ese319 transverse components for wg modes in terms of longitudinal components

Ese319 transverse components for wg modes in terms of longitudinal components

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Unformatted text preview: TRANSVERSE FIELD ComPDNEA/TS m/ WAVEGWDE MODES M“ w TERMS or LoflatrupguAL CoMpoNEWs MM By ww’b’n) ow‘f +43 193 and. z camPonenfs of «king Maxwell Curl ezdé‘bb'IS’,’ H7 1'5 733459 sham {513(7) 5&3» wove-3m?!” k modes 91709995313 along Hm 003923911216 ax"; z 0.33"“; 63mm? 1,!) firth-blah) er {cram-verse camfaneni’s of ehc‘én‘c and magnefib £9145 £114., Wanme along >4 and y (39%”) may Le exfn’esscai «in ferns of £8: Tang"4ud'%al cowpanenfs as sham helm: “ " 4° 4° 402 CW1 E=~jcfiflofl - ~’< ‘3 * .. ” 2. 9. 2. = ~jwflo“ 97¢ 33 '32 Ex E1 jCafb'k 1) 2. » ~J$< e z Van‘a‘fnm hence z 82 :0; 1°? :22 a 9—- —- It :: F‘Wflafl @ E 093) 8369’) £10”) _ 4192 (Acre “\e mh‘fi‘ow Ex 099,3) r Excx'y e 1': “$34 The 3 dampened: e25 6:9 CD are 392099) “my? EyCXJ-J = «foo/Ha fl): 33 "J'kz‘EwaJ - 3520‘”) : “W”? 46% @ 3% 35,999} ,. w) : ~J’Wv g“2r '3’?” 93 gt'wM/ 6‘: ME: jot) spew-E cg“ 2,6214; ‘9‘? “W8 songbmene guns @ 1 351,099 _J. k: fig (mu : J «76,6, 6X Ow) '3 ‘j 5‘ , 3 ‘ (x, ) "J {‘2 fixCx/f’) _° z 3 955009) 3%, ow) —. a)! 35 Show By 0Com] same algebra Had @ and C? 3937»! 47k; fauna-rm] arm-“Fons fm 9;“ny £Yan5VBI/‘se mponenfs 6N6”, z jog e, e, 83 093) @ : er 620/51) 92 $5, __ ,. 3.. k ,3 +0.) 9,... 9%: — ’- J '____. 2— 2 2 fl; Emery“: ’63 ugh“: : [1,50 " 2 Ac fendenf \larrbLles TE. If“??? .91”. 974%“) o'er-Pm"! 1,, Hm mzw‘wmt 3: “if? 7:2: C5) C3D .Mgotreéflor “WOW JGJC‘MA 5] %z:0/ 6 7/20 Z 6%: «J91, 2?: kg 9% 5 = '- 32 5 kit 93 flat: jwéoér,af_z @ k; 93 %3_:,_JC0606¥ E! k; 97‘ €25...— -,ey ~ V .a .1: are, 0% 'flx gysfiemfiwé 507/" 4:0 _F1'fwtu'n3 H", Soluia'm TE modes 9%91. Oann Hue general so’lu‘fi‘m fay %z of 'H‘e ane 2 2 ‘7 $62 + 346: = 0 sh? 2. APP’LJ 3.6. {:0 Hue general :01“ The 8C 1'5 4%“: Jr!” ‘congw-L‘o'l size 43210! sf fie meh’l. anus 1.09.43 {the WG- 4'5 zerv. Th5 BC 13 ezm‘nlenf {p «gnaw-n9 figf {142, is maximum 3f “we Me’cfl 00311: $56? 3- Shaw ‘Hxaf five {3:27.435 in fig Tirade! int/e evaeJSI'ovs __ .Wflo . a. z a- L». (at) H, “5(a) 5mm?) 84“: a E __ ,. Jeni/"o (7437,)“ M “C‘Cnxflj e—jkzz ‘6‘ "T '5" o 5 a "5" k5 “pg-xx nit? “J'ktz H. “‘(T) “(T e 3 ,Tw: m%.<«mm..osm .mSw magi? «a? S\¢<w.:‘lmu 4m 33.3 .35 Eqimm mug , . mfig §Es .. : :53” a druu UN ifs 1N ! $6 00%“ 00m W m9 MW; N . ...r~ \ .. 1 SE 3 a 33 g N .\ m mx- \m .m 9. nafiemaVMSNd m Eu -wm‘ Jr 4.3 t .e a g 3b ~ 1 \ mm" :Vme :21 m a; w m 2,. n max N . d: n z; I x. I .r 1E an.