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ece166_fall2008_hw1_Solutions

# ece166_fall2008_hw1_Solutions - Problem#I = C/Ee-ﬁr A =...

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Unformatted text preview: Problem #I = C /\/Ee-ﬁr A = via/70 = c MFu/ee-Hc) = (3xr03)/(<ero?-Vfl.6)) =~ 0.0.176M i'L': 20- NH" : 5'0. f—F—O.7L-60° = “F r—o.7[_—6o* 36M 83. .25 (—60.2 (a) 5) 723m! Val-huge a+ ﬁe (and WW) = vo++vo- = va++ r-v.,+ = wow = !- (I+0.4;—5o') = l-35-]0.6r (V) c.) FM) = {Frexp(}‘0)exp(*/‘278f) = Ir! exp E )(o—aﬂﬁﬂ 605611 (9 = 2,812 -—1JT , V 64: 1668 MAXFMHM vame .8= Cur/a) 6 “—"66' =-—'rr/3 , 9—1pﬁ = —2—Tr {Tr/3)-2.(2n/A)-£ = -27r f: (5/12) )1 when 0 = zﬁﬂ-rr , V has ﬁe mPn?mum Vame . -CTFI3)—-2.(2Jr/A).£ = ——1r Q = (I {6) A 2 ® me = Va+fr+lrlj = (-(r+o.0)=1.av (Where i = (51:2)A ) @ VMFn= Vo+fl-II'IJ= [-(I-o.q)=o.3l/ (Where 2.20/6“) when V has Murmam Varue J I has MFnFMUM WINE Wham Villas mfmhnum Value , I has Max?mum Vance . (3) ~90, Imrn=Io+D—Irl] =6MA-Vmin (Where 1:: (IS/[3.) A) 51)!» @ IMGX:L+EI+IT’]=54-MA:M (Where. 2=(I/6)A) 9°" \ F= 0-0 eXP(-??r/.3) 0’) as?) = %- Miami-113%) g: Cur/x) (—r-EXPC/‘a-ﬂz) A= 3cm, 2a=5o m) = 20. 1+ ITleXPCJts‘Je-XPCI-jéi‘) I— Irlexp OMEXP (PM) so. r+ 0-9 e_xp («—j‘rr/3) exp (Z («r/0.03 ) 22 I—— onexp (w? W3) exp C] our/0.03) z) 1! 4+ 99:00:41 , *Co)= 32.19 +j46.04 (.n.) 4+ iL=-—o.4 cm, iICHo.+) = 4!.33 4—)1/543 (a) 4+ %= —o.&cm, Z—c—o.3) = ro.5!-—)-L/.44 (m) (1+ Z—= *L2cm , Elf—ML) = (0.5! +/\a—/.44 (a) 41+ .3: -—l-6 cm, Hams) = W-BS +)II3.13 (IL) . )2 , ‘60“ can 5630 use. 2%.: '20 ELHE‘D-Iw‘ (H 2-; h; 20+52L+Npej p“ . '— [5:932 ,E: o,q,o.?,c,£c.. e) V012): Vo+expcnjpz) + Vo“exp (4???) = V04“ QXPc—Ipz) E l+ Papcﬁpﬂ] 1(a) = (Vo+/¥o) - €xP(—}\$i‘) [ I*P€’<PC?*¢32)] C Vo+=fw),(6==ur/A ) 2:31:14) F=o.qﬁ-—6o‘> VSWR =3 {+H'l = Vina): = 5.6’) I‘ll—l men ﬂe—ﬁarWazmr pom/er (19+) p+=_.1Vo+’-=o.ozw =2omw 539 The. 64;!!qu Pan/eh (P’) P“ = . _. “-14: WNW" = 0.0093 w = 9&8 ww 2‘2: The. Power JFSIE‘Pq-fad F11 ﬁe {cad PCloacI) :: P‘f' -— p" = :o.2' WW Magnitude lrms Magnitude Vrms _. a .‘3‘ 01 0.035 0.03 P a N 01 0.02 1' 53 O .4. 