is selected, whichcorresponds with a slot side of ds = 4.08mm and a patch sideof dp = 2.52mm in order to have the PRS resonance just at14GHz. Furthermore, the reflection phase value necessary forobtaining the cavity height in (1) can be directly obtained fromFig. 3. In this case, φ = 164.3°, which gives D = 10.24mm.The frequency response is represented in Fig. 4, where theideal phase from (2) is also illustrated with a dashed line(Fig. 4b). In addition, the results from the electromagneticsimulation of this design are also shown, proving that themodel is accurate enough. The slight discrepancies betweenthe model and the simulations can be explained by the TX linesimplification, layers parasitic effects not taken into account inthe model, coupling effects between the layers and numericalerrors from the simulation. Nevertheless, it can be perfectlyused as a base for these designs.B. Non-homogeneous designAs a type of leaky-wave antenna, FPCAs share the char-acteristic decaying electromagnetic field along its radiantelements. This effect cause a non-uniform PRS illumination,which translates into a lower aperture efficiency. To solve this(a) Trimetric view.(b) Top view.Fig. 5. Non-homogeneous Patch-Slots design (v1) overview.problem, leaky-wave antennas tend to present an increasingleakage factor as you move away from the feeder. In thissense, a similar approach can be followed for FPCAs. It hasbeen aforementioned that the resonance condition dependson the phase of the reflection coefficient, and from Fig. 3a very relevant conclusion can be drawn: it is possible toobtain different reflection magnitudes along the same phaseisoline. This way, the resonance condition can be met whiledecreasing the reflection coefficient of the PRS radially.Consequently, the transmission through it would increaseto compensate for the field decay, and achieving a morehomogeneous PRS illumination.For the bandwidth increase effect to be maintained, aproper phase isoline must be selected. Unfortunately, for thisunit cell, these isolines do not have a shape that adequatelyoverlaps with the resonance frequency ones. Therefore, thechoice of the reflection phase value will depend on whichphase isoline is closer to the unit normalised-frequency isolinealong the range of desired reflection magnitude values, whichwill give the bigger phase gradients.Two similar NH designs are carried out following theprevious guidelines. Both present reflection coefficients whichdecay linearly with the distance from the PRS center, from0.9 (v1) or 0.95 (v2) at it, to 0.45 at its corner unit cells. Forthis range of values, the used phase is 170°, since its unit cellsresonance frequencies are relatively close to 14GHz (Fig. 3).Hence, D = 10.41mm is obtained from (1). In addition, thecomplete PRS is square-shaped with 15 unit cells of side. Anoverview of the design v1 is shown in Fig. 5.V. SIMULATION RESULTSFirst of all, to have a complete comparison, a slots-onlyPRS is also designed to have a reflection coefficient magni-12 12.5 13 13.5 14 14.5 15 15.5 165101520Fig. 6. Simulated directivity at broadside (θ = 0°) for the different designs.Slots Patch-Slots NH v1 NH v2ǫap 23.5% 19.5% 34.1% 37.2%BW 2.45GHz > 2.87GHz 2.78GHz 2.74GHzFBW 17.8% > 21.4% 20.4% 20.0%GBP 5.05 > 5.44 8.25 8.85TABLE I. FIGURES OF MERIT OF THE DIFFERENT DESIGNS.tude of around 0.61 (similar to the patch-slots homogeneousdesign). The slots side used is ds = 4.84mm, the obtainedreflection phase is 127.6° and, accordingly, D = 9.15mm.This and the designs from subsections IV-A and IV-B aresimulated in HFSS using a simple horizontal half-wavelengthdipole as the primary source inside the cavity. The dipolehas a length of 9.54mm and is placed 3.57mm above theground plane parallel to the y-axis, as this configuration iswell adapted without a PRS.The results for the broadside directivity are presented inFig. 