A novel Bezier spline-based geometry for printed monopole antennas is presented. Quadratic curves are used to describe the outline of the radiating element. The geometry is optimised by a genetic algorithm. A small number of control points are used to define the geometry, ensuring a small search space for the GA. The resulting antenna has an impedance bandwidth from 1.44 to 14.7 GH

Ammann, Max

John, Matthias

English

Arrow@TUDublin

Technological University Dublin ARROW@TU Dublin Articles School of Electrical and Electronic Engineering 2007-01-01 Spline Based Geometry for Printed Monopole Antennas Matthias John Technological University Dublin, matthias.john@tudublin.ie Max Ammann Technological University Dublin, max.ammann@tudublin.ie Follow this and additional works at: https://arrow.tudublin.ie/engscheceart  Part of the Electrical and Computer Engineering Commons Recommended Citation John, M. & Ammann, M. (2007) Spline Based Geometry for Printed Monopole Antennas. Electronics Letters, vol. 43. no. 6 March 15, 317-319. doi:10.1049/el:20073802 This Article is brought to you for free and open access by the School of Electrical and Electronic Engineering at ARROW@TU Dublin. It has been accepted for inclusion in Articles by an authorized administrator of ARROW@TU Dublin. For more information, please contact yvonne.desmond@tudublin.ie, arrow.admin@tudublin.ie, brian.widdis@tudublin.ie. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License Spline-based geometry for printedmonopole antennasM. John and M.J. AmmannA novel Be´zier spline-based geometry for printed monopole antennasis presented. Quadratic curves are used to describe the outline of theradiating element. The geometry is optimised by a genetic algorithm.A small number of control points are used to define the geometry,ensuring a small search space for the GA. The resulting antenna has animpedance bandwidth from 1.44 to 14.7 GHz.Introduction: Geometries of recent UWB antennas are based onsimple geometric elements, such as rectangles [1], circles [2] orellipses [3], or a combination of these [4, 5]. This Letter proposes ageometry based on quadratic Be´zier curves (splines). Splines arecurves generated by quadratic interpolation between control points.The benefit of this technique is an inherently rounded shape of theradiating element. The design overcomes the geometrical constraintsof a circular or elliptical disc and the difficulty of combining simplegeometric elements. A genetic algorithm (GA)-based optimiser isused in the design process. GAs have been used for a variety ofelectromagnetic problems [6, 7], including the design of printedmonopole antennas [8, 9].Fig. 1 Be´zier spline outline and its control points (Pn), virtual controlpoints (Pvn) and boundaries of the control pointsSpline-based geometry: The outline of the radiating element isdescribed by a quadratic Be´zier spline. This spline curve is definedby eight control points P0–P7. Fig. 1 shows the outline curve and itscontrol points. Point P0 is fixed at (0,0), the point where the antenna isfed by a 50 O microstrip line. Points P1–P3 are defined by their x- andy-co-ordinates. Point P4 is fixed at y¼ 0 and can only be positionedalong the x-axis. Points P5–P7 are derived from points P1–P3 bymirroring them along the x-axis. This creates a radiator with x-axissymmetry and provides quasi-omnidirectional radiation patterns in theH-plane (y–z plane). The low-frequency resonant modes yield omni-directional properties irrespective of the symmetry, but the highermodes are travelling-wave modes [2] and their patterns are improvedwith symmetry. To achieve a closed curve in CST Microwave Studio,the curve is constructed in the following way. A ‘virtual’ control pointPvn is placed in the middle of each line between two control points. Aquadratic Be´zier curve is than generated from each adjacent pair of‘virtual’ points with the real point between them. The tangent on eachof these ‘virtual’ endpoints is the same for the two curves that meetthere, so that a smooth transition between adjacent curve segments isensured. The virtual points are marked by circles in Fig. 1.The expression defining the set of quadratic Be´zier curves Bn(t),n2 [0, 7] is given by:BnðtÞ¼ ð1 tÞ2PvnxPvny þ2tð1 tÞ PnxPny þ t2 Pvnþ1xPvnþ1y ; t2 ½0;1;n2 ½0;7where Pvn is the ‘virtual’ control point before Pn, and Pvnþ1 is the‘virtual’ control point after Pn. For the case of n¼ 7, Pvnþ1 is Pv0. Theresulting curve does not pass through any of the endpoints Pn.Genetic algorithm optimisation: The position of the control points isoptimised by a genetic algorithm. The problem is encoded in binaryformat. Single-point crossover and tournament selection are used. Themutation rate is 1%. The population size was set to 30 and evolvedover 20 generations. Multiple objectives are used in the fitnessfunction. The GA operates on points P1–P4 (P5–P7 are mirroredand not in the scope of the GA). The boundaries of these points arealso