Directivity of an antenna embedded inside a Fabry-Perot cavity: Analysis and design

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1 Diectivity o an antenna embedded inside a Faby-Peot cavity: Analysis and design Halim Boutayeb, Kouoch Mahdjoubi, Anne-Claude Taot, Tayeb Denidni To cite this vesion: Halim Boutayeb, Kouoch Mahdjoubi, Anne-Claude Taot, Tayeb Denidni. Diectivity o an antenna embedded inside a Faby-Peot cavity: Analysis and design. Micowave and Optical Technology Lettes, Wiley, 6, 48, pp. -7. <./mop.49>. <hal-33695> HAL Id: hal Submitted on 7 Feb 7 HAL is a multi-disciplinay open access achive o the deposit and dissemination o scientiic eseach documents, whethe they ae published o not. The documents may come om teaching and eseach institutions in Fance o aboad, o om public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diusion de documents scientiiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche ançais ou étanges, des laboatoies publics ou pivés.

2 Diectivity o an Antenna Embedded Inside a Faby-Peot Cavity: Analysis and Design H. Boutayeb, K. Mahdjoubi, A.-C. Taot and T.A. Denidni INRS-EMT, Univesity o uébec, 8 ue de la Gauchetiee, Montéal uébec H5A K6, Canada. boutayeb@ins-emt.uquebec.ca. Fax: (54) IETR (Institut d' Électonique et de Télécommunications de Rennes), UMR CNRS 664, Avenue du Généal Leclec, 354 Rennes, Fance. Abstact The enhancement o diectivity o a monopole located in a Faby-Peot type cavity is studied. The analysis is based on the esponse o the cavity excited om its inside by electomagnetic waves. To validate the poposed antenna, an expeimental pototype was designed, abicated and measued. Key wods: Peiodic stuctues; Faby-Peot cavity; Diective antennas

3 . Intoduction Diective and low-cost antennas composed o a single eed pesent an attactive solution o seveal wieless communication systems, such as high-speed wieless LANs, satellite systems and point-to-point links. Thei single-eed system allows to incease the gain with low complexity compaed to eeding netwoks used in conventional antenna aays. In this pape, a diective antenna composed o a monopole embedded inside a Faby-Peot cavity is poposed. Recently, seveal authos have developed techniques to obtain high diective antennas by embedding a dipole inside a Faby-Peot cavity [-3]. In [], a elation between the hal powe beamwidth and the quality acto o the cavity (at the esonant equency o the cavity) has been poposed and validated numeically, wheeas in [], it has been demonstated that this diectivity impovement has an analogy with past eseach in optical physics. In [3], a study on the input impedance o the antenna has been pesented. In [4, 5], an antenna based on a Electomagnetic Band Gap (EBG) mateial with a deect has been poposed. The antenna consists o a Faby-Peot cavity between a patch antenna and the EBG mateial. Anothe way o poducing a high-gain antenna has been intoduced in the 5's [6]. This technique uses a Patially Relecting Suace (PRS) to intoduce leaky waves and beamoming eects when placed in ont o a gounded waveguide apetue. A ay theoy has been poposed, showing that the diectivity o the antenna inceases when the electivity o the PRS inceases. This kind o antenna has been evisited ecently [7], whee the PRS has been optimized to enlage the antenna bandwidth. To ou knowledge, the diectivity at dieent equencies o antennas based on a Faby-Peot cavity has not been suiciently studied. Indeed, the diectivity (o the beamwidth) is oten calculated at the esonant equency o the cavity. Howeve, as it is shown in this pape, the maximum o the diectivity (o minimum o the beamwidth) is obtained at anothe equency. In this contibution, a ay method is applied to pedict the ocusing chaacteistics o the poposed antenna. To demonstate the poposed appoach, an antenna pototype was build and measued, and the expeimental esults show a good ageement with the pedicted ones.. Analysis The analysis pocedue o the poposed antenna is given in the ollowing sections. In Section., the stuctue is chaacteized using the equency and angula esponses o the Faby-Peot

4 cavity to a plane wave excitation, which is in the cente o the cavity. This equency and angula unction is called T. Usually, in the Faby-Peot inteeomete, the souce is outside the Faby- Peot cavity [8], wheeas hee the souce is placed inside the cavity, which necessitates new omulas o the chaacteization. Using the calculated unction T, in Sections. and.3, the elationships o the bandwidths at the hal-powe and at an abitay powe atio ae developed and pesented. In Section.4, these elations ae then used to calculate new esults o the hal powe beamwidth o the adiation patten o the Faby-Peot-antenna, and the main esults ae inally applied in Section.5 o the antenna design... Chaacteization Figue (a) shows the geomety o the poposed stuctue. This stuctue consists o two metallic wie ows located on each side o a point souce, whee a TM-wave excitation is consideed. The wies ae spaced peiodically with the peiod P, the distance between the two ows is and the diamete o the wies is a. In ode to chaacteize the stuctue in tems o equency and adiation patten, the ays going at the diection θ ae consideed (Fig. (b)). The ows o wies act as patially electing suaces to these ays, with the complex election and tansmission coeicients and t. An ininite numbe o ays exit om the cavity at the diection θ. The amplitude o the diect tansmitted ay (t ), using an abitay eeence o phase, is equal to t. The amplitude o the once-elected ay (t ) can be witten as whee jkd jkd / tan ( θ) sin( θ) cos( θ) jkd cos( θ) t = te = te () π k = is the ee space wave numbe, is the equency and c is the velocity o wave c popagation in ee space. In Eq. (), ( ) ( ) kd cos ( θ) n epesents the phase vaiation duing displacement and kd / tan θ sin θ is the path dieence between ay and ay. Thus, the amplitude o the nth-elected tansmitted ay ( t ) is witten t = t e n n jnkd cos The total tansmitted amplitude is then witten as ( θ) n jnkd cos( θ) t T = tn = t e = jkd cos( θ) (3) e n= n= D () 3

