498 Impovement in Accuacy fo Design of Multidielectic Layes Micostip Patch Antenna Sami Dev Gupta*, Anvesh Gag and Anuag P. Saan Jaypee Institute of Infomation Technology Univesity Noida, Utta Padesh, India Tel: 9-0-59-0877; Fax: 9-0-40-0986; E-mail: samidev.gupta@jiit.ac.in VOL. 3, NO. 5, NOVEMBER 008 Abstact- In this pape multidielectic laye antenna has been designed using confomal mapping techniques with impoved accuacy. Fomulating an algoithm has eliminated ect of inaccuacies that can have compounding ect fom the design stage to fabication of multidielectic laye micostip antenna. The algoithm has been successfully tested on both thin and thick dielectic substates having low pemittivity. The antenna designed fo the given esonant fequency has been obseved to be coesponding to the patch dimension with accuacy exactly to sixth decimal place. Index Tems-Antenna Paametes, Micostip Antenna, Pemittivity, Resonant Fequency. I. INTRODUCTION Thee is a need to accuately design the micostip patch antenna at a desied fequency of opeation and also to follow a pope analysis technique that will accuately pedict the behavio of antenna unde consideation. The analysis of ectangula patch micostip antenna employing multidielectic layes is caied out using confomal mapping technique. The design consideations ae based on the chaacteistics of the substate, the patch geomety and the location of the feed. Design paametes based on empiical fomulae fo evey vaiable need to be calculated and ae intedependent and hence time consuming. An ective and icient algoithm has been developed and a pogam using MATLAB7 which gives the esult, accuate to 6 th decimal place. Configuations of stack patch antennas of diffeent dimensions designed fo a given esonant fequency has been analyzed. The accuacy in the physical dimension of the patch calculated is inceasing at each step. II. DESIGN OF MULTIDIELECTRIC LAYERS MICROSTRIP RECTANGULAR PATCH ANTENNA A. Design Paametes A ectangula patch of width W and length L with thee dielectic layes, and 3 and height h, h and h 3 espectively as shown in fig. (a) & fig. (b). Confomal mapping technique involving Wheele s Tansfomation [7] the complex vaiable plane z= x+jy is mapped to a plane g= u+jv as shown in fig. (a), fig. (b). The fist appoximation leaving the aeas S 0, S, S, and S 3 is unchanged. Hence the elation fo the quasistatic pemittivity is as follows: * e = * q ( q + q ) + * q + 3 3 ( q q ) ( q q q ) + q 3 3...() Whee q, q and q 3 ae the filling factos, defined espectively, as the atio of each aea of S, S and S 3 to the whole aea S c, of the coss section in the g-plane [3]. The dispesive behavio can be detemined as: [5] ' e = '...() + P( f ) Whee e is detemined by equation () and ' is the pemittivity that takes into account the IJMOT-008-3-96 008 ISRAMT
499 VOL. 3, NO. 5, NOVEMBER 008 multilaye ect on a micostip line as all the fomulas calculated wee fo single laye. Hence ' is given by equation below: [8] ' ( e * ) + = + A A...(3) The paamete A is taken to simplify the above equation, which is expessed as * h A = ( + )...(4) W Fig. (b). A multilaye dielectic ectangula micostip antenna [3] Since ΔL is the incease in the length due to finging ect [], found fom the elation in [6] with (', u') eplacing ( e, u) and the height h eplacing h. ΔL = h * ξ * ξ3 * ξ5...(5) ξ 4 Fo ξ, ξ 3, ξ 4 and ξ 5 efe the elation in [6]. The length L of a patch fo a given patch width W and esonant fequency f is detemined [8]. Fig. (a). Confomal mapping of a multilaye dielectic ectangula micostip antenna [3] L = C ΔL...(6) * f *( ) Fig. (b). Confomal mapping of a multilaye dielectic ectangula micostip antenna appoximated [3] Fig. (a). A multilaye dielectic ectangula micostip antenna patch [3] B. Antenna Paametes- Effect of Inaccuacies The analysis of multidielectic layes micostip antenna is based on empiical elations. Futhe when the antenna is fabicated cetain eos IJMOT-008-3-96 008 ISRAMT
500 VOL. 3, NO. 5, NOVEMBER 008 esults due to the manufactuing pocesses. The eos need be minimized to a lage extent because the anomalies can have a compounding ect. An illustation shows the ect on the esonant fequency due to change in length of the patch. With incease in the length of patch by 0.000mm (fom 0.0334 to 0.0335 mm) thee is a change in esonant fequency of 7.4MHz (fom.78 GHz to.706 GHz), which is significant as compaed to change in the length. Refe Table. C. Accuate Computation of Antenna Paametes Calculation of vaious paametes of the antenna involves lage numbe of computational steps that ae epetitive and pone to calculation eos. Confomal mapping technique involving Wheele Tansfomation function [7] to map one complex plane into anothe complex plane involves equations, which