Circuit Theorems. Introduction

Transcription

1 //5 Crcut eorem ntroducton nearty Property uperpoton ource Tranformaton eenn eorem orton eorem Maxmum Power Tranfer ummary ntroducton To deelop analy technque applcable to lnear crcut. To mplfy crcut analy and help handle the complexty.

2 //5 near Crcut A lnear crcut one whoe output lnearly related (or drectly proportonal) to t nput near crcut cont of lnear element lnear dependent ource ndependent ource Example 4. For the crcut n fg 4. fnd when = and =4.

3 //5 Example 4. K x x (4..) become 6 Eq(4..) and (4..3) we get 6 (4..) (4..) (4..3) Eq(4..), we get When When 76 4 Example 4. A 76 4 A howng that when the ource alue doubled, double. 3

4 //5 nearty Property Homogenety (calng) + Addtty Homogenety property: ( k) ( k) Addtty property: Applyng and ( ) A lnear crcut follow the relatonhp below: Output Contant nput (,, ;,,, uperpoton *For a lnear ytem the DC oltage (or current) gen by n m M ) n m : ndependent ource ( K, KC and Ohm' law ge lnear equaton.) A, n n M A, m m (,, n,,,;,,) A (,,;,, m,,,) A, n n, m m (,, ;,, ) (,,, ;,,) (,,,,;,,) (,,, (,, ;,,,) (,, ;, M ;,,),,,)... (,, ;,, M ) 4

5 //5 uperpoton Baed on lnearty property tatement e oltage acro (current through) an element the algebrac um of the oltage acro (current through) that element due to each ndependent ource actng alone. (,..., ; (,...,;,...,)... (,..., (,...,;,..., M ;,...,),...,)... (,...,;,..., A turned-off oltage ource = a hort crcut A turned-off current ource = an open crcut ) M ) uperpoton uperpoton nole more work but mpler crcut. uperpoton not applcable to the effect on power. 5

6 //5 Comment on uperpoton Two requrement :. Keep dered property n each crcut element. nput near For retor, ( ) ( ) Crcut : controlled gnal For dependent ource, let ac where. C : control gnal ac ( ) a( C C) ac For ndependent ource, oltage ource : Current ource: nput near Crcut Comment on uperpoton. Two crcut law mut For KC, enterng, enterng, For K, T, T, leang, leang, T, be atfed. enterng, T, enterng, leang, leang, 6

7 //5 Example = () + Example ' " Keep dependent ource! = + 7

8 //5 Example 3 3 ource Tranformaton Tranformaton between oltage ource and current ource. Equalence mean dentcal - charactertc. + ab _ + ab _ For arbtrary ab, 8

9 //5 9 Cont d ab ab ab ab and and ) ( ) (. arbtrary for et ab + _ ab + _ Applcable to Dependent ource or

10 //5 ource Tranformaton mpoble ource Tranformaton: deal oltage ource ( = ) deal current ource ( = ) Example /3 /6 4-

11 //5 Example A x x x () () 4.5 x 6/ 3 - Charactertc For a lnear two-termnal network, t - cure (DC) mut be a traght lne n the - plane. ( ) : ere connecton : Parallel connecton ( )

12 //5 Equalent Crcut Equalent crcut: ame - relaton at the termnal lope =/c () d c + _ c d -d/c d () d/c c + _ c d d c c eenn eorem A arable element eenn equalent crcut

13 //5 Cont d = A mple oltage dder. Proof of eenn eorem * A lnear crcut wth ndependent ource *By,,, uperpoton,,,, M dentcal - charactertc = A A where A A B n A, n B A A n n * When, n oc M m n, m m M A m * When all nternal ndependent ource turned off, we hae B, m m. 3

14 //5 Fndng and f no dependent ource ncluded. the equalent nput retance of the retor network. A retor network f dependent ource ncluded, two method can be appled to determne. External oltage ource method. External current ource method. Cont d 4

15 //5 Example = Example = oc 5

16 //5 orton eorem = By ource tranformaton, eq orton eorem orton equalent crcut n 6

17 //5 Example = More Comment eq = External oltage ource ( o = ) may olate the requrement o =. Ue external current ource to fnd. eq = External current ource ( o = A) may olate the requrement o = A. Ue external oltage ource to fnd. For other Both ext. = = 7

18 //5 8 Maxmum Power Tranfer max *To achee maxmum power tranfer, gen by delered to *e power p d dp p A lnear crcut Applcaton: ource Modelng oltage ource Current ource p p p

19 //5 9 etance Meaurement or, When x x x x e Wheattone brdge 3 f x