Prelim 2 Solutions

# Prelim 2 Solutions - PRELIM 2 ECE 303 26 October 2004 NAME...

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Unformatted text preview: PRELIM 2 ECE 303 26 October 2004 NAME 50hr 7L' V“ 5 SECTION 1. (30 points). Fresh water has a conductivity of about 10‘3 S/m (much less than the conductivity of sea water), a dielectric constant (8780) of 81, and a permeability u = no. A plane wave propagates in this water in the positive 2 direction, and at z = 0 the average power density in the wave is 1 watt/m2. What is the approximate (to within 2%, say) power density in the wave at z = 200 m if the wave frequency is (a) 104 Hz, or (b) 5 x 106 Hz? Firéf“ oﬂécréeﬂ 710 (45+ /055 5/} /W 3/1me . [é’ﬂ—V/cd >>e’ m <<c~’3) IO g’= 8/60: 81(9291/0‘” ) = 717 we p/w. 6” = E t [0—3 : {'99 XIO~9 (645? gr 5) at“; [3953) V arr-F 7— 31/? W0» /(wb => /W ha?) [:0 q ,7 r3791 {4) 45:34 /oss 1% 3%:4719/«0 0’ : [W/ll) )[qﬂ’wo )/0 J -3 ,i : 211’ ~x/O w: 73 [232mml ~20€8 ‘qﬁ—AZ) WW“ * * ‘-‘ <9 r 5 2 .09: P{?:&) L 2 5’ 2C 6 -HV d:17_£{el) war/v ) : '7 57/057,?) 3"?" ; ,a207 W" C; " Inc/10"?) 3.”? 7,17 —2o(/2m) .. 6'34 __9 5a Pfarzao h.) :1« e = e, _— 2.3wo wvﬁ/m‘ » I 50 Ma’yé‘wwq‘fm‘», I}; ﬁfe/#963? MHKA Wbig ;i4 Ilélaf 495 462mm,: (596%: avﬁfép 1'6le 77% As; M Wye/12:17M ls /€\$5 , AH} MW a: 4+ WW Mew/26754; 51’) ZN»: , PRELIM 2 ECE 303 26 October 2004 NAME 50/“7L’” 5 SECTION 2. (30 points). A linearly polarized wave, with E parallel to the x axis, propagates in the negative y direction. The frequency of the wave is 500 MHZ and the measured phase velocity is 2 x 108 m/s. The instantaneous value of E at y = t = 0 is 1 V/m in the positive x direction, and the wave attenuates by 5 dB in 200 meters. (a) Write a complete expression for the electric ﬁeld E in complex notation, giving the values of all the parameters in the expression. (b) If u = no in the medium, what is the value of the (complex) permittivity constant a? 4001‘ +ﬁgl 1" 0(5) (a) if = ED ex e a? , VHF/P. L ? _/ ,.\ 9' LU,“ ,0: wayoD)/0 :TF/o s }A:_“_)_. : "(/0 );5-7.,. \$245,, 2003) :157 “4*, +2-l-3 ” 1’0’003- e :"5 new) 3:-200M 56) — #0’0 0Q {/0)(003He) S—lfgopx [IL/373) : F‘s/ -3 , ﬁnal 30 X: 9?.5’5’Ylt') 144- am‘} Li : / V/w‘ (b) 1455*Wui 74/7 4 SW, 7K?“ Zéw' 555 a?pr 13 Valley ,9— c: 4 ‘ : C : ‘ZX/O 475m ﬂo é 6' I 2 fr so 6 : f2} .: 2.2; )é’: 2.256, f” (2/ W . EU /197Y/0Pl Ell/VA) M’W‘WM 06363 M42- — ha ., «‘ZW/szvﬁa‘é \ ->e —~—— who a 3,”? 1>p2 573‘ Wm" H 2 .13 _¢ 4Mo’7a—M é, : ,___ _— 2/239) I0 ; 3,67 Mo 5' F“ 3’71” 9 u -q “H (30 [0'42 /OSS 51 ﬁx (it. é: ) : 7.3\/‘/O~5F/W’l:én PRELIM 2 ECE 303 26 October 2004 NAME fry/H hm 5 SECTION 3. (40 points). The electric ﬁeld of a plane wave propagating in free space is described by El: E01[ax +3jay]ej(“’“kz) :7 £2 : +1? .42 1" 04c {70} (a) Give an expression for an orthogonally polarized electric ﬁeld E2 with the same average power. ( 5) (b) Sketch the instantaneous values of E1 and E2 as a ﬁmction of time for z = 0 (show the vectors at (Dt = 0 and cot = n/Z). 00) (0) Give an expression for H1 that corresponds to E1 and sketch this ﬁeld also as a ﬁJnction of time at z = 0. p p r 1;) ((1) Write an expression for a right circularly polarized wave, with the same time and space variation, and then resolve this wave into a sum of the two orthogonal waves E1 and E2, i.e., ﬁnd the values of E01 and E02 in terms of ERC. K tiff: + i ) ,_)<15 9 E 9‘. “MM 4156 q no Wrﬁ-fm 0": 4’ E: [Lott-O) .1 m. In“! M Ira-IS.) 0/ ‘ Mot—ﬁle) (0i) ze+ 5 = E (gs—447)e racpul.W) ‘ Okmjé—VFJ r7) race/H we a saw 5+1 '71, 14:11.”;th WW5 E.) +5.31 [gm/— Era (‘5,ﬁd‘5j) : E; /£x + 355’) + 3;“ (33* -487) 07%») express’ltms 'Ev’j E2 tail/519‘? L, - SO Er: : E5: + 3 Eai ;;> ID go: 2‘2 Erc glad. 7‘ —.2I3r< J'Wé‘lgwfs "rc :3Eo,_ E IOE :J-L’F'? ’:+’LIF_, 02 ’rc 91 I ’f‘g ...
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