Chapter 9 Transient Response

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1 har 9 Transn sons

2 har 9: Ouln N F n F

3 Frs-Ordr Transns

4 Frs-Ordr rcus Frs ordr crcus: rcus conan onl on nducor or on caacor gornd b frs-ordr dffrnal quaons. Zro-nu rsons: h crcu has no ald sourc afr a cran m. I s drmnd b naural rsons and h nal condon. Zro-sa rsons: h crcu has no nal sord nrg.

5 Frs-Ordr rcus w For zro nu rsons > characrsc quaon : s s : m consan

6 Frs-Ordr rcus / / / / / > > >

7 Frs-Ordr rcus Dssad owr b h rssor / d w > aacor s nal sord nrg

8 Frs-Ordr rcus srucural dual of h crcu m consan : : quaon characrsc s s / / I I I > >

9 Gnral Frs-Ordr rcus olag or nducor currn caacor : zro nu rsons / / > Y Y q q Inal slo-y / If < hn h crcu s unsabl.

10 Examl 9.: Zro-Inu sons / 4 / / > > Ω ms q q

11 S sons S rsons: rsons o a s nu OFF o ON wh zro nal condons. D sad sa < u > Zro nal nrg Ku < K > For a lnar m-naran crcu TI h rsons o Ku- s sml K- whr s h un s rsons.

12 Frs-Ordr rcu Thénn [ ] olag :sad sa condon nal q. nonhomognous dff. / / / q c >

13 Frs-Ordr rcu [ ] :sad sacurrn / / q S I I u I > Noron

14 Gnral Frs-Ordr rcus [ / ] Y > Y afr 5 Yss nalslo 5 o rach sad sa rs m %-9%.

15 Examl: S sons of an rcu 4 8. > > m s q s µ

16 Puls sons Puls rsons: zro-sa rsons wh a rcangular uls xcaon. qur nal alu sad sa alu and m consan. S rsons zro sa Zro nu rsons

17 Puls sons D Y D Y

18 Examl 9.3: nalss of a la Drr 5 3ms / Noron : q.ms 3ms 6ms I 5/ 5 m /6 5m 69m m < 3ms 69 3/6 53.ms 4m m oal acua m ms > 3ms

19 Swchd D Transns Swchd D ransns: h sourc swchs from on consan o anohr consan. hoos a sa Fnd nal alu Y arabl Fnd sad sa alu Y Fnd m consan Thnn/ Noron Y Y > / Y / > Ohr crcu arabls ar smlarl drd from sa ma no ha connu or Y Y arabls

20 Gnral D sons / / / S rsons : Zronu rsons : for aralll crcus for srs crcus Y Y Y Y Y Y Y

21 Examl 9.4: Squnal Swchd Transns Par I Par II

22 Examl 9.4: Squnal Swchd Transns Par I I I q 6 m m kΩ I 6k µ I I.6s / /.5.5 /.6 /.6 m

23 Examl 9.4: Squnal Swchd Transns Par II m s k m I m I q.4 /.4 / Ω

24 Examl 9.4: Squnal Swchd Transns

25 Swchd Transns

26 Swchd Transns Th aramr of an ac sourc undrgos an abru chang. nalss s h sam as swchd dc ransns xc ha h forc rsons s dffrn. D sons : Y Y Y > Y / > sons : Y F Y cos ω φ Us hasor analss o oban m F

27 Swchd Transns o oban Us hasor analss afr 5 sad sa sons : / / / Y Y F F F F F F > >

28 Examl 9.5: Transns n an M amlud modulaon ado Sgnal Phasor analss for < : I 6 6 j5. 3.cos5 3 j5i 3 6 3cos5 6 S 6cos5 cos5 < > I.cos 3 S

29 Examl 9.5: on. 6 6cos5 3.4 cos5 for > F F cos cos5 6 ω T s

30 Scond-Ordr Naural sons

31 Scond-Ordr rcus scond-ordr crcu conans wo ndndn nrg sorag lmns.. nducors or caacors. Frs-ordr ransn s characrzd b dcang xonnals. Scond ordr naural rsons ncluds ordamd undrdamd and crcall damd bhaors. aacor olags and nducor currns ar sa arabls.

32 Srs rcu K : S S or S or S ll crcu arabls shar h sam Sa arabls:. d Examl : d form of naural d d rsons

33 Paralll rcu Basd on K w ha S or S

34 Gnral Form of Scond-Ordr rcus frqunc :rsonan For srs : For aralll : ω ω ω ω f

35 Examl 9.6: Scond-Ordr rcu wh Two Inducors K K K Pck as sa arabls.

36 Examl 9.6: on. S s x s x x x x x x x s x x x s x I : quaon In marx form sa an b gnralzd o n-h ordr crcus.

37 Examl 9.6: on. ar rlad. and nrg sord n Frs ordr crcu hn f quaon : - h ordr dffrnal an In h form of n s s x s x x x x ω

38 Examl 9.7: Scond-Ordr wh a onrolld Sourc Phas-Shf Oscllaor ou K / x ou ω K K ou ou

39 Scond-Ordr Naural sons condns. b nal ar drmnd gn alus...c. frquncs naural alus characrsc roos : s s N N N N ± ω ω ω

40 Scond-Ordr Naural sons ± ordamd : undrdamd : crcall damd : dsnc ral roos In som books : losslss : magnar roos > ω ω < ω comlx conjuga ω rad roos roos

41 < ω Undrdamd Im Fx w dcras osslss ω rcall damd ω Ordamd > ω Unsabl <

42 Ordamd sons as sabl.. / / > N N

43 Examl 9.8: Naural sons of a Srs rcu s.h 4 4Ω 4 5msms 4s 4 4 F

44 Undrdamd sons cos losslss f unknowns rqurdfor wo condons wo nal cos * mus b ral :damng coffcn damd frqunc : * j j N d N j j N d d d d d ω ω ω ω ω ω ω ω

45 Undrdamd sons

46 Examl 9.9: Naural sons of a Phas-Shf Oscllaor From xaml 9.7 as ndfnl 5.5 K.5 K 5 K ω ou K 3 5 ω d ω d cos ou 968 ou 5 5 cos968 cos968 Unsabl

47 rcall Damd sons ad oos N N a a : soluon

48 Plas rfr o Tabl 9..

49 Scond-Ordr Transns

50 Scond-Ordr Transns Two nal condons ar rqurd for scond-ordr crcus. onnu If for sa arabls : and ar known Inal slo

51 Examl 9. alculang Inal ondons > < S <

52 Examl 9. alculang Inal ondons Thn

53 Swchd D Transns Swchd D ransns for h hr s of scondordr crcus ordamd undrdamd and crcall damd. Smlar o frs ordr crcus: ω ω Y > Y N >

54 Swchd D Transns: Ordamd > ± Y Y Y N ω

55 Swchd D Transns: Undrdamd cos cas Sam asn h ordamd > ± ± Y j d d ω ω ω

56 Swchd D Transns: rcall Damd Y Y >

57 Examl 9.: Undrdamd Zro- Inu sons 9 cos wh Srs 5 > ± > < I j j j s ω

58 Examl 9.: on. ngng

59 Examl 9.: S sons wh arabl Damng Srs s < 3u 3 > 5 ω 3 64 Mab ordamd undrdamd and crcall damd dndng on.

60 Examl 9.: on : ordamd 3 >

61 Examl 9.: on. 6.8 cos ordamd : 5 > ± j j j

62 Examl 9.: on crcall damd: > o o

63 Examl 9.: on.

64 har 9: Problm S

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