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Class Note for ECE 6341 with Professor Jackson at UH


Class Note for ECE 6341 with Professor Jackson at UH

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This 28 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 36 views.

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Date Created: 02/06/15
Input Impedance of Patch Antenna A filamentary probe feed is located at x0 yo rectangular microstrip patch antenna Assume one basis function on patch JS 2 A xy managcosgjl Input Itmpedtance cont x0 7 yo x top view Note The equivalence L principle is used to replace the patch with its surface current OHS Etx9yQ El 1amp5 419 Input Impedance cont Galerkin testing on patch 5xy 13dS L xyE1p9 Note that t AEt Hence A lt 3 E 1pgt The reaction is defined here as aabFM39EMJ W V SO Input Impedance cont The input impedance is then given by h Zin JEz x09y09ZsdZs O E117 dV Jam1w Mai1W or z AltJ BgtZ m p9 pr0be Z probe P E1pJ dV or Z AltBJ gtZ m 9 p probe by reciprocity Input Impedance cont Input Impedance cont The probe impedance can be B J gt2 calculated approximately by 9 19 using the parallelplate waveguide model discussed gt previously in the cylindrical wave chapter We can add this to the final result to improve it Neglect mebe lt Z N Z Define Then Input Impedance cont Calculation of Zxx Zxx lt JBsx Ex Bsxdxdy S Exxy0 1 TTBmkxky ixxkxkyejkquotxkyydkxdky 27r2 where Input Impedance cont Hence we have Z 271r2 kxkyCixx kx Mg 3 ejkx kyyczxdydkxdky or 1 Zxx 2 2 BM kxkyGxx kxkyBsx kx kydkxdky Input Impedance cont Nma g h fk Hence 1 00 00 Zxx lt2zgt2 M or This is valid for the dominant mode basis function j Gxxkxky1 kxkydkxdky Input Impedance cont In polar coordinates Input Impedance cont Calculation of sz p9 Input Impedance cont From Notes 40 E2 x0 ymzs 1 T I ka ejkquotx kyy0 kxkydkxdky where zekxk kquot IiTMzs wgogr 42DMIWJLZIWtk h z23 Input Impedance cont The integration in ZS gives us the following term 0 kzllz Zsz k cosk h sinckzlh coskzlh h tanc kzlh if coskzlzsd 1 sinkzlh cos 21 tan x x where tancx E 14 Input Impedance cont 1 jkxx0kyy0 kx 1 mm m 1 ht k h dk dk JZITM tank21h anc zl x y Input Impedance cont Hence 00 00 TM j77 jkxxokyyo kx oo oo 21 We now use these symmetry properties I Even kx kx MW dkx IEvenkx kx 2 j sinkxx0 Jdkx OO 0 32 Even ky eff1W dky TEven ky 2 cos kyJo Jdky 700 0 We then have 16 Input Impedance cont In polar coordinates 18 Input Impedance cont Note The SDI method can also be used to find the mutual coupling between two patches details omitted Results 5 r d tans 0005 39 15cm 39 Measured 6 Caculuted 6 6cm Calculated 256 03I39f5cm D M Pozar quotInput impedance and mutual coupling of rectangular microstrip antennas IEEE Trans Antennas Propagat Vol AP30 pp 11911196 Nov 1982 Fig 5 Measured and calculated input impedance of a coaxfed micro 6 E H Newman and P Tulyathan Analysis of microstrip antennas using moment methods IEEE Trans Antennas Propagat Vol AP 29 pp 4753 Jan 1981 strip antenna compared with calculations from 6 19 20 Results D M Pozar quotInput Impedance and mutual coupling of rectangular microstrip antennas IEEE Trans Antennas Propagat Vol AP30 pp 11911196 Nov 1982 O T S s W7 3 LI el ls l IO w L EPlune HPlune ED 395 0 Measured Carver N 20 Calculated I o I 30 l HPlune 40 O l l g 0 025 050 075 00 25 Sx0 Fig 8 Measured and calculated mutual coupling between two coax fed microstrip antennas for both E plane and Hplane coupling W 1057 cmL 655 cmd 01588 cm 6 255f 1410 MHz Two Basis Functions y Using two basis functions is important for circular polarization 260 L 14w Astx w AyBsy W EFIE Ex AxExBsxAyExBsyE sz0 on S x Ey AxEyBsxAyEyBsyE JZP0 on S y Two Basis Functions cont Galerkin testing Lagwwzo S 0 Two Basis Functions cont 14me Anyy sz Anyx i AyZyy Zyz nyZZyx reciprocity By symmetry Zyx 0 since Ey Bsxxy Oddy from symmetry BSy xy 2 Even y Zyx ltBsyBsxgt j Bsy x yEy Bsx x ydS S Two Basis Functions cont Hence the two testing equations reduce to x1me Z AyZW Z XZ yZ The solution is Two Basis Functions cont Two Basis Functions cont Note To calculate Zyy and Zyz we can use the formulas for Zxx and sz and make a simple set of substitutions actual problem rotated coordinates xovyo WI In the Zxx sz problems the parameters are first labeled with quotprimesquot to avoid confusion with the actual coordinates 26 QEEQ QWmS Q u T u N nwzswmm 303 wcosocsn mmmm 0gtgt Two Basis Functions cont where ayltkxakyaxltkxaky W gtL L gtW kx gtky ky gt kx ECE 6341 Spring 2009 Prof David R Jackson ECE Dept Notes 42


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