Analysis of a Fractal Microstrip Patch Antenna

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1 124 Analysis of a Factal Micostip Patch Antenna Vibha Rani Gupta and Nisha Gupta* Bila Institute of Technology, Mesa, Ranchi , Jhakhand, India. vgupta@bitmesa.ac.in, ngupta@bitmesa.ac.in Abstact- Thee ae numbe of methods that can be used to educe the size of the antenna especially when it is too be used at lowe opeating fequencies. Factal is one of the ways which can be used to miniatuize antennas due to thei space filling ability. It helps in fitting lage electical lengths into small volume. In this pape the effect of incease in electical length at each iteative step in the geneation of the factal is studied. Index Tems- Factal patch antenna, Compact micostip antenna, size eduction. I. INTRODUCTION Mobile communications has become an impotant pat of the life. Oiginal applications such as mobile phones, GPS, Bluetooth technology have shown temendous gowth, and new applications such as tagging, wieless local aea netwok, wieless intenet ae emeging eveyday. Mobile means pactical fo use and easily tanspotable. Thus the mobile teminals fo wieless application should be light, small, and should have low enegy consumption to satisfy these equiements. Due to geate integation of electonics, the size of tansceive needed fo the mobile applications have deceased dastically. Hence the size of the antenna should be compatible with the dimensions of the eceive o the epeate system, especially at the lowe micowave spectum. Seveal techniques fo educing the size of the patch have been pesented in the past. Simplest of all methods is the use of substate mateial with high dielectic constant [1] but it esults in naow bandwidth and poo efficiency due to suface wave excitation. Cost of low loss, high dielectic constant mateial is anothe poblem. Othe methods epoted in the liteatue ae shoting posts [2, 3], use of shot cicuits [4, 5], patially filled high pemittivity substate [6], and cutting slots in the adiating patch [7, 8]. The shot cicuit and shoting posts pose the poblem of coss-polaization and patially filled pemittivity substate sometimes offes fabication poblem. Factal geometies [9, 10] in the antenna application ae becoming majo concen fo many eseaches these days. Due to the factal configuation lage electical length is fitted into the small physical volume. Thus the high convoluted shape of a factal allows to educe the oveall volume occupied by the esonating element. In this pape the effect of incease in electical length at each iteative step in the geneation of the factal is studied. II. ANTENNA DESIGN Fist of all, a conventional squae micostip patch antenna with patch dimension L W as 28.2 mm x 28.2 mm, pinted on a dielectic substate FR-4 ( = 4.4) of thickness 1.6 mm, with esonating fequency 2.46 GHz is designed as shown in Fig.1. This conventional antenna is teated as the basis fo the compaison in tems of size eduction. Next, the stuctue is modified by the addition of multiple V-goove along the length and width in thee steps, which coesponds to the thee

