EECE 210 Notes Prof.'s Notes Ch 9, Spring 2014

Sinuscidal Steadly- State Anakysia ' ep de ony tiled dea f= So for we fave oliSauded crretuté aspth Constant Souter. Lnthis chapter tue wif Conaiciér cireusifs ve hax} Hime~Vvany ing Curler _— urttage SOULE « We dae airy been tee tr SEUICES to) The velfagea Auel Cevvibay tS vay ng AUNMUAC) dally lb time @ecause duck Sewites ars. Adee Wr Fhe genwatisn J Arce Serer) , and ast butty &} eteeNie paver. Ol The Sinuseielald Syuree A sinuscical wllage source procheceo a veltage that ‘ ONS, Vets ainurodally whth toe. The snuosiclal urltage t Source ta ex srradect Bo 4 Us Vor la(ut+)) / The Curve bb plotted aD: r A The dinw ole fine Hor re poeats atself at (2g volar Jrtavels. Gack untorml ne , lg pulsed aud -Obnrted by T, The reaprocal of T giver the number of cyckes Nr Secsnd ot fi eiue nly : f= 'A7- (hertz) a (te) 9, a Tha. Coefticitnt gq t ws Te angular fregucnty Fa We Ant roel/'5 The an ge od “ fhe. srhase ange. of Ptr gakpuoel ola vetlage TE oledermines He vabr og ‘The voltay & at t=O. bo expressed dn radians. é Aino ther impatar & Charé efeus He oF Pha uot Fog la 4h fout-mea N-Sguane ( Lr. ms) velus olefined by ; V [, tr : i Lng = * 2 => ms [tf tor (ut-rd) le => é Uo (2/ Example 9, As The fms og rriang wl. warvefovan / Vy yas = Caltrlate tar ms of a triangular WAVE Curent Shown bale: nections / tert Lf pea t & ud Tha. analy wal Lx pressisn 57 l ty+ L(t) = 47 t oft <T% i ~ ’ So EAT Va. [ eedt= 4 [6 Lot — IpT 4 7? 3 A 4, Hento. Lemsg x te {3 D2 The Siause dal Koo ponise o , a f , 5 The Gener VLb favnse A Sao) dat SEULLED 9 craukz nN . fl asf LD phe ws may be Infroducacd saving 7? As folie) a . 75 Any ate) R Ws L Us = Vin asa (wt+) The S) (flew bial epua AION) oles! Lyn 1G Phe. Clraut Ls ph tuned vt ing FENML, s Lot, Riz Vm @luted) 98 dt . D4 The sotufion to Ths above DE 6 Given by: ((t)= — In &(G-6)0 V4 Im bo (ut rp-6) 99 whine z Vin ~ StL Dy 2 nn 2k Os tan’(¥b) ne z / z/ f Ptg Wwe i Ly , y ,o. 4 The first team on The rhs Ge (99) Tee transient Component which decays aa t tnirtnats. The Atcond term t The ateacly j-State eornpanent oy Hu sathtion, Thou a sinwodal function. A, The frepeanty op Hho reo pend la teleutt col to Phat of The Sewr lo. 3. The maximum anya th Aude of Phe Crprent aenenonmtig — 10d pon se. bo P IVER Ba Im = Vn /. Rey ty be é 4. The phaor Gangs. of TAx Current reSpomn $e é q ba differen ‘a fro? me pohaae cin FE og fhe Sur la. 9,2 Th Phaser. Tha P Aa Sar. bo a Cpe x Nambér that Carries tha ain Pll fu de | phGer. amas sv for- Plitucde ano Va aa va 1 fe matmn, The J2rasan Con Ge fat éy raoked 1 Salon's Ales Ary 3 ye , | So . les 6= fer } ow Que LOO & pn { ay @ ] “a oa. rf OH # fly B.4) to Fhe MBOUSE ‘af cwlhage : Ta. ian oe Vin @. CaAMts the “supine Baa! phages ang te 2. of Fhe Fiven Sinuoadel wllage. The by ole Ainiher 1 He phasor represenkaHar\ Fhe Qinuas dal SIP nak. Le tu Of tained UGH G a] Same” the /? haa trawfam (YP -; Ven Pim cower} — Gus) The Phassr Prana; yew chang? fhe. fd wre. function nro a Corn, plex Alden bn, pwobied Us aloo called He fe ein tf ME YIEL op f 1 a oe Ceualisn ONS L FAL potir frm a / may Bbbrenakd sole the anges sno da any + oe Vin 1d prrasdr elute. The ee og) ay é? alla A y / _ ‘ (PR CTEATY OSE TEV Op Hh (IMAITL by 3 at Ve Vin sod) aa / Vin hans a) (s on ) The Trverss Paaon. Tran sfian 9? oi Von oO *4 = Re § Vine 2 j f *s oe whys FP sag pth tt - wy oleray oy a eg, a # The P MODEL. ot Pi. Covreut / res [PEN SE. ( Stea dy Sta te) by+ The olensmne tur bs thee PS ban fram os Ph. corm ja he x pumber Ze Katja) known ae Tht im pedana.- av Jd 27 Example aS ¢ Adding COsine | fe Lg etet Nes using Phi a by = 20 Ga (wb-30°) aud Af, = 40 te (wh+ 60) * i a . C bon fh - f 7 mt i a1 ax pe ress Ye we, AY, ag @ hag ol I eal fuin cH ev! i / ed vad wel "8 So Ys 20/-30'4 do / 6° = (17.32 =//0) + (20 4) 34.64) = 37.32 4f/2H EY = gage, /2343" _ 7 ~} , Y = o" y/s G? { A472 [32430 ms _garernenemeccmnesisienton Ya 44.72 Cn (Wb+ 3345 Asses sgment Problem 9.1 Find ths phabtr oy each tro eneme AIC function: a) w= 170 ten (377 - 40) Vv | Va Pivgt= ‘70 ov 170 [40 Vv b) t= so an (foot +20) A i= PF = 10/206 OS C) le & Colut + 36.875) 4/0 Csr (wt ~$3./3') A. T= Pfife 5/3687 410 /=53./3 = A+/3 4+ 64/8 = /0-~j5 = M18 [-26.57° A. AiP 92 —_, _ } 1 . a! Hind Ths time dsrnaivy 2xponesston covets pen wg fo 2ack jahastr , ; Q) Ve 13.6 [-5%? V Ue if vps (8:6 Co (wt~sye) V b) I= 20 / 4S° - §0/-30" mA. = (4 1G2 aj (442 — 43,20#j25 mA: = -291/64/391. = 48.8) 126.62" mA n fae! ‘ e et t-S Tj = AEE) Cs (Wwt+ 2668) mA. C) Vs (z01'so)- 30f/5 V = (20 4jeo) ~ (28.984) 7-765) = -S.984 5 72:24 = 72,79 / 9708 => ee ennsniniiritrnnawet oe TS? She 72.79 Ley (WE+IT/ 08) V 9.4. The Fassive Cireuit Elements \ ~ Be, Ss uy tho r7reé PUOUCY Loermnaer] ad The VT Reb» +f 8%) sip fer a Rais AOL ‘ c R Fa a veofster with Current ¢ , S a is arn Shown, The wlsage Vis + _ vi G ven kan Odm's law : S VUeRe So if b= I, ho (wt+®)) TAbar Us ke Lyn > f to b+ on ) f 2,25) 0 iS twhredr may be wriHen aa 4 EQnuahen 9,25 ay Pha Prhadn. dang ln be brea 4 a But L» [© (by the praoer aut fa 7b. seratiin, 1 a the Siauat Ve SL curcétul. Sy V-RI (9.27) The. Phaser. vob fade ts the phaote Cu rrink Hines tha (bails fOr has D0 Tho VAT Kelby Hon am an Za ductéer Gnsi dea an jaductor. L with arent Lz Lo OL VY 0 couareia aa é + OS = The utlage ts Give Ap 4 Je ur Age bs Jiven leaug uel Es =~ WLIm olin (wt+8:) > . | Afe -wkh Ip, dso (urt+ 8, ~ 90°) The Phaser VESITEDED da td ogy 4 uw oi mp8 _ tl@- 92) Ve fs Vr ye—Whlm a JO 9P “JF =-WLhIme 2 /e~ 2+) |) ( So Ve /ool IT (9,30) Jol. OI VY 1 etait ee seems ra) imal Foy. Another. tuQsf op Lor hina Mahisy) G80 e+ <r a Y= wll, JO; +90"