5 Using the enegy consevation elation modulus o T can be witten t = [8] and ate simpliications, the squaed T = cos ( kd cos( θ) ϕ ) (4) whee ϕ is the phase o. In ode to obtain simple analytical esults, the election and tansmission coeicients and ae consideed constant (i.e. independent o the equency and angle). This appoximation is usually consideed valid in the equency band o inteest [6, 7]. t When the esonance condition kd ( θ) = ϕ cos is veiied, T achieves its maximum value T max T max = = (5) Fo instance, we conside =. 84, ϕ =.5 ad, and D = 4mm. In Fig., T is plotted vesus equency at θ = in the ist abscise, and vesus cos ( θ) at the esonant equency = 3 GHz in the second abscise. The bandwidth o T vesus equency at its hal squaed maximum amplitude is deined as /, whee is the quality acto o the cavity []. Figue 3 shows T vesus angle at dieent equencies. These adiation pattens exhibit diective beams at the nomal diections ( θ = and θ = 8 ) o equencies lowe than. Fo equencies geate than, lobs appea on each side o the nomal axis. θ 3 db is deined as the hal powe beamwidth o the main lobs at the nomal diections (see Fig. 3). In the next sections, the quality acto is ist witten as unction o the election coeicient between the hal powe beamwidth and the quality acto is developed... Hal powe bandwidth, and then, the inteelation To ind the expession o / as a unction o the election coeicient, the ollowing equation is esolved cos = T max ( ψ ϕ ) = ± (6) 4

6 ( ) whee ψ = kd cos θ, and ψ and maximum o T. Then, esolving Eq. (6) gives ψ ± / can be expessed as = ϕ = ϕ ψ = ψ ψ ae the values o ψ coesponding to the hal o the ( ) ± ac cos (7) ψ ψ = ac cos ( ) ϕ (8) The appoximate elation is obtained by consideing close to, which is the condition to obtain high diectivity [6, 7]..3. Bandwidth o an abitay powe atio x The hal powe bandwidth / is obtained o T /. We can also deine a bandwidth / max x detemined o T / max x. Fo this, we have to esolve the ollowing equation : cos = ( ψ ϕ ) x x± (9) which leads to the ollowing expession o / x : x ψ = ψ x ( ) x ψ = ac cos ( x ) x () ψ x ϕ x whee x = T / T. The appoximate elation is obtained by consideing close to and x is max such that ( x ) ( ) << esonance..4. Hal powe beamwidth. Then, the appoximate elation is valid o equencies nea the The bandwidth obtained o T /(x) is noted /. To esolve the inteelation between the max angula beamwidth and the equency bandwidth, a gaphical method that is descibed in this x 5

7 section is used. Two cases ae consideed: the case, and the case. Note that is not deined at > θ 3dB, because o these equencies, the level o T at nomal is ineio to the hal o T. The link between the beamwidth θ 3 db and the bandwidths / max and is shown in Fig. 4, o obtained / x x. Fom this igue, the ollowing elation can be θ db = cos () 3 x With the appoximation o a small beamwidth, the elation can be witten : x θ x x 3dB Using Eq. (), the beamwidth is then given by () x x θ3db, (3) Figue 5 shows the elationship between the beamwidth θ3db and the bandwidths / and / x when. Fom the cuve pesented in Fig. 5, the ollowing equation can be obtained Then, at x beamwidth can be expessed as θ = cos 3dB x θ 3 db, (5) θ 3dB (4), with the appoximation o a small beamwidth, and using Eq. (), the Now, the link between and is obtained o all equencies. Figue 6 exhibits the beamwidth vesus equency using Eqs. (3) and (5). Fom this igue, it can be seen that the minimum o θ 3dB is obtained o /. By minimizing Eq. (3), one can see that the minimum o is obtained o x =.5, and then it can be witten θ 3dB θ 3 db min (6) 6