2 125 iteations of the factal geneation. The addition of the goove is based upon the Koch cuve. thee equal pats. The middle pat is eplaced by two staight lines meeting at 60 0 angle (a bent) and they fit into the oiginal gap in an equilateal tiangula fashion as shown in the Fig. 2. Thus the dimension of each newly geneated staight line is now one thid of the oiginal staight line and each side of the squae when stetched out, inceases by one thid of the oiginal length. The iteative pocess of dividing a staight line into thee equal segments and eplacing the middle by a bent cuve is continued. In the tue factal, this pocess is epeated fo infinite numbe of times. In the pesent wok, thee iteations ae consideed and the factal patch obtained is shown in the Fig. 3. This figue shows the popotionate eduction in patch aea by keeping the total peimete of the squae constant afte each factal iteation. Thus with each iteation, the total peimete of the squae inceases by 4/3 times the oiginal peimete of the squae. It is obseved that although the length of the adiating patch with popotionate eduction is kept constant at 28.2 mm but the esonant fequency does not emain constant at 2.46 GHz. The factal patch configuation pinted on the same substate of the same thickness is modeled in the IE3D and simulated fo each iteative step. Afte each iteation, the dimension of the factal patch and feed position ae optimized using genetic algoithm optimize, to obtain the stipulated fequency of 2.46 GHz. The size of the factal patch obtained afte each iteation to make it esonate at 2.46 GHz. is shown in Fig. 4. The electical chaacteistics of patch afte each iteation is tabulated in Table 1. A factal patch antenna pinted on FR-4 substate, with coaxial feed is shown in Fig. 5. The esult fo the esonating fequency was veified expeimentally and is shown in the Fig. 6. A good ageement between the simulated and expeimental esult is evident fom the chaacteistic obtained. To study the effect of the substate on size eduction, a simila factal patch configuation is The stating stuctue is a squae patch. Each staight segment of the squae is divided into simulated with the same thickness 1.6mm on a foam substate fo the same opeating fequency 2.46 GHz. The compaison of eduction in patch aea of two factal patches with the є = 4.4 and є = 1.07 is shown in Table 2. III. RESULTS AND DISCUSSION The esonant fequency of the patch is detemined afte each iteation. It is found that the esonant fequency of the patch educes afte evey iteation due to incease in the electical length. Afte the thid iteation the patch aea is calculated using equation (1) and is found to be educed by 54% with є = 4.4 and by 56% fo є = 1.07 at a given fequency of opeation. patch aea = (Length) 2 - aea of slits o/and gooves (1) It is evident that the eduction in patch aea deceases with highe iteations. Each iteation adds length to the total cuve. The total length at the end of the last iteation can be calculated by (2) Total length = 4 L 3 n (2) Whee n is the numbe of iteations and L is the oiginal stating staight length. The popotionate eduction that is keeping the peimete same fo all the patches geneated afte each iteation and actual aea eduction obtained afte the optimization to esonate at the same stipulated fequency 2.46 GHz. is not the same. Afte fist iteation, patch aea educes by appoximately 40% fo є = 4.4 and by 48 % fo є = 1.07, but fom second to thid iteation it is only by 5% fo both the cases. The eason is evident fom the Fig. 7, showing the vecto cuent distibution on the factal patch (with thid iteation) obtained as a esult of simulation. It can be seen that the cuent does

