Ch01 Analysis of Resistive Circuits 1s09

# Ch01 Analysis of Resistive Circuits 1s09 - Chapter 1 Topics...

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Analysis of Resistive Analysis of Resistive Circuits Circuits Department of Electrical and Electronics Engineering University of the Philippines - Diliman Chapter 1 Artemio Artemio P. P. Magabo Magabo Professor of Electrical Engineering Department of Electrical and Electronics Engineering EEE 33 - p2 a. Network Reduction Techniques 1. Series and Parallel Circuits 2. Delta-Wye Transformation 3. Current and Voltage Division 4. Source Transformation b. Dependent Sources c. Application of Circuit Analysis on Operational Amplifiers d. Nodal Analysis e. Mesh Analysis f. Ladder Method Topics Department of Electrical and Electronics Engineering EEE 33 - p3 T wo electric circuits are said to be equivalent with respect to a pair of terminals if the voltages across the terminals and currents through the terminals are identical for both networks. Equivalence a b V 1 Circuit 1 + - I 1 If V 1 =V 2 and I 1 =I 2 , then with respect to terminals ab and xy , circuit 1 and circuit 2 are equivalent. x y V 2 Circuit 2 + - I 2 Department of Electrical and Electronics Engineering EEE 33 - p4 Resistors in Series and in Parallel n 2 1 eq R ... R R R + + + = + - R 1 + - - + a b V 1 + - I 1 R 2 R n Resistors in Series Resistors in Parallel - + a b V 1 + - I 1 R n - + R 1 - + R 2 n 2 1 eq R 1 ... R 1 R 1 R 1 + + + = Special Case Two resistors in parallel: 2 1 2 1 eq R R R R R + =

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Department of Electrical and Electronics Engineering EEE 33 - p5 Delta-Wye Transformation The transformation is used to establish equivalence for networks with 3 terminals. Wye R 3 x y z R 2 R 1 Delta R a x y z R b R c For equivalence, the resistance between any pair of terminals must be the same for both networks. Department of Electrical and Electronics Engineering EEE 33 - p6 2 1 3 3 2 2 1 a R R R R R R R R + + = 3 1 3 3 2 2 1 b R R R R R R R R + + = 1 1 3 3 2 2 1 c R R R R R R R R + + = Wye-to-Delta Transformation Equations c b a b a 1 R R R R R R + + = c b a c b 2 R R R R R R + + = c b a a c 3 R R R R R R + + = Delta-to-Wye Transformation Equations Department of Electