CIRCUITS AND ELECTRONICS. Basic Circuit Analysis Method (KVL and KCL method)

Transcription

1 6. CIRCUITS AND ELECTRONICS Basic Circuit Analysis Mthod (KVL and KCL mthod) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

2 Rviw Lumpd Mattr Disciplin LMD: Constraints w impos on ourslvs to simplify our analysis φ B t q t Outsid lmnts Insid lmnts wirs rsistors sourcs Allows us to crat th lumpd circuit abstraction Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

3 Rviw LMD allows us to crat th lumpd circuit abstraction i v - Lumpd circuit lmnt powr consumd by lmnt vi Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

4 Rviw Rviw Maxwll s quations simplify to algbraic KVL and KCL undr LMD! KVL: j ν loop j KCL: j i j nod Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

5 Rviw a R R b R d R R c DEMO v ca vab vbc KVL i ca ida iba KCL Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

6 Mthod : Basic KVL, KCL mthod of Circuit analysis oal: Find all lmnt v s and i s. writ lmnt v-i rlationships (from lumpd circuit abstraction). writ KCL for all nods. writ KVL for all loops lots of unknowns lots of quations lots of fun solv Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

7 Mthod : Basic KVL, KCL mthod of Circuit analysis Elmnt Rlationships For R, V IR For voltag sourc, V V R For currnt sourc, I I V I o lumpd circuit lmnts Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

8 KVL, KCL Exampl a ν V ν R b R ν ν d R ν R ν R c Th Dmo Circuit Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

9 Associatd variabls disciplin i ν - Elmnt Currnt is takn to b positiv going into th positiv voltag trminal Thn powr consumd by lmnt νi is positiv Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

10 KVL, KCL Exampl a ν V i ν R i L b i i L R ν ν i R d i ν R L ν R c Th Dmo Circuit L Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

11 Analyz ν ν, ι ι. Elmnt rlationships v V givn v i v i v i R R v i. KCL at th nods a: i i i b: i i i d: i i i : i i i. KVL for loops L: v v v L: v v v L: v v v L: v v v R R R v i rdundant ( v,i) rdundant Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur unknowns 6 quations indpndnt quations indpndnt quations unknowns quations

12 Othr Analysis Mthods Mthod Apply lmnt combination ruls A R R R RN R R R N B N i R i N C V V V V D I I I I Surprisingly, ths ruls (along with suprposition, which you will larn about latr) can solv th circuit on pag 8 Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

13 Othr Analysis Mthods Mthod Apply lmnt combination ruls Exampl I? V R R R I I V R RR R R I V R V R R R RR R R Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

14 Mthod Nod analysis Particular application of KVL, KCL mthod..... Slct rfrnc nod ( ground) from which voltags ar masurd. Labl voltags of rmaining nods with rspct to ground. Ths ar th primary unknowns. Writ KCL for all but th ground nod, substituting dvic laws and KVL. Solv for nod voltags. Back solv for branch voltags and currnts (i.., th scondary unknowns) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

15 Exampl: Old Faithful plus currnt sourc V V R R R R R I Stp Stp Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

16 Exampl: Old Faithful plus currnt sourc V V R R R R KCL at ( V ) ( ) ( ) R I for convninc, writ i R i KCL at ( ) ( V ) ( ) I Stp Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur

17 Exampl: Old Faithful plus currnt sourc V V R R R R KCL at ( V ) ( ) ( ) KCL at l ) ( V ) ( ) ( I mov constant trms to RHS & collct unknowns ( ) ( ) V ( ) ( I ) ( ) V ( ) quations, unknowns Solv for s (compar units) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur R I i Stp R i

18 Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur In matrix form: I V V conductivity matrix unknown nod voltags sourcs ( )( ) I V V Solv ( )( ) ( )( ) I V V ( )( ) ( )( ) I V V (sam dnominator) Notic: linar in,, no ngativs in dnominator V I

19 Solv, givn 8.K.9K.K I ( )( ) V Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur ( ) ( ) V If 8... V.9. 8V, thn V V V I Chck out th DEMO