U1. Transient circuits response
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1 U. Tr crcu rpo rcu ly, Grdo Irí d omucco uro 6-7 Phlp Sm phlp.m@uh. Dprmo d Torí d l Sñl y omucco
2 Idx Rcll Gol d movo r dffrl quo Rcll Th homoou oluo d d ordr lr dffrl quo Exmpl of d ordr crcu Il codo Tr rpo xmpl o d ordr crcu u of h r rpo ly u plc rform
3 rcu ly / Tr crcu rpo / Rcll Rcll dw v, dq dq Rlo bw d v for h pv lm R,, For R: For : For : v R Ery h lm: Dpd R: q v d v Sord d : W dv WR R R v W v R v v R R
4 rcu ly / Tr crcu rpo / Gol Gol W w o olv crcu for whvr ppld ourc o oly D d Suodl Sdy S Drc roluo h m dom Roluo u plc rform I prculr w w o udrd wh hpp wh brup ch k plc h crcu, whch wll produc h r rpo. 4
5 rcu ly / Tr crcu rpo / Movo Movo Sl rmo S.S.S. Tr rpo
6 6 Exmpl of d ordr crcu R-rl hp://.wkpd.or/wk/r_crcu R-prlll d d R d q d R v v v R d v dv R v d d v d v dv R d R Ery corvo hr corvo rcu ly / Tr crcu rpo / Exmpl d ordr crcu
7 rcu ly / Tr crcu rpo / Iroduco Tr rpo Rpo of crcu vol or curr wh brup ch hpp.. wch Tm voluo ul chv w qulbrum Th ro fuco follow xpol vro dcr or cr, flucu or o flucu Thy r oluo of lr dffrl quo 7
8 rcu ly / Tr crcu rpo / r dffrl quo Grl oluo r dffrl quo of ordr : d y d y y y y, h p... y, y h h oluo for =: h omplmry, url or homoou oluo. Gv h r bhvor of h crcu du o h pv lm. I dpd of h l codo. y p prculr oluo for h v ourc or forc fuco. Th prculr oluo look lk h forc fuco,..: - If co, h y p co - If uodl, h y p uodl.. h S.S.S. Th homoou oluo dcr xpolly o h y y p 8
9 9 Th homoou oluo y h h oluo for = xrl ry upply = Th oluo h h form: y h = xp z rcu ly / Tr crcu rpo / Th homoou oluo k k k d : c k k h k y... },...,, { chrcrc polyoml quo,...,, r obd wh h l d/or boudry codo chrcrc polyoml quo Ewr
10 rcu ly / Tr crcu rpo / d d ordr dffrl quo d d ordr lr dffrl quo ordr dy y, m co how f y h dcr For crcu co o ry or lm or d ordr d y dy y, For crcu co wo dpd ry or lm clld h dmp ro ccou for h ry lo clld h url frqucy mxmum ry or hp://.wkpd.or/wk/dmp
11 rcu ly / Tr crcu rpo / Ejmplo crcuo º ord Exmpl of º ord crcu R-rl hp://.wkpd.or/wk/r_crcu d R d R, d R-prlll d v dv v R, R d
12 rcu ly / Tr crcu rpo / Il codo Il codo For ch ry or lm w d l codo = : For : v = = V For : = = I E v W v W
13 rcu ly / Tr crcu rpo / Il codo odco cl Wh brup ch hpp = crcu, hr lwy couy h vro of h r d Thr couy h vol : v Juo d v Thr couy h curr rouh : Juo dpué d o o for h curr o o for h vol v 3
14 rcu ly / Tr crcu rpo / Tr rpo Exmpl of r rpo Il codo : v E Dchr of h cpcor For For d R q, d R d, Homouourcfrquo wh oluoof, hrcrc quo quo: : R h form Oc kow w c ob v : d v vr v R 4
15 , v c, V rcu ly / Tr crcu rpo / Tr rpo + + =, If v, 4 Typ of oluo of h homoou quo 4, b d R : Ovrdmpd R, E E, u : - E E Th vol dcr. Th curr fr cr oppo drco h dcr o zro bcu of h ry dpd R x -3,,4.6 5
16 6 Typ of oluo of h homoou quo π,... π,, frqucy url h udmpd 4 : hr Udrdmpd : 4, 4 If d E E E d v dmpd ul frqucy Udrdmpd rcu ly / Tr crcu rpo / Tr rpo Th ocllo coquc of h ry xch bw d. Fr mov from o, o h wy om ry dpd by R. Oc h rm ry ord mov bck o dp om ry R d o o ul ll h ry dpd by R.
