Electromagnetic Analyses and an Equivalent Circuit Model of Microstrip PatchAntenna with Rectangular Defected Ground Plane

Dalia Nashaat(l), Hala A. Elsadek(2\ Esmat Abdallah(2\ Hadia Elhenawy(3) and Magdy F.Iskander (1)

(1) Hawaii Center for Advanced Communication, Hawaii, Honolulu-USA.(2) Electronics Research Institute, Cairo- Egypt.

(3) Faculty of Engineering, Ain Shams University, Cairo, Egypt

Abstract:- This paper presents an investigation of both electromagnetic wave model andequivalent circuit model for microstrip patch antenna (MPA) with rectangular defectedground plane structure (RDGS). The objective of the proposed design is to reduce antennasize from Wi-Fi wireless band to the Bluetooth band. The first part of the paper describes theelectromagnetic wave modeling using the High Frequency Structure Simulator (HFSS®)software to study the effect of RDGS on antenna resonant frequency. An optimization tooltogether with curve fitting were then used to formulate an approximate equation that describesthe identified trends from the simulations. Second part is focused on estimating, using theAdvanced Designing System (ADS) software the parameters of an equivalent circuit modelfor MPA with RDGS. The developed equivalent circuit consists of lumped elements for bothMPA and RDGS structure and also include representation of the electrical and the magneticcoupling between rectangular grounded slot and MPA. Optimum values of the equivalentcircuit elements were determined, and the overall simulation results were confirmedexperimentally.

Index Terms: Microstrip patch antenna (MPA), rectangular defected ground structure(RDGS), high frequency structure simulator HFSS® and advanced designingsystem (ADS).

I. IntroductionAn antenna is a critical component for any RF transceiver and microstrip patch

antennas have been particularly popular for use in wireless applications. Microstrip patchantennas have many advantageous including light weight, low volume, low profile, planarconfiguration, which can be easily made conformal to host surface, and low fabrication cost,hence can be manufactured in large quantities, etc. Miniaturization of MPA presents acritically important design issue in wireless applications. In this paper we use a defect groundstructures (DGS) approach to achieve the miniaturization objective. The used of DGS hasrecently gained significant interests as it rejects certain frequency bands, and hence is part ofthe so called electromagnetic bandgap (EBG) structures [1]. Due to their excellent pass andrejection frequency bands characteristics [2], DGS circuits are widely used in various activeand passive microwaves and millimeter-wave devices. Also the use of one cell of defectground structure often resulted in antenna size reduction. In this paper two methods are usedto analyze an MPA with a defect ground plane structure. Both a full wave analysis using theHFSS® simulator and an equivalent circuit model using the ADS simulator [3] are used in thedesign and characterization of the proposed antenna. In the first part of this paper weinvestigated the effect of RDGS on resonant antenna behavior. HFSS simulation results arethen used to investigate an approximate mathematical formula that describes the effect of thedimension and position changes of one rectangular defect in the ground plane on the antennaresonant frequency. Second part of this paper is focused on using ADS simulations to developa new equivalent circuit model for the MPA antenna with RDGS. The investigated Equivalentcircuit is used to explain electrical and magnetic coupling between MPA and RDGS. Aprototype of the designed antenna is constructed and experimental measurements of the S­parameters confirmed the simulation results.

978-1-4244-3647-7/09/$25.00 ©2009 IEEE

IL Full Wave MethodThe first part of this paper describes a full wave method for analyzing MPA antenna withoutand with rectangular defected ground structure as shown in figure 1. Starting with inset fedmicrostrip patch antenna [4] with side length La= 16mm, side width Wa=15mm on duriodsubstrate with thickness h= 0.813mm and dielectric constant Er =3.38. The ground planedimensions are 25 x 25 mm2 and the distance to the antenna edge is g=3.25mm. The 50ntransmission line feed width is 1.85mm. The reflection coefficient results is presented asshown in figure 2 with resonance frequency at 5.28GHz and an antenna gain equal to IldBand efficiency 11 equal 98%. HFSS is then used to determine the effect of the RDGS onantenna parameters such as antenna the resonant frequency and gain. This is done throughmore than 900 simulations. The process starts by removing a rectangular shape of DGS withlength (L) and width (a) as shown in figure la at distance Xd from the substrate edge, then thevalues of a and L are chosen and fixed. The first step in the procedure is to change the DGSposition on ground plane from Xd=g=3.25mm to the end of antenna length at 16 mm withincrement step length =2mm. The curve showing the changes in resonant frequency withlocations of DGS is illustrated in figure 2. Curve fitting is suggested for these data set withpolynomial equation of order n=3. The resulting curve fit equation (1) gives averagepercentage error of 2.5%. Secondly, same previous procedure is repeated with fixed defectwidth (a) but with changing the defect length L. At each L value, same changing steps ofXd

are repeated as in the first procedure. Thirdly, same procedure is repeated but with fixed Land changing defect width (a). The start value of (a) is 0.3mm and the increment step is also0.3mm up to final value of a=2mm. The start value of L is 2mm with step increment of 2mmup to a final value L=22mm. Table 1 summarizes simulation results. Equation 2 givesaccumulated percentage of error around 7% from the actual values of HFSS simualtions.From above HFSS simulation results, we obtain the value of the minimum frequency whichhappened when equals to 1-1.5mm or at (0.08 to 0.088)Ag from antenna length center. Thisreduction is attributed due to maximum coupling between radiating patch antenna and RDGSin a ground plane.Table 1: shows the coefficients of the polynomial in equations 1

a Coefficient ofX3 Coefficient ofX2 Coefficient ofXl Coefficient Constantmm (A3) (A2) (AI) (Ao)

