har 9 Transn sons
har 9: Ouln N F n F
Frs-Ordr Transns
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.
Frs-Ordr rcus w For zro nu rsons > characrsc quaon : s s : m consan
Frs-Ordr rcus / / / / / > > >
Frs-Ordr rcus Dssad owr b h rssor / d w > aacor s nal sord nrg
Frs-Ordr rcus srucural dual of h crcu m consan : : quaon characrsc s s / / I I I > >
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.
Examl 9.: Zro-Inu sons 4.5.5. / 4 / / > > Ω ms q q
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.
Frs-Ordr rcu Thénn [ ] olag :sad sa condon nal q. nonhomognous dff. / / / q c >
Frs-Ordr rcu [ ] :sad sacurrn / / q S I I u I > Noron
Gnral Frs-Ordr rcus [ / ] Y > Y afr 5 Yss nalslo 5 o rach sad sa rs m %-9%.
Examl: S sons of an rcu 4 8. > > m s q 7 4 5 8 8 5.5 5 5 5 s µ
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
Puls sons D Y D Y
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 53.-. 3.9ms > 3ms
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
Gnral D sons / / / S rsons : Zronu rsons : for aralll crcus for srs crcus Y Y Y Y Y Y Y
Examl 9.4: Squnal Swchd Transns Par I Par II
Examl 9.4: Squnal Swchd Transns Par I I I q 6 m 8 4 6 8 4 6.5m 8 4 8 4 6kΩ I 6k µ I I.6s / /.5.5 /.6 /.6 m
Examl 9.4: Squnal Swchd Transns Par II m s k m I m I q.4 /.4 /.5 4.53.5.73.4 4.5 5.3-9.73 Ω
Examl 9.4: Squnal Swchd Transns
Swchd Transns
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
Swchd Transns o oban Us hasor analss afr 5 sad sa sons : / / / Y Y F F F F F F > >
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 6 7. 5.73
Examl 9.5: on. 6 6cos5 3.4 cos5 for > F F 5 6 6 5 4.5 6 6cos5.73 3.4cos5 6 ω T s
Scond-Ordr Naural sons
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.
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
Paralll rcu Basd on K w ha S or S
Gnral Form of Scond-Ordr rcus frqunc :rsonan For srs : For aralll : ω ω ω ω f
Examl 9.6: Scond-Ordr rcu wh Two Inducors K K K Pck as sa arabls.
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.
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
Examl 9.7: Scond-Ordr wh a onrolld Sourc Phas-Shf Oscllaor ou K / x ou ω K K ou ou
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
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
< ω Undrdamd Im Fx w dcras osslss ω rcall damd ω Ordamd > ω Unsabl <
Ordamd sons as sabl.. / / > N N
Examl 9.8: Naural sons of a Srs rcu s.h 4 4Ω 4 5msms 4s 4 4 F
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
Undrdamd sons
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 8 968 cos ou 968 ou 5 5 cos968 cos968 Unsabl
rcall Damd sons ad oos N N a a 4 3 4 3 : soluon
Plas rfr o Tabl 9..
Scond-Ordr Transns
Scond-Ordr Transns Two nal condons ar rqurd for scond-ordr crcus. onnu If for sa arabls : and ar known Inal slo
Examl 9. alculang Inal ondons > < S <
Examl 9. alculang Inal ondons Thn
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 >
Swchd D Transns: Ordamd > ± Y Y Y N ω
Swchd D Transns: Undrdamd cos cas Sam asn h ordamd > ± ± Y j d d ω ω ω
Swchd D Transns: rcall Damd 3 4 3 4 4 3 4 3 Y Y >
Examl 9.: Undrdamd Zro- Inu sons 9 cos76 3.95 9.974 76 5 76 5 3 3 76 5 3 64 5 wh Srs 5 > ± > < I j j j s ω
Examl 9.: on. ngng
Examl 9.: S sons wh arabl Damng Srs s < 3u 3 > 5 ω 3 64 Mab ordamd undrdamd and crcall damd dndng on.
Examl 9.: on. 3 3 3 3 3 3 7 34 : ordamd 3 >
Examl 9.: on. 6.8 cos76 3.6 3 6.8 5.8 3 76 5 76 5 76 5 5 5 ordamd : 5 > ± j j j
Examl 9.: on. 4 3 3 4 3 8 6 crcall damd: 8 8 3 4 3 > o o
Examl 9.: on.
har 9: Problm S 5 7 3 6 4 3 4 44 46 5 6.