01 0.01 0.005 Problem 1e : Plot the Voitage and Current magnitudes -5 -4 -3 -2 Distance from load in cm -5 -4 -3 -2 Distance from load in cm (1;) fr‘neross‘z c.3d5/cm 0.3% = «cargo/”VLF: lo/gCVr/Va.) (Vi/1A): 10—43 fr: (Vt/Va.) = in ((0 .02 M) = 0.035 M» 0.3 dﬁ/cm = 0-035Np/cm \$o(=o.oss (71:0.7) Inch- Var-bye F‘s a-f—‘H/VD Wan/e J’s/357%: dWay .1 £=9JL= 23r3 =66": ¢+ '2‘: -2 (Input-1L) [VFrH‘I '—‘ fVo+ - . .__ = l.exP('o.O35X€) :r..23 (v) lVE‘n“ l = H'LI axm—MM- IVrn+l = 0.0xexp(_2xo.ossxa)m.23 \$[rrnfzo'46 : 0-57 (V) VapvRCa-f- ﬁpuw‘) = !+ In“ .: (+0.46 = 2.7 :- mm. (#046 VSWR (H react) =~. r+ IFL' .-.- {+0.7 .-= 5.67 1“ (Val ’"0-7 +68 ﬁhWar-d Pawen -‘ Pr‘n"' = [MVP/£0 = 30.3 now He back'Wam’ power: : Pr‘n' 1“ (V:‘n'"/"/i’b = 6.5 MW (one-4L = Pa+—P?n‘ =3 Bang—6,5 == .23. 67 WW PA+= {Ve+f“/5.‘a = 20 MW Pat"; {Vv‘I’L/z‘e 1': IFgl‘.IVa+!‘/Z~a=?..§mw PL = PM“ — PL“ = (0.2 MN PO’Fne (m) -= Pnef- -pg -_~ 23.9-40.2 =/a.6‘ (mm) [Dhaﬁ/em #45 => Md'fC/fed’ T-}uac1‘r‘bn 3: = 45.12. 14-” 'é-ﬁlfne {eff-H: are '2er Vat—— %,-e—?r:5 Em Q 4') “29‘"®= R+ Emmy/(Ham = &+ CR+2o)/-L = (BLLM-f— 0/3.”: “BF ("timed Cﬂﬂd?*;0ﬂ) 293\$ = '20 ODOR—r— (f/L)R —.—_ a, 3:: 0/3)}, = 2.551, _. mﬂeCﬁ‘on Coef-chr‘en-f- 4+ p0r+® [5:0 6ecau5‘e. for+® (3‘ Ina-fried ) ( ‘Tﬂe egaFVa/en+ cFmP+ *ﬁkam poz~+® ) VX 7-": [RL /CR+RL)J ‘ VIA == (943)» = 0.60 (v) VL= [219/ CR+?o)J ~ Vx =- (WNW-#3) = (VJ—NV) VL=V3 =0.5'V ( because 0+ no ne-Hccﬁ‘m, jcarv'ard were 2‘: ﬁre node voHnJe ) PM I Pan/en PnCPJen-f- a+ pon+® == Ivo+1*/zo =QI/x75) -- 13.3 mm) Pa. : Pan/eh defrvmd 4+ par+® = [VLF lilo :(o.5=~/qs ) =—62—6-9mw P3 = Power- deiE‘I/ened 4+ pan-6(3) = a, 33 mN 3. 33 Pawn“) = P?» -—P-=L ”P3 = 6.67 «mw -——> 50 x Power Rs comm/med ./ 530:7511 '2‘?n® £19 ‘26: [ RN CR+%?] +R as»: R: (7/3 ) it: _ (3/5) 2.: :4“; T». = _(.—_ﬁ?"?”) = 45425“ = *(_/_) (a MA.) 4—:+45 4 V: = Var++ Va“ 2 1+(—r/4) .-_— (3/4.) (v) V): ': ER” CR+¥0)J ‘ V! = a}? X.— : :34— (V) k-f- CR/ICR+?0)] 55’ ,4’: @/ Ck+%)]'Vx= (an->000 =(r/4)rv) =3, ML: 0‘ p,+ = [vaﬂk/ z» = {3.3 MW IE—Ffecfed power 4+ pom!- @ Pr= lF'mV-PH = 0&3 2w pan/en tie/mm; in MN ® P3=1Val’/‘Zo= 0.9.? mW Power derrv’ereaf 40 PoM— ® ,0; = o (no Mohave , 00 port/er) 3o +— Var" ' ¥o=45a 22o 2WD 4?: 0/3)?» _ 2%?) = R—I— f (Mm/x fie-#22:)J = aQ-F f (Ki—BR) I («+6103 = «98.6312 7—71} .2: fine kHz—o : 33.63““75‘ = o‘oya \$393; -+ a, £9. 63 +7.5“ Voiﬁ‘: I}?! ‘ Val+ = 0-033 (v) V; = VEH+ + Va," = (.033 (v) Vx = CR-ﬁ‘ow/ 02+ 22:.) . y,- R+[CR+?