“ :mu m . s“ ‘. w. m: a m: m E, .3. t...rfl x, , p” §£§£a£ m N 3 M iv u NAN K m. u N z 3: “N. N43“ MM; u“ memv .I. I.“ W N Am wu ,AWV him : N" [Wu (VF WM: $quwa :3» .3 rs" finch MY? roue \Sm (a) The electric field in a rectangular waveguide mode has a purely y- directed component of electric field in the standard convention of co— ordinate axes used for rectangular waveguides. The waveguide is air filled. The waveguide dimensions are a = 3cm, b = 1.5cm. The instantaneous expression for this electric field is E(r, t) = i, 2 sin(1001tx) sin (41: x 1010i: - kzZ), V/m. i) Identify the waveguide mode. ii) Find phasor expressions for all of the electric and magnetic field components in this mode. iii) What is the guide wavelength kg? What is the cut-off frequency for this mode? v) Find the time—average power carried by this mode. “J. fizz Ef ,jz smCIooflfi) 5 _. an... ,L OJMO 43) m3: .3. =tooxv -——~ mzioaxzxso :3 a, ‘ - ’ =0 Vafla‘lnm W‘H'L 31/ n There 4‘; we ate 44.45.???“ "(Ego ma “fizz ‘ “ ] W» ’5‘) Ear): 4:, [’32 smmonx) e . , of €166 Q , JV .. only ‘5 WWW" 5.6 35.3” is, one To 9"“! ‘We’ mane mfifl W93 SMGC E15 {awn 5% 1‘5 r .. 3 w s " 2 —-'l< baa/10V” awe 2% 3 H o 5y o . o E an; id}; szEH +41 331% 05/00 p '3‘ 97g ....J 2‘2 z} 0 o ,..' ( xoortxg "5 2 if)” k1 ::O:-:o(03t-*5)fi- “’5 mm”) 6 @(‘d :- 0 '214 _- jxiJ—Ed'ji sv'nOooatx) 65592} 0 flika +1923. {E22771 “50003:” eJ zg .— ‘ "ink z or’ Hg: #2“: SinCIOO'JCfi) 6“ 2 ‘ “Mo “‘2 Hz: 9:931! cos (want) 6 2) {flufge'r “Wu 23$ 4“) 9’9” T22 2 2 k2 k2w’k, kzflkz NOW kx *‘4154‘ z" 0 z 0 X :: 2 2" «wt 2 (-255 (:7) _. 2'“ 2 2. ’ 75 “C flame adhere 3C : vi? 2 3f. COJTEBD ‘ a axcuxake 5‘ and %en K, using 60-11mm? “2;! CO’TEJO ’ or = 9-) _. 206441) and fining 23!; W5 "‘L" H“? ngmu’Ia 9p 23 3 yr 3C {earns ‘ ‘0 “0 52°36 = g" = w = \6 cm: flqse’qr, 30 a 27(3/cm o 0 o ‘ p #56 -¢ ’fy f: V “ ”" E H c: J. ,, )QWZ" fVam Egv 1‘28 0 3 0 “‘9‘ fix 0 Z .. ,L , @awz ’ 2 Rei ~32 swoon-Jug) / awe 2“: sfnzOOO’JCX) WA: : COMO J ' ‘aL Ly Hm wave, A's T0101 VoweraC-figmevav) :rxe - 0L PTO‘er—j, 5&3‘52 x hog-'30 a. 2“: .2C xx) " , / sm 100 ., 4,, job: awe C51»! ° 9.34 ‘0 301x 5"“ 0003‘") g 77%;: 0 ‘M Jan-[r Hus W‘M’eflr. 5 "2 c1. 2 V = 3’31 , w Arm" ’Wm awn 1‘ “whim” ...
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This note was uploaded on 03/16/2011 for the course ESE 319 taught by Professor Dhadwal during the Fall '08 term at SUNY Stony Brook.

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Ese319 transverse components for wg modes in terms of longitudinal components

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