3 126 not stictly follow the edge path, but athe follows a slight cuved path. Going fo highe iteation means addition of moe edges in the patch. But additions of these small edges do not help much in inceasing the electical length, esulting in decease of eduction in patch aea fo highe iteations. The eduction in patch aea with each iteation is shown in Fig. 8 fo both the substate. It is evident fom the figue that the eduction in aea with each iteation follows appoximately the same tend iespective of the substate used. The tend in vaiation of gain can be seen in Table 1. Obviously, the gain deceases with each iteation, which is less affected with the ai as a dielectic substate. The patten plot of the factal patch pinted ove dielectic substate with є = 4.4 obtained afte thid iteation is shown in Fig. 9. IV. CONCLUSION Factal patch antennas ae good candidates fo size eduction as lage electical length can be fitted into the small physical volume. Howeve, to make the antenna esonate at a paticula fequency the useful ange of size eduction lies only upto thid iteations. Maximum size eduction esults afte fist iteation only. Subsequent iteations esult in decease in pecentage of size eduction such as only 5% o less than this is obtained afte thid iteation. Theefoe one can limit the iteations upto thid iteations only. Going fo the highe iteation adds mostly the small edges, which is pactically not useful in inceasing the electical length. [2] R. B. Watehouse, S. D. Tagonski and D. M. Kokotoff, Design and Pefomance of Small Pinted Antennas, IEEE Tans. Antennas Popagation, vol. 46, No. 11, pp , Nov [3] S. S. Pattnaik, G. Lazzi and O. P. Gandhi, On the use of wide-band, high-gain, micostip antennas fo mobile telephones, IEEE Antennas and Popagation Magazine, vol. 40, pp , Febuay [4] J. S. Kuo and K. L. Wong, A low-cost micostip-line-fed shoted patch antenna fo PCS base station, Micowave and Optical Technology Lettes, Vol. 29, pp , May, [5] K. F. Lee, Y. X. Guo, J. A. Hawkins, R. Chai and K. M. Luk, Theoy and expeiments on micostip patch antennas with shoting walls, IEE Poc.-Mico. Antennas Popag. Vol. 47, pp , Decembe [6] B. Lee and F. J. Haackiewicz, Miniatue micostip antenna with a patially filled high pemittivity substate, IEEE Tans. Antennas and Popagation, Vol. 50, pp , August [7] W. S. Chen, C. K. Wu, and K. L. Wong, Novel compact ciculaly polaized squae micostip antenna, IEEE Tans. Antennas and Popagation, Vol. 49, pp , Mach [8] J. Geoge, C. K. Aanandan, P. Mohanan and K. G. Nai, Analysis of a new compact micostip antenna, IEEE Tans. Antennas and Popagation, Vol. 46, No. 11, pp , Nov [9] John P. Gianvittoio and Y. Rahmat-Samii, Factal antennas: A novel antenna miniatuization technique, and applications, IEEE Antennas and Popagation Magazine, Vol. 44, pp 20-36, Febuay [10] Camen Boja and Jodi Romeu, On the Behavio of Koch Island factal bounday micostip patch antenna, IEEE Tans. Antennas and Popagation, Vol. 51, pp , June ACKNOWLEDGEMENT The authos acknowledge the financial suppot ganted unde the Self-Assistance Pogam (SAP) of Univesity Gants Commission, Govenment of India, New Delhi. L f p h REFERENCES [1] T. K. Lo, C.O. Ho, Y. Hwang, E. K.W. Lam and B. Lee, Miniatue apetue-coupled micostip antennas of vey high pemittivity, Electonics lettes, Vol. 33, pp. 9-10, Fig.1. Top and side views of a conventional squae micostip patch antenna

4 127 0 Retun Loss Vs. Fequency L db st iteation 2 nd iteation 3 d iteation -25 conventional Antenna Fig.2 Factal geneation based upon Kotch cuve -30 Factal Antenna Fequency (GHz) Squae Patch 1st Iteation 2nd Iteation 3d Iteation Fig.6a Simulated Retun loss chaacteistic of factal patch antenna designed fo 2.46 GHz as shown in Fig. 5. Fig.3 Popotionate eduction in patch aea by keeping the total peimete of the squae constant with each factal iteation Squae patch Fist iteation Second iteation Thid iteation Fig.4 Geneation of a Factal patch fo esonating fequency 2.46 GHz f p h Fig.6b Measued Retun loss chaacteistic of factal patch antenna designed fo 2.46 GHz.. Fig.5 Factal patch obtained afte thid iteation

5 128 Fig.7 Cuent distibution and path on the suface of a Factal patch antenna % Reduction in Aea = 4.4 = 1.07 Fig. 9a Radiation patten of factal patch antenna at 2.46 GHz in X-Z plane Numbe of Iteation 4 Fig.8 Pecentage eduction in aea with each iteation fo substate with = 4.4 and = 1.07 at f =2.46 GHz Fig. 9b Radiation patten of factal patch antenna at 2.46 GHz in Y-Z plane

6 129 Table 1Chaacteistics and pecentage eduction in aea afte each iteation duing factal geneation keeping the opeating fequency constant at 2.46 GHz. VSWR BW Gain Gain S.N. Shape (MHz) (dbi) (dbi) = 4.4 = Conventional Squae Patch st Iteation Factal 2 nd Iteation Geneation 3 d Iteation Table 2 Compaison of factal geneation with two substate with = 4.4 and = 1.07 S.N. Shape New Patch Dimension (mm) = 4.4 = 1.07 % Reduction in Aea =4.4 = Conventional st Iteation Factal 3 2 nd Iteation Geneation d Iteation

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