6. All designs effectively have their maximum directivityaround 14GHz. In addition, a clear evolution can be observedfrom the simpler slot-only to the NH designs. Qualitatively,the homogeneous patch-slots design achieves a greater band-width (extends below 12GHz) than the slots-only one, havinga more constant directivity over a wider frequency range,thanks to the positive phase gradient technique. Incorporat-ing the non-homogeneity, the increment in the directivity issignificant, taking into account that the bandwidth has notexperimented a detrimental effect with respect to the slot-onlydesign, but even a slightly improvement.Regarding specific figures of merit, in Table I some nu-merical values are shown, such as aperture efficiency (ǫap),half-power bandwidth (BW), fractional bandwidth (FBW) andgain-bandwidth product (GBP), which is defined as follows:GBP =∫ fUfLG(f) dffU − fL(fU − fLfC)= GAVG FBW (5)The improvement in the GBP of the NH designs is no-ticeable, as a higher directivity has been achieved withoutworsening the BW. Furthermore, as the v2 design has a higherstarting reflection magnitude, it achieves a slightly betterdirectivity as expected. Of course, these designs could achieveeven greater directivity values making the PRS bigger, thushaving smaller lateral lobes. However, the main focus in thisstudy is how to exploit the same PRS size to obtain higheraperture efficiencies.VI. CONCLUSIONSA comprehensive process to design non-homogeneous FP-CAs in order to increase the aperture efficiency has beenpresented in this contribution. Moreover, the positive phasegradient technique has been proven to successfully widen theBW, having clearly shown the evolutionary process from asingle layer PRS to a NH multi-layer one.On the other hand, in order to obtain greater bandwidths,several points regarding the unit cell design could be furtherstudied. These would include achieving higher quality factorsin order to better satisfy the resonance condition over a widerfrequency range, and trying different geometries which mayhave a better overlapping between their phase and resonancefrequency isolines. Although the optimum reflection decay toobtain maximum efficiency is still to be studied, simply usinga linear decay with reasonable bounds has already increasedthe maximum directivity in almost 3 dB, proving the potentialof this technique, which resembles metasurfaces design.As immediate future work, a realistic primary radiationsource should be designed and adapted. The latter can beachieved in a computationally efficient way using impedancelayer conditions in HFSS. Finally, a design should be fabri-cated and measured in real conditions.ACKNOWLEDGEMENTSThis work has been supported by the Spanish Ministerio deCiencia, Innovación y Universidades (MCIU) (Contrato Juande la Cierva-Incorporación) under Grant IJC2018-038440-Iand by the 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] F. Qin, S. Gao, G. Wei, Q. Luo, C. Mao, C. Gu, J. Xu, and J. Li,“Wideband circularly polarized Fabry-Perot antenna,” IEEE Antennasand Propagation Magazine, vol. 57, no. 5, pp. 127–135, 2015.[3] N. Wang, Q. Liu, C. Wu, L. Talbi, Q. Zeng, and J. Xu, “WidebandFabry-Perot Resonator antenna with two complementary FSS layers,”IEEE Transactions on Antennas and Propagation, vol. 62, no. 5, pp.2463–2471, 2014.[4] R. Lian, Z. Tang, and Y. Yin, “Design of a broadband polarization-reconfigurable Fabry–Perot resonator antenna,” IEEE Antennas andWireless Propagation Letters, vol. 17, no. 1, pp. 122–125, 2018.[5] M. L. Abdelghani, H. Attia, and T. A. Denidni, “Dual- and widebandFabry–Pérot resonator antenna for WLAN applications,” IEEE Antennasand Wireless Propagation Letters, vol. 16, pp. 473–476, 2017.[6] Y.-H. Lv, X. Ding, and B.-Z. Wang, “Dual-wideband high-gain Fabry-Perot cavity antenna,” IEEE Access, vol. 8, pp. 4754–4760, 2020.[7] L. Zhang, X. Wan, S. Liu, J. Y. Yin, Q. Zhang, H. T. Wu, and T. J. Cui,“Realization of low scattering for a high-gain Fabry–Perot antenna usingcoding metasurface,” IEEE Transactions on Antennas and Propagation,vol. 65, no. 7, pp. 3374–3383, 2017.[8] Z. Liu, S. Liu, X. Zhao, X. Kong, Z. Huang, and B. Bian, “Widebandgain enhancement and RCS reduction of Fabry–Perot antenna usinghybrid reflection method,” IEEE Transactions on Antennas and Propa-gation, vol. 68, no. 9, pp. 6497–6505, 2020.[9] P. Mateos-Ruiz, A. Hernández-Escobar, E. Abdo-Sánchez, andC. Camacho-Peñalosa, “Design and fabrication of a Fabry-Pérot cavityantenna for the Ku-band,” in URSI Málaga, 2020.[10] A. P. Feresidis and J. C. Vardaxoglou, “High gain planar antenna usingoptimised partially reflective surfaces,” IEE Proceedings - Microwaves,Antennas and Propagation, vol. 148, no. 6, pp. 345–350, Dec 2001.

Non-homogeneous Fabry-Pérot Antenna Design at Ku-band

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Non-homogeneous Fabry-Pérot Antenna Design at Ku-band

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