17 7 Typ of oluo of h homoou quo. π,... π,, Udmpd :, If. rcllydmpd :, 4 If E E E d v E E E d v R Udmpd rclly dmpd rcu ly / Tr crcu rpo / Tr rpo udmpd ul frqucy
18 rcu ly / Tr crcu rpo / Tr rpo Dchr of h cpcor Typ of oluo of h homoou quo 8
19 rcu ly / Tr crcu rpo / u of h r rpo u of h r rp R-r. Th rul dmp ro : R R-prlll. Th rul dmp ro : R I proporol o R bcu h ry dpd R cr wh R: p R R R v R I vrly proporol o R c h ry dpd R dcr wh R: p R R R v R 9
20 rcu ly / Tr crcu rpo / ly u plc rform Tr crcu ly u plc rform By u plc rform h crcu c b olvd much ly: No dffrl quo h o b obd W wll olv lbrc d of dffrl quo No d o prform h dou opro o clcul h co,, of h oluo
21 rcu ly / Tr crcu rpo / ly u plc rform plc rform Th oluo r uprpoo' of xpol dcr fuco r from h l = Th plc rform llow o rform h dffrl quo o lbrc quo wh coffc y y y
22 rcu ly / Tr crcu rpo / ly u plc rform Som propr of ll, F= [f] f3 f bf F3 F bf of drvo Tm rlo f f f f '... f f, f f f Trlo dom F f Thorm of h fl d l vlu lm f lm F, lm f lm F. Ohm d Krchhoff lw r ll vld -dom Dffrl quo r rformd o lbrc quo
23 3 of om fuco Sp fuco dplcd m Slop Rc fuco Drc dl fuco Prodc fuco wh prod T u u u u u u u T T f, T u u f T f rcu ly / Tr crcu rpo / ly u plc rform
24 rcu ly / Tr crcu rpo / ly u plc rform of om fuco Expol S o co I prcc w wll u bl wh h mo commo vr plc rform - ud for h roluo of h propod problm 4
25 rcu ly / Tr crcu rpo / ly u plc rform Roluo u plc Th crcu wll b olvd h plc dom: Drw h crcu h rformd dom, for h h l codo r ddd:, v. Th rformd crcu h olvd u h kow mhod, hu, by pply h Krchhoff lw o h rformd curr d vol: I, V. O you kow h plc rformd vol or curr, h vr plc rform ppld o h curr d vol h m dom I, v V *: ovo: plc rformd vrbl cpl lr * 5
26 6 rform of h ducor. ], [ ], [ I d v V v V I rcu ly / Tr crcu rpo / ly u plc rform
27 7 rform of h cpcor. ], [ ], [ v I I q q v V v V I rcu ly / Tr crcu rpo / ly u plc rform
28 rcu ly / Tr crcu rpo / ly u plc rform rform of h ror fr h wch: = G For xmpl: E E, co If h wch hpp, prform m rlo by df: =-. Th h o b k o ccou by prform h vr rform., 8
29 rcu ly / Tr crcu rpo / ly u plc rform Il codo Th l codo w d r: Th curr rouh ch of h col ju fr h wch k plc: + Th vol h rml of h cpcor fr h wch k plc: v + If hy r o kow, h hy hv o b clculd by prvou bfor h wch roluo of h crcu, Rmmbr: + =, v + =v 9
30 rcu ly / Tr crcu rpo / ly u plc rform Roluo h -dom Th rformd crcu olvd by pply h mh or od mhod of h rformd vol or h curr whch dpd o h vrbl. Th follow xpro for h vol or curr h o b obd: Y f whr h domor h chrcrc quo: From whch h roo d r obd, h llow: Prdc h kd of oluo Fd h vr h plc rform bl, 4 3
31 3 Prdc of h kd of oluo If h rood r rl d dffr For qul d rl roo For complx cojud roo:, =pjq Imry roo:, =jq y f f Y q y q p f f Y p y f f Y q y q f f Y rcu ly / Tr crcu rpo / ly u plc rform
32 rcu ly / Tr crcu rpo / ly u plc rform Ivr plc rform - Th roo of h chrcrc quo llow: To kow bforhd h kd of oluo I mk r o fd h vr plc rform h vr plc rform bl. Do o for: f hr w m hf, ubu by - h vr rform. Th obd oluo dfd for m rvl fr h wch. hck h l codo. 3
33 rcu ly / Tr crcu rpo / ly u plc rform Exmpl I h crcu of h fur, h wchr poo c = -. =/ h wchr ch o poo. Ob h mporl voluo of. D: =co V, R=, =H, =.5F. 33
34 rcu ly / Tr crcu rpo / ly u plc rform Exmpl I h crcu of h fur, h wchr poo c = -. = h wchr wch o poo. Ob h mporl voluo of v. D: =V, R =R =, R =, =H, =F. 34
35 rcu ly / Tr crcu rpo / Smulo Smulo wh 5Spc 35
36 rcu ly / Tr crcu rpo Smulcó co 5Spc 36
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