B03 B13 B02 B12 Bol B11 Boo BIO

0.3 0.08748 0.00219 0.0849 .002913 5.135 0.1 5.188 0.0070.6 0.0945 0.0029 0.085 .003 5.2 0.105 5.17 0.0071 0.26 0.01 .049 0.029 5.951 .107 5.1 .0007

1.6 0.03 0.07 0.05 0.078 12 0.388 5 .0007

~ =0.002oosH(341) ~02 = 0.00327a 2 BO! =8.337a Boo =5.2-0.04341L

~=02416 ~I2 =0.199la-0.09( 2 Bll = 9.37a-l.226 ~o=O.OOllL

Substituting best fit values functions Ao, A}, A2 and A3, hencef i[ GHz. ]1 [ ]x 3 1 0.003277 a

2L -

j=--- -0.2415aL2 +(0.00232 cosh(I.34a))L d +-10000 100 (0.199 a - 0.09a 2 )L2

X d 2 - -.!..-[S.337 asin(9.37 a -1.226)L]xd + (5.2 - 0.04336 a 2 L - 0.007 aL) (2)10

III. Electrical Equivalent Circuit ModelTo help explain the cutoff and attenuation characteristic of the DGS section, an

equivalent circuit model is developed. To help with the development of the equivalent circuit,it is expected that the circuit could exhibit low-pass and band-stop filters performances at thesame time. At a frequency less than the resonance frequency, the circuit behaves like an

(3)

inductor. The equivalent inductive reactance can be easily calculated by using the prototypeelement value of the one-pole response. The parallel capacitance value for the given DGSsection can be extracted from the location of the attenuation pole. On this basic concept, onecan propose that, the defect is electrically coupled to the host microstrip line through the linecapacitance Ck since it is etched in the ground plane, whereas the magnetic coupling can bemodeled by the mutual inductance M1 as well as mutual inductance M2 between the line andLk• Note, L] and L2 model the inductance of the microstrip line (L), where L]=L2=L/2.Accordingly, it is worthwhile to conclude that, the splitrings/wires are electrically and magnetically coupled to the line through the capacitance Ck

and the mutual inductance M2/Ml. ADS simulator is used to deign antenna at wireless bandwith resonant frequency 5.2GHz.

Finally, antenna with defected ground plane is modeled to investigate theeffect of one unit cellon antenna performance. The total equivalent circuit from ADSis shown in figure 3. In the model, the microstrip patch antenna is separated into equalsections and placed between them the equivalent circuit of one unit of defectedground plane. As explained, Ck, Lk presents the effect of magnetic and electricalcoupling, respectively. However from various results, Lk represents the effect of slotwidth (a) and Ck represents the effect of slot length L. The results of Lk and Ck areimplemented in curve fitting algorithm to investigate the resonance frequency.Equation 3 illustrates resonance frequency as a function in Lk and Ck. The ADSsimulation gives antenna reflection coefficient shown in figure 2.f =(1.764L

k

2 +3.116)Ck

-(0.4662-0.025Lk +O.Ol/Lk )

Where Ck in PIand Lk in nH andI in GHz.

The average percentage of error between ADS results and formula equation 3 isaround 3%. For results verification, the antenna is fabricated with DGS of dimensionsL=22mm and a=2mm at distance Xd=9mm as shown in figure 4. Figure 2 shows the reflectioncoefficients comparison between the fabricated and simulated antenna. As it may be seen,good matching between ADS and HFSS results. Further work will be done in near future formany practical cases of dimensions and position of the ground plane defect.

IV. ConclusionThe design and miniaturization of MPA with ground plane defect are described.

Specifically, a microstrip patch antenna design with one cell of rectangular defected groundstructure was simulated using HFSS and an equivalent circuit model was developed usingADS software. Simulation results are used to derive empirical equations by curve fitting datasets with circuit parameters models for both the antenna and the defect ground plane.Equations as function of defect length, width, as well as defect position on antenna groundplane are investigated. The resulted equation from HFSS gives accumulated percentage error7% while the error from ADS equivalent circuit model is 3%. It is concluded that, by usingone cell of RDGS the resonant of the designed MPA is reduced from 5.25GHz to 2.45GHzwith corresponding reduction in antenna size around 50%. The HFSS and ADS models arevalidated by constructing a prototype of the antenna and measuring its S- parameters.Obtained results show good agreement between simulation results and experimental data.

V. References[1] J. A. Ansari and Ram Brij Ram, " Analysis of Broad Bandwidth V-slot Microstrip patch

antenna," microwave and optical technology letters, Vol. 50, No.4, April 2008.[2] J. J. Wang, Y. P. Zhang, Kai Meng Chua, and Albert Chee Wai Lu, "Circuit Model of

Microstrip Patch Antenna on Ceramic Land Grid Array Package for Antenna-ChipCodesign of Highly Integrated RF Transceivers," IEEE Trans. Antennas Propag., vol. 53,no. 12, December. 2005.

[3] R. W. Deamley and A. R. F. Barel, "A comparison of models to determine the resonantfrequencies of a rectangular microstrip antenna," IEEE Trans. Antennas Propag., vol. 37,no. l,pp. 114-118, Jan. 1989.

[4] Balanis, C.A., Antenna Theory: Analysis and Design, John Wiley & Sons, Inc,1997.

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