8 The equency θ3db min coesponding to this value is obtained om θ. 5 3dB min =.5 (7) Then θ3db min Fo close to, the quality acto is high and then is close to. θ3db min (8).5. Applications Fom the pevious esults, consideing close to, the minimum o the beamwidth θ 3 db is obtained at a equency, which is slightly smalle than the esonance. This equency can be witten as θ3db min θ3db min At θ3db, the beamwidth θ 3dB is given by min (9) θ 3 db min () At, using Eq. (5) with x =, the ollowing elation is obtained θ 3 db, () The quality acto is obtained om the ollowing equation ϕ () The knowledge o the election coeicient allows then to obtain impotant paametes o the adiation pattens o the poposed antenna. Fo this, numeical simulations using the Finite Dieence Time Domain (FDTD) method wee caied out to obtain the election coeicient, o an ininite gid o metallic wies with the ollowing chaacteistics: P = mm a = mm. In Fig. 7, T is plotted using Eq. (4) and the computed coeicient, which is consideed now dependent on the equency. Fom this igue, the esonant equency o the and 7

9 stuctue is = 3 GHz. The modulus and phase o at ae.84 and.5 ad, espectively. These values ae used to calculate / in Eq. (). Then, it is possible to evaluate the equency o maximum diectivity and the beamwidth at this equency and at the esonant equency using Eqs.(9)-(). In the ollowing section, esults om Eqs.(9)-() ae compaed with expeimental data. 3. Expeimental esults To validate ou appoach, a pototype o the stuctue was abicated and measued. A monopole is used as an excitation souce. Figue 8 gives the photogaph o the abicated antenna. The wies ae 5 cm length and mm diamete, the numbe o wies in each ow is 8, the cavity is D = 4 mm width, the peiod is P = mm, the monopole is 5 mm length and mm diamete. The dimensions o the gound plane ae..85 GHz 6 cm The adiation pattens o the poposed antenna wee measued in an anechoic chambe located at INRS, in Monteal. As an example, the measued adiation pattens o the antenna in the H-plane and E-plane at ae plotted in Fig. 9, showing two diective beams at the nomal diections. Figue exhibits the measued diectivity vesus equency. Fom this cuve, the maximum o diectivity (coesponding to the minimum o beamwidth) is obtained at.85 GHz. Fom Eq. (9), it is obtained. 846 GHz, which shows a good ageement with θ 3dB min measued ones. The measued beamwidths ae 8.8 and 4. at.85 GHz and 3 GHz, espectively. The esults obtained om Eqs. () and () ae 3.8 and 43.6, these show also a good ageement with the pevious expeimental data. To conclude the expeimental pat, note that the matching o the antenna can be done at the equency o maximum diectivity using conventional techniques (e.g., stubs on the eeding line). 4. Conclusion An analysis o enhancing the diectivity o an antenna based on a Faby-Peot cavity has been pesented. The equency o maximum diectivity and the beamwidth at dieent equencies have been pedicted with new analytical expessions. An antenna pototype has been abicated and tested, and a good ageement has been achieved between theoetical and expeimental esults showing the useulness o the poposed appoach. 8

10 REFERENCES. T. Akalin, J. Danglot, O. Vanbesien, and D. Lippens, A Highly Diective Dipole Antenna Embedded in a Faby-Peot Type Cavity, IEEE Micowave Wieless Compon Lett (), R. Biswas, E. Ozbay, B. Temelkuan, M. Bayandi, M. Sigalas, and K.-M. Ho, Exceptionally diectional souces with Photonic Band-Gap cystals, Optical Society o Ameica 8 (), H. Boutayeb, K. Mahdjoubi, and A.C. Taot, Design o a Diective and Matched Antenna with a plana EBG stuctue, IEEE Antennas and Popagat Society Intenational Symposium, AP- (4), M. Thevenot, C. Cheype, A. Reineix and B. Jecko, Diective Photonic Band-Gap Antennas, IEEE Tans Micowave Theoy Tech 47 (999), C. Seie, C. Cheype, R. Chantalat, M. Thevenot, T. Monediee, A. Reineix, and B. Jecko, D photonic bandgap esonato antenna, Micowave Opt Technol Lett 9 (), G.V. Tentini, Patially electing sheet aays, IRE Tans Antennas Popagat 4 (956), A.P. Feesidis and J.C. Vadaxoglou, High gain plana antenna using optimized patially elective suaces, IEE Micow Antennas Popagat 48 (), E. Hecht, Optics, Addison Wesley, San Fancisco, CA,,

11 Figue Captions: FIG. : (a) Geomety o the antenna based on a Faby-Peot cavity (b) Sum o the tansmitted ays, outside the cavity, at the diection θ. FIG. : T vesus equency (at θ = ), and vesus cos ( θ) (at ). FIG. 3: Nomalized T vesus θ (logaithm scale) at dieent equencies. FIG. 4: Relationship between θ, and at 3dB / x / x FIG. 5: Relationship between θ, and at FIG. 6: Beamwidth 3dB vesus equency. θ 3dB. / / x. FIG. 7: T at θ = (computed with Matlab, using, calculated with a FDTD method). FIG. 8: Photogaph o the abicated antenna. The monopole is ed via an SMA connecto. FIG. 9: Measued adiation pattens at.85 GHz. FIG. : Measued diectivity in the H-plane vesus equency

12 FIG.

13 FIG.

14 FIG.3 3

15 FIG. 4 4

16 FIG.5 5

17 FIG.6 6

18 FIG. 7 7

19 FIG.8 8

20 FIG.9 9

21 FIG.