shown in Fig. 1. The x- and y-co-ordinates of points P1–P3 andthe x-co-ordinate of point P4 are encoded in a binary format.Altogether, these seven parameters are encoded to only 35 bits.This is a very small search space considering the complexity of theresulting geometry.The design goal consists of two parts. The first is to optimise for awide band between 0 and 20 GHz; this is weighted at 70%. The secondgoal is to reduce the lower edge frequency; this is weighted with 30%.The FDTD simulation software returns the S11 as a list of 1000frequency points. The fitness function is as follows:fitness ¼ 0:7BW þ 0:3ð1000  fLEÞwhereBW ¼ P1000n¼0ðS11ðnÞ  10 dBÞand fLE¼ point of lower edge frequency, i.e. the smallest n where S11(n)10 dB. The final geometry optimised by the GA is shown in Fig. 2.It can be seen that the element curves away smoothly from the feedpoint. The maximal possible height is exploited as point P5 is placed35 mm away from the feed point. The computational time needed forthe 600 evaluations amounts to four days on a single computer.Fig. 2 Optimised geometry of antennaAntenna geometry: The antenna is printed on Rogers microwavelaminate RO4350B of 0.762 mm thickness, er¼ 3.48 andtan d¼ 0.0037. The substrate has a size of w¼ 45 mm by l¼ 85 mmwith the groundplane located on the rearside. The dimension of thegroundplane is lg¼ 45 mm square. The antenna is fed by a wf ¼ 2.5 mmmicrostrip feedline. The dimensions of the spline-based radiating elementare ls¼ 33 mm by ws¼ 32 mm.ELECTRONICS LETTERS 15th March 2007 Vol. 43 No. 6Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on April 24, 2009 at 10:05 from IEEE Xplore.  Restrictions apply.Fig. 3 Simulated and measured return lossFig. 4 Measured radiation patterns in y–z and x–z planesResults: The simulated and measured return losses are shown inFig. 3. It can be seen that the measured return loss is greater than10 dB from 1.44 to 14.7 GHz. This is an impedance bandwidth ratioof 10.2:1, which is very wide for a printed monopole. Measuredradiation patterns are shown in Fig. 4. The H-plane patterns areomnidirectional up to about 8 GHz. The gain is 2.8 dBi at 2 GHz,4.3 dBi at 6 GHz, 4.8 dBi at 10 GHz and 5.3 dBi at 14 GHz. Theradiation efficiency at these frequencies is 91, 96, 92 and 89%,respectively. The antenna is proposed for multimode use in highercellular, WLAN and UWB systems.Conclusions: A novel Be´zier spline-based technique for the design ofprinted monopole antennas has been presented. Only seven para-meters are necessary to define the geometry; this also allows for asmall 35 bit search space for the GA. It has been shown that thistechnique can give very wide bandwidths of 10.2:1.Acknowledgment: This work is supported by Science FoundationIreland.# The Institution of Engineering and Technology 200711 December 2006Electronics Letters online no: 20073802doi: 10.1049/el:20073802M. John and M.J. Ammann (Centre for Telecommunications Value-Chain Research, School of Electronic & Communications Engineering,Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland)E-mail: max.ammann@dit.ieReferences1 Chen, H.D., Li, J.N., and Huang, Y.F.: ‘Band-notched ultra-widebandsquare slot antenna’, Microw. Opt. Technol. Lett., 2006, 48, (12),pp. 2427–24292 Liang, J., Chiau, C.C., Chen, X., and Parini, C.G.: ‘Study of a printedcircular disk monopole antenna for UWB systems’, IEEE Trans.Antennas Propag., 2005, 53, (11), pp. 3500–35043 Angelopoulos, E.S., et al.: ‘Circular and elliptical CPW-fed slot andmicrostrip-fed antennas for ultrawideband applications’, IEEE AntennasWirel. Propag. Lett., 2006, 5, pp. 294–2974 Chen, Z.N., et al.: ‘Planar antennas: promising solutions for microwaveUWB applications’, Microw. Mag., 2006, 7, (6), pp. 63–735 Karacolac, T., and Topsakal, E.: ‘A double-sided rounded bow-tieantenna (DSRBA) for UWB communication’, IEEE Antennas Wirel.Propag. Lett., 2006, 5, pp. 446–4496 Haupt, R.L.: ‘An introduction to genetic algorithms forelectromagnetics’, IEEE Antennas Propag. Mag., 1995, 37, (2), pp. 7–157 Johnson, J.M., and Rahmat-Samii, Y.: ‘Genetic algorithms in engineeringelectromagnetics’, IEEE Antennas Propag. Mag., 1997, 39, (4), pp. 7–218 Griffiths, L.A., Furse, C., and Chung, Y.C.: ‘Broadband and multibandantenna design using the genetic algorithm to create amorphous shapesusing ellipses’, IEEE Trans. Antennas Propag., 2005, 54, (10), pp. 2776–27829 John, M., and Ammann, M.J.: ‘Optimisation of a wide-band printedmonopole antenna using a genetic algorithm’. LAPC - LoughboroughAntennas & Propagation Conf., April 2006, pp. 237–240ELECTRONICS LETTERS 15th March 2007 Vol. 43 No. 6Authorized licensed use limited to: DUBLIN INSTITUTE OF TECHNOLOGY. Downloaded on April 24, 2009 at 10:05 from IEEE Xplore.  Restrictions apply.

Spline Based Geometry for Printed Monopole Antennas

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Spline Based Geometry for Printed Monopole Antennas

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