equie igoous calculations. The dimension of the antenna i.e. the substate and the patch ae in millimetes and micometes espectively. The esonant fequency that has been calculated is in the ange of gigahetz. Hence a vey small vaiation in the dimension of the antenna paametes will esult into a vey significant change in the esonant fequency. It is to be noted that these calculations caied out ae epetitive as a esult, of which the eos is cumulative at evey step theeby esulting in a notable change in the fequency. To minimize the compounding eos an algoithm has been designed. The algoithm aims towads minimization of eos at each step ultimately poviding a esult, which is highly accuate. Antenna designe can ovecome the manual tedious pocess of detemining patch dimension fo a equied fequency of opeation whee citicality can be accounted fo diffeent values of substate pemittivity. It is impotant to undestand, in an envionment whee thee ae multi emittes opeating in the same fequency band, a few MHz deviations in esonant fequency can matte and esult in intefeence. Citical design and esult obtained theeof though igoous simulation not only can ensue accuacy in fabication, but also can povide the equisite toleance fo mino vaiation in dielectic popeties of the substate obtained fom the manufactue D. Algoithm I. START MODULE II. Input the height h, h and h 3 and the coesponding values of elative pemittivity,, 3 efe fig. (b) and 0 = (pemittivity of fee space). III. Input the esonant fequency f fo antenna design. IV. Input the width W (efe fig. (a)) of the patch, citeion W/h fo h efe fig. (b). V. Computation of length L of the patch is caied out in following steps: Step : The ective line width W e and quantity V e values obtained fom the fomulae in [3]. Step : The filling factos q, q and q 3 efe fig. (a) & fig. (b) descibed in efeence [3]. Step 3: The quasi-static ective pemittivity e, efe equation (). Step 4: The ective pemittivity that takes into account the Multidielectic layes, efe equation (3). Step 5: U=W/h and U =W e /h. Step 6: K 0 is fee space wave numbe computed at esonant fequency f. Step 7: Function P(f), is a fequency dependent tem efe[5] notation (, u ) eplaces ( e, u) and f h =47.73*K 0 * h,efeed [] eplaces the appoximation f h =h/λ 0 efeed [5]. Step 8: The ective pemittivity based on the fequency facto, efe equation (). IJMOT-008-3-96 008 ISRAMT
50 VOL. 3, NO. 5, NOVEMBER 008 Step 9: The ΔL due to finging ect efeed [6] wee (, u ) eplaces ( e, u). Step 0: Length L of the patch computed based on the expession C L = ΔL * f *( ) VI. Pass the values h, h, h 3,,, 3, K 0, W and L to MODULE VII. START MODULE VIII. Computation of esonant fequency f v (veification fequency) at the Length L found in MODULE. Step : The ective line width W e and quantity V e values obtained fom the fomulae in [3]. Step : The filling factos q, q and q 3 efe fig. (a) & fig. (b) descibed in efeence [3]. Step 3: The quasi static ective pemittivity e, efe equation (). Step 4: The ective pemittivity, which takes into account, the multidielectic layes efe equation (3). Step 5: U=W/h and U =W e /h. Step 6: Function P(f), is a fequency dependent tem efe[5] notation (, u ) eplaces ( e, u) and f h =47.73*K 0 * h efeed [] eplaces the appoximation f h =h/λ 0 efeed [5]. Step 7: The ective pemittivity based on the fequency facto efe equation (). Step 8: The ΔL due to finging ect efeed [6] wee (, u ) eplaces ( e, u). Step 9: The esonant fequency f v based on the fomulae in [3] whee notation f v eplaces f and the fomula is given as: c fv = *( L + ΔL)*( ) IX. Retun the values of f v to MODULE. X. STOP MODULE. XI. Compae f v and f if equal than MODULE is validated. XII. STOP MODULE. III. ANALYSIS The algoithm has been conveted into a MATLAB7 pogam and the esults obtained ae shown in a tabula fom. Refe Table. Significance of accuate length calculation and its ect on the esonant fequency can be obseved. It is impotant to note that changes in the esonant fequency in case thee is vaiation of patch length at 4 th, 5 th, even at 6 th decimal place. e.g. patch esonant fequency of opeation at.700 GHz, positive vaiation in its length at 4 th, 5 th, at 6 th decimal place esults at coesponding changes of fequency 8MHz, 0.8MHz and 0. MHz espectively. Similaly changes in the negative diection vaiation in patch length leads to vaiation in esonant fequency, details shown below. Case studies Ratio of W to h should be geate than o equal to and atio of width W to length L should lay between and []. In both the cases the paametes fo antenna design ae width of the patch 3.5mm, substate pemittivity of laye ( ), ( ) and 3( ) as,.3 and.3 espectively, height of substate (h ) taken as 0mm and height of substate (h ) taken as 3.8mm. The height of substate3 (h 3 ) has been vaied [3].. Case I (Thin Substate) Fo simulation in this case W (width of the patch) is taken as 3.5mm, L (length of the patch) is equal to 33.48mm, length of the micostip feed line is taken as 5.75mm with edge feeding technique. The substate pemittivity of layes IJMOT-008-3-96 008 ISRAMT