°)//(R+2‘Eb)] C63. 63 / «9163):: (r. 0093 7 II = 0.767 (1/) Vi = [770/(1?+?o)] V”'¢05¢PCV) v3 = [22” CR+2izo)J Vx = o 600/) ”aﬁeff'ed Power ct-F MINI-CD Pr": ”To I'L~PI+ ‘2 0‘07 ’"W power ate/Were! +0 Pow—Q pL= (vql/ 29 = 4.49 mw PoWer de/FI/‘emd +0 pon+® P3: NSF/2» = 6 mv ) pm: xa-a mw PROBLEM #3 G) For Mew-r toads , f) l A 6 Va" I -———__—5 I it, I-_—) Vaaj' Vol I <_____ Rp Ié——- V6.15": O l r 5 ‘ (~.- Here I“: no ref/awed wave 790"” ”5+3 ) I I 7' arm—2., = (Mm—95° = i A £m+zo (ﬁpx/&)+¥u 2szo+%‘ TA = (mp/v03) = Cch+/Vor+) = Mn 2 fznf.zo/(2sza+¥o‘)] VRP’ 72‘Va!+ ‘ szzv fszpz.+zw)] t/on‘ Zrn=CRP//%) Pkp= Warp/Rap P+ = wa'lLl=k / go PK? : 'VRPIL' \$9" = M (A) W ’Vol'f-{l‘ 1% (wag. + az)‘ 2.) To max?m7¥e ﬁne power +o Rf, 12:29. cu den‘ra-f—r‘on. e3 (,4 ) —-> o @{ng/P+) = o % [email protected]{—F(x) ? l: frr12Z(>C)—7C(¥)Zrm) 9199 Jet) R700 'r‘" 55:3(zepzo+zo=~)‘“-—4Rpazos-2cm&+%*>-2a =0 2R???" + E"3")4“ P5 p+ .. “5‘23 3—) To Max‘im‘i‘ze power +0 QCPRS/P+) :0 (BR: «Hazar H I). P (ﬁeﬁecfed ) IEI‘IIVOI‘HJL/ & o.:sp+ ¢—-.. nun—h. h.— C no ref/Md war/e. ) _ 3-714: 77! \$11-on 7:3 :( VA / Vor+)= l-r-FA _[.zoes+zo)/ (szzoﬂ Va: 4g, /CR.s-+zo)] - v4 / =[Rs / C§J+ZD)J ((+54) van“ R3 _____._= Vor' ﬁts-+221: I/or* :C;RJ/(Rs+2?o)] Vw+ PI“: 'VRS! /Rs P+= [Vor'FI‘L/i‘" - (6’) A35) ﬂKe a deni‘mﬁ‘m 423 (49—90 42., (Rs+2zu)*—~4exza (R.r+3a‘z?c:)><a = o (Rs+2zov* Mtg-#229) *Mgﬂz =0 Rnnzz, = 24:2; IR3=2£0| Pa+ 193:2'30 (‘5 695(5) PK: ._ 32f __/_ “£2 I P+ ”727:=% , m==~('4ao/') Pfre‘Hec-fed) = 'T'All"v°'—.+P = 2910+ 25 V°l+=VAX_§__= 22., - +:._/ + ma» m V" 2- V" *1 PC’f‘I‘dnSMF'f‘f’ed) = ,Voﬁ‘fL/ﬁ .-.-__— [Vo;+{‘” X “—(- 5, 4— l3 Pros/em #4— ””9 V0!+_.__) ' A ‘8 C t=o — ' +4 I 3‘ a) . _ V” E I 0.5.? age I _. 1 1 30.!1 " g? : I R1. = 300.12 AV :2 w E : I I 1 .9 =30“ I n0+ Ina-failed +0 ﬁe (Me (‘3 Rt. 95 53o) ﬂ J} Wed-En do?” occur 41+ ﬁe (0;:th LT 3:32... _ M = 0.5 V34“ ALL-+53 Bea—Hoe @Mxﬁm coeffr‘cr‘en-f- 41" ﬁle [and impedance -i‘o = 30—100 _-'-_——0.54_ RJ-rilu 304400 6'-Ne+!.ec+{r‘¢m Coeﬂ?c?en+ 0+ ﬁnevenemfoﬂ Emoea’aﬂae v3+= 13v;— = [3‘11" v.+ ’9 +Z° V3." =rLVS+=EflrL3 Vl'f‘ -"-' 3!:0 ‘2 =I‘S4[V) V4+ = Eva": UJQJVH 0 {0° V4“ = I1 v4+ = 53114 VH‘ V!“ = I}.- VH- = 0-00 (v) VL Vy++ VF-r- V¢++VJ+V3++V3‘+ = r+Cf+T1+FfI+ r31: + r541 +--- = Cr+n_)(r+r3n+ (13(1) + (QT‘:.)3+ => (’*TE = Vr+-U+712 = {.54x §I+osz 3J6 (v) (7-4371) ((—03—7) (S Vr+= I-Stﬂ/ ’Up‘: 6 /\/EJ,: = (ammo/W V”: 0’7“” - Lsxmc? (M/S) VL+ «~— ‘0‘4—9—V - V4: = “OJ-F V T = 3/ up = (5x10—1)/(/-3XIO") Vs+ = o.(/v = 3.3mm“ V3—= 0-051” '" 0.33xro‘9 V4+ ="°_~°3V é:- o.:3 nJ‘ VA wuvr—WH L3'9 ‘ “ 4. - .L V!+V|+V.2 *V:+Vs 4 —_"j v.++v.‘+ v;.*+v.1‘“+ V: +- V' +Va‘-I~V4+ i=0 1' 2T 3T 41' ST 6T ’PT 31— VB 33?! “9*? VIJ' _. 051‘ 1.51" 1-5T 33'1“ 4 51’ 15.51' 5.5T r) 51' I I 1 I 1 I I l l l I I I 1% Miégta 91‘ m- 15‘167“: #9115 a; A’Ppwx. HM. MM 22 Kim :2 SW bes. 12 L WW: 3' K 3 .._ ﬁr b) #0 + 4 ii r—-§ V2 0 :2 {06.0. )é—V/F t€VLh Q M-er : Rthocﬁr H _ 94/ ._ T V" ‘_2;”_:_‘_! W4H£ed *‘0 456 We (1' ﬁg: 2a,) 9 S0 Deﬂeﬁm 00?” 00+ orccu— 61+ ﬁe {oa..c{ VFW. __ 195—20 W" ’I : Tame = 0 M G=.—'QJ_“‘21: o 15 F AQj-f-iLo I V + - 2‘” f _ VA 9% IV I——“‘—__—“‘ :2: {V {r 2.0 ”I Pmb/em #5 ._ ____/i//'_LL__ = iii}. =94? E) VSWR "‘ {milk} (—0.4 p+= “6"“,1/5'69 = f/jb==2o now P“ = IFL/‘P'F =Co~4 )‘x 0/50) = 33“” PL: P+ ( r— [rm-L: (pt-”W; 20 —- 9.8 = (0.2. MW =3 Same as PHL/em # Ice) +) a! :0.035 (a: calcura-f-EJ rnoéremm 6+) ) R = 6 cm (= 2A) + =-;« wave-r "’93:; '—9VL+ V'g-F = vﬁexp (—zxﬂ) ‘ '6‘ w. VI." = [L VL+ == 72 - Vo+ exp c—orJ?) : Vo' = VL"- eXP r—dﬁ) = I"; v¢+exprnzd£) ”Pitt 104:! . _ I pFn :1 Vo- -.-.- ﬁ.aKP(—_2,b(£) :— 0.4.6 it \ Vp-ﬁ VS‘WR C¢+ F‘npu'f") == r-r- {PTn’ - 2.7 {"‘ ,thI ' VWR (4+ (and) =~ f+ IF...) I: S_6‘7 3“ ’17:.) sze F; alto same ( —H; e ﬁrwerd )0 awer hefrec-H‘on CoeﬁCFCr‘Cnf doe; na+ Marge ) PM = {V?a+/‘/\$D =2 20 mm/ ‘HIC bacmamfPOWEPi Pu": [PTnI;JW+IL/iz” 241232 ’"W Pne+ =Prn+ _ a": r340 (mw) Pg+ 1‘ {y,_+{-1/go = (3.26nw) , PL: PL+ rPk"'-J.3MW PL” -"-‘ {VL'I'L/ﬁo = 6- 4 (m W) purine {0.93) ..—_- Pne-r— .—/>1L .: I500 “5.8 = 8. 9/) (MN) Magnitude Vrms .. I; f: m 0.035 0.03 F3 0 NI (:1 0.02 . Magnitude ln'ns I'D '3 0'! 0.01 0.005 -7 Problem 5f: Plot the Voltage and Current magnitudes with a line ioss Distance from load in cm Distance from load in cm mmwmmmmmm m 4 4 1 [an] 4 PM «rmmmmmnm V1 ms — am was i am g n 015 0-71 ones I [an] rmrvmwhmmmrnm 1 a u 1 . gm. Eu ' MN ”m. mamwmmm 11ml] ...
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