MECH321 Dynamics of Engineering System Week 4 (Chapter 6)

Transcription

1 MH3 Dynamc of ngnrng Sytm Wk 4 (haptr 6). Bac lctrc crcut thor. Mathmatcal Modlng of Pav rcut 3. ompl mpdanc Approach 4. Mchancal lctrcal analogy 5. Modllng of Actv rcut: Opratonal Amplfr rcut Bac lctrc rcut Thor Two mportant varabl n lctrcal crcut analy: Voltag, : rprnt th potntal nrgy n th crcut urrnt, : rprnt rat of charg q wth rpct of tm. t can b potv or ngatv, dpndng upon th drcton n whch th lctron flow. Drcton of flow of lctron (t) Unt : voltag (V) = J / coulomb + - Unt : ampr (A) = coulomb / dq Drcton of currnt

2 Bac pav lmnt tanc: unt ohm () = volt / ampr Ohm law apactanc: unt farad (F) = coulomb / volt q t t nductanc: unt Hnry (H) = V. / A d d ( t) Ung Ohm law th followng rul govrnng lctrcal crcut can b drvd: Sr crcut total 3 Ohm law total Paralll crcut total total

3 Ohm law Ung th r and paralll crcut thor, combnd rtanc of r/paralll rtor can b calculatd: t Krchoff law t Krchoff aw urrnt law (nod law) : th um of all currnt ntrng (+) and lavng (-) a nod zro

4 nd Krchoff law nd Krchoff aw Voltag law (loop law) : th um of th voltag around any loop zro (a r n voltag (+); a drop n voltag (-) On-loop crcut r r r Two-loop crcut ft loop : 3 ght loop : 3 3 Mathmatcal Modlng of Pav rcut: Tranfr Functon: crcut From Krchoff voltag law around a loop d () = crcut o Takng aplac tranform of both d / G t t / Stp nput 4

5 Mathmatcal Modlng of Pav rcut: crcut f o th output and th nput, th tranfr functon of th ytm crcut From Krchoff voltag law around a loop oop oop Takng aplac tranform of both quaton G( ) Mathmatcal Modlng of Pav rcut: crcut From Krchoff voltag law around a loop crcut d Takng aplac tranform of both quaton f o th output and th nput, th tranfr G( ) functon of th ytm 5

6 6 acadd lmnt From Krchoff voltag law around a loop Takng aplac tranform of th quaton Aftr lmnatng () and (), th tranfr functon of th ytm obtand. ) ( G acadd lmnt ampl (B-6-9) Obtan th tranfr functon o ()/ () of th crcut blow. (oluton wll b don n th lctur) Tutoral

7 ompl mpdanc Approach ompl mpndanc: Ung th approach tranfr functon of mpl crcut ar obtand drctly a th aplac-tranformd quaton. ondr agan crcut: ( ) Z( ) ( ) ompl mpndanc of: an nductor Z = A rtor Z = A capactor Z ompl mpdanc Approach Ung compl mpndanc, th aplac-tranformd quaton ar: Z Z Z Z Th quaton wll gv th tranfr functon Z Z Z Z G( ) 7

8 laroom rc ampl (B-6-) Obtan th tranfr functon o ()/ () of th crcut blow ung th compl-mpdanc mthod. (oluton wll b don n th lctur) Mchancal-lctrcal analog: Forc-voltag analogy d dq q q q q 8

9 9 Forc-voltag analogy p k b m q q q d o d,, Forc-currnt analogy Mchancal-lctrcal analog:

10 Forc-currnt analogy Mchancal-lctrcal analog: P k b m d P d v k bv v m ( ) A-6-6 (p.34): Fnd an lctrc analogy k b k k b m d

11 A-6-7: Fnd a mchancal analogy d m b k d m k k b b Modllng of Actv rcut: Opratonal Amplfr (op-amp) rcut + Dffrntal amplfr - o Vry larg gan 5 K K nput voltag dffrnc Op-amp ha a larg nput mpndanc, o t draw a nglgbl currnt.

12 Op-Amp Amplfr: proportonal amplfr Applyng Krchoff nod law 3 = + 3 But 3, ' ' K' Op-amp ha a larg nput mpndanc, o t draw a nglgbl currnt. / / K Bcau K vry larg Op-Amp Amplfr: ntgrator Z f () = / Z () = Thtranfr V Z f ( ) ( ) functon, G( ) V ( ) Z ( ) n th tm doman v ( t) t v

13 Op-Amp Amplfr: dffrntator Z f () = Z () = / Thtranfr V Z f ( ) ( ) functon, G( ) V ( ) Z ( ) n th tm doman, dv ( t) v ( t) laroom rc ampl 3 (B-6-5) Obtan th tranfr functon o ()/ () of th followng opratonal-amplfr hown blow. (oluton wll b don n th lctur) 3