50 VOL. 3, NO. 5, NOVEMBER 008 Table Detemining the length fo a given fequency and detemining the accuacy in the fequency by vaying the length Standad Paametes Cove Thickness h 3 (mm) Resonant Fequency of opeation f (GHz) Length L (m) Veified Fequency (GHz) Change in L at 4 th Decimal Place Veified Fequency (GHz) Change in L at 5 th Decimal Place Veified Fequency (GHz) Change in L at 6 th Decimal Place ΔL= ΔL= ΔL= ΔL= ΔL= ΔL= +*0-4 -*0-4 +*0-5 -*0-5 +*0-6 -*0-6 CASE : THIN SUBSTRATE 3.8.78 0.03348578.706.754.77.787.779.780 6.36.70 0.0334689.693.708.700.707.7009.700 CASE : THICK SUBSTRATE 9.54.688 0.03345603.6806.6953.687.6887 --- ---.7.678 0.03344509.6707.68533.677.6787 --- --- W=0.035 m, = 3 =.3, =,h =0,h =0.0038 m ( ), ( ) and 3 ( ) ae taken as,.3 and.3 espectively, height of substate (h ) taken as 0mm and height of substate (h ) taken as 3.8mm and h 3 as 3.8mm efe Fig. 3(a) Deviation in the fequency is obtained f =.79GHz afte simulation fom the one equied i.e. f =.78GHz and is about Mhz, which is acceptable. Fig. 3(a). Basic Patch Constuction on Momentum IJMOT-008-3-96 008 ISRAMT
503 VOL. 3, NO. 5, NOVEMBER 008 Fig. 3(b) shows the etun loss (S ) of -7.7db at a esonant fequency of.79ghz, which is a good design. Fig. 3(c) shows field plot in Catesian coodinate. Fig. 3(c). Catesian plot of Field in theta (oange) and phi (geen) plane. Case II (Thick Substate) Fig. 3(b). Retun loss at the esonant fequency Fo simulation in this case W (width of the patch) is taken as 3.5mm, L (length of the patch) is equal to 33.48mm, length of the micostip feed line is taken as 5.75mm with Fig. 4(a). Basic Patch Constuction on Momentum edge feeding technique. The substate pemittivity of layes ( ), ( ) and 3 ( ) ae taken as,.3 and.3 espectively, height of substate (h ) taken as 0mm and height of IJMOT-008-3-96 008 ISRAMT
504 VOL. 3, NO. 5, NOVEMBER 008 substate (h ) taken as 3.8mm and h 3 as.7mm efe Fig. 4(a). Fig. 4(b) shows the etun loss (S ) of -.65db at esonant fequency of.677 GHz. S is low because of the suface wave losses due to the thick substate. Deviation in the fequency obtained at f =.677GHz afte simulation fom the equied i,e f =.678GHz and is about Mhz, which is acceptable. Fig. 4(c) shows field plot in Catesian coodinate. V. CONCLUSION By devising the algoithm the vaious paametes of the Multidielectic Laye Micostip Antenna has been calculated with the help of MATLAB7 pogam. The esults have been veified and validated by caying out the simulation of the antenna using Momentum Advanced Design System Softwae. Hence an antenna design have been achieved with utmost pecision whee the eos afte 6 th decimal place ae insignificant in case of a thin substate multidielectic laye and afte 5 th decimal place in case of thick substate multidielectic laye. ACKNOWLEDGMENT Authos acknowledge the guidance of Agilent Technologies development team fo thei assistance in Momentum Simulation REFERENCES Fig. 4(b). Retun loss at the esonant fequency Fig. 4(c). Catesian plot of Field in theta (oange) and phi (geen) plane The esults show that the patch is optimized fo the paametes calculated by implementing the algoithm in MATLAB7 pogam [] R.Gag, P.Bhatia, I.Bahl, and A.Ittipiboon, Micostip Antenna Design Handbook, Atech House. [] A. David Wunsch, Complex Vaiables with applications, 3d edition Peason, Addision Wesley, page 59. [3] Shun-Shi Zhong, Gang Liu, and Ghulam Qasim Closed Fom Expessions fo Resonant Fequency of Rectangula Patch Antennas With Multidielectic Layes, IEEE Tansactions On Antennas And Popagation, vol.. 4, No. 9, Sept 994 [4] H. A. Wheeles, Tansmission line popeties of paallel wide stips by a confomal mapping appoximation, IEEE Tans. Micowave Theoy Tech., vol. MT-, pp. 80-87, Ma. 964. [5] M. Kischning and R. H. Jansen, Accuate model fo ective dielectic constant of micostip with validity up to millimete-wave fequencies, Electon. Lett., vol. 8, pp. 7-73, Ma. 98. [6] M. Kischning, R. H. Jansen, and N. H. L. Koste, Accuate model fo open end ect of micostip lines, Electon. Lett., vol. 7, pp. 3-5, Feb. 98. [7] J. Svacina, Analysis of multilaye micostip lines by a confomal mapping method, IEEE Tans. Micowave Theoy Tech., vol. 40, pp.769-7, Ap. 99. [8] I. J. Bahl, P. Bhatia, and S. S. Stuchly, Design of micostip antennas coveed with a dielectic laye, IEEE Tans. Antennas Popagat., vol. AP- 30, pp. 34-38, Ma. 98. IJMOT-008-3-96 008 ISRAMT