EECE 210 Notes Prof.'s Notes Ch 8, Spring 2014

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MB /09 KCL at Fhe toy nook & the ie) COUN t: t ws aot +T,+ CW. vs, a" ti de @/ 6 ( 7 ne Uy bt, 20) Noke Hat T, o He ryihad currenbin b C44, c.Co)) Aud thon. + Voy ts fd tA M a ; had vel +09 ma aAcrass Cc (tie, wee)). . | / 0 é 1 mz ‘ ( 4 eo By o/ 4 PADI 110 af 1g CGO Aan &, / ) CY) wn J) ng by C : arcu LAKEANDIOG we obtarca* alien / ol Ue (8,3) yh Laon Ste RO ot + TS O 3S Genvral Sotation of the Sezent/-Order Orfherenhal ED ua hen We note Shat The Aetend cleruvatirr ep Ths dotutien W Rlur a Gmsiaat times ib first oleate, jelua @ a Conofant times Ha erbrh'on at self »emust be epuak +O 3a for a webu gl tL, The £x poner hak fim char can sat's ty His cerdbihty , duc Hus 4t 1 whose a ) 49 partials Solu A av) to abdsuyme that Ves Ae fo 3.32 Quid that at muot Sot sfy at fer all values / . ; C 7 ; a ¢; so ky dubshhag wunto (83) we get St ; ; sv Ase + £ls ou Ae -~ ©} = RC aa Ak’ ( s+ 3 4 +) =O (8.6) ROC Le So fo Al est a>) bs a Sohn , they) Thr pareutiiss term must be equal to pa / oy fs. =O (20 The @ bove 2qia “FEN io calla the cha raAaChEnInst Te eQuin kien. Its rootfare given byt Ss- [7 ’ Zac? (Ze) -/ . fd ee se=— sae > Mxge)- ce ze Lé . Bry wh f etior root ta dubshyt uttil An tu @ SSinec! im A t a7 ’ “) . é [Par ticukan Soly flan, (UE Gotan @ Setnlis7) for 8,3 regard oP the vabluo ay A. ThstAna. ’ J boftn Se Sif” Ws A, a’ Cline U2 Ar @ SS ahi r Ay ED. &,3 » Phat tev bo the Sota Pifén a Eb. 83 as Cern Ge -e20a/ ty vewifree! 2 So: 7 A Sit ga t Os Ul 4U_= 1€ +fAlre @: /3) / a Cory tauts Al ctatce A a Be oblarmer! fro cater eemifhinga on oar aud du/dt at t=O. 7k root a Pha Charatfeusie Gun Alona art te wally tr) BAA tu hs followin f fivm + Sa - Oo + ote we / Wo= rz) Bett bar ke) aan Yue! aa The valuta S, awd Op bet. Kas oe) da Fhe. CharacteuiSH Ye (0h a wmplix Mepuen ces, eeennemtmiotoEtn tenner BS Th vee possible cutcomer aw possible ; 2 2. t) Ovurdampud reopanse : bohiwn & > Ww, bot 00H §, and s, art wal aud Wishact. - 2 2 tt ) Under darn ped rea fs e When & <M. then Sy Quid S, a. eompdthy 9 Ju eate valuta, “3 Ro . yp, , a LLL) Cu ically Van peel Uuaprnse + dhe tly = & Fs 2. Tht Thea. roo s, aud S Art 20nd Aarel equal , ra f Sen. Ex Ginpte &,j ) | ,, ; P- Ale cessme'p & 2 bole m &,] Tk. years fan ta. Cuid an vuctaude of A pa rallel PLC orcirl R= 1005S Car LaKkO mp) a ) Find Cc that meokbas The as KP SYISE, Cu picolly darn ped, rd au. ou ANC al Aaanpare 9 ae Fetes & i f 7 RRC, Ze oo Ox Le _ 20x10 “x10 Fs S00 nF 6) Le Xe 5x/0 rad/s Cnepper (Peiuency ) , Find C aud The charactenrcohre roots ; a= + 2 Sd => C= —L_- ’ © Fhe ON RPS BRO Bej0Ox SID? -& me = /y/O €.6 To determine The natin of thy Usp Se, we need 40 calinly be ( = uw,” ) aud! keen Ve at to x*; we = é OS = 50%x/0 ROXIO % 10 * 2 Aus Kk = 25x10 ° 2 rm Sina *% < wh tin Saud % an Comphx conjugate valuta : 2 \ ——~7 2 5 = - Sxl0 + /f 50-25 x /0 = -~Sos0 rj 5000 rad/s S,= — Soro ~/ 5000 fad /s. ¢) If Cow adljus tes to give a woman t fepuen cy of 2O kel /s , Pros! C ancl Tha Charactu'estfe roots. 2 6 We = _ = ZOx/0 => Ww, = GZOoOR 10 — fie? LC Ce J 2 8 25 4/0 L. we OPED 2 ZO w/o) 4 _ oO 125 Mrs 125°0F te An 104 1038/5 = eee “= RRe ~ Rx/00» 0.2540 6 Xe 16 w10° % - & *) (ee ) thes 2(-1bx10 ) We (= AxiD" ) Then é slaw % 8.7 Thow The C eS PUP, Se ty BYCA a Aan fated ate S, anol So being a eal dishret value g So AHO” *yfie-4 x10" = 5359 rad/s nica ~~ dylo’/ 16-4 x/ote ~ 74.641 rad/s. 8,2 The Farms oy the Natal Sa Donat ga ForalleX RLe Circuit i) The oveanclampd Moponse: When of Sw He olution yt wrlsAage ts wa S$) / st ar (+) = Ae =f } Fle @ La/7A S, aud Sy being real auvl dishinet, The Cone taur}s A, aud Fla an sue ol from Tht ins hall Capac fr ured; AGA Quo anitel nue tor Cupelul / rl") = A,t A &, 19) at but dao &C 2. Mt.) / at Cc R aa Tha poroless of finding Ay dud As i Sem marized ; 1) Sod The foots Ss, aud from ths Vvalute of RL ,audl, 2) Find V0) avd olen? caving Circuit anafpsio 3) Fino A, au 10 wa nf Lgnyattine 819 Aud §,20. S fucty Cxanflis 8:2 and 8.3 | 2 Assessment Problem 32 Vat tha integral rlahonshy between L, and v tofind an expressim fo lt» the follow iO9 Crrtutt i le ~ aL Cz O,2MF Y L sie Be AL L=- 50m#H Pe ve a R = 200.2 Vie (QV Quad L,=30mA D Calerlode rocks x 2 the chatacteriste Speen . * 6 maf! “-(—/0__ - /S6,25 x10 \2RC | 22008 OZ / G 6 wee fe /O _ foo % /0 A eens erties Zc S00" 7% 0.2 6 2 L Sing % No Tha Ped puns iS Sven ve an jae ¢ a ae) Ge oy tof of” — We as | = — /2,5x%/0 4/156, 25-/60 ¥ /o — _ (2500 + 7S00= —~ I9ORO rad/s S. = —(RSc0 — 7500 = — XO 060 rad/s E10 — S650 6 ~2a0a0l U (é)= + Ut) dt + TF, (>) eo = -crsot’_ _~ 2000 - _! Clye be seco’ +) db Sax! S0x/O t —Ste0t — 2666 _ ) 7 Me 5 26 eo é a SOxlt Sdx/0°% | S600 Agese ° —soet ee = 00560 — 0.0268 A EPO ~wbt ~ 2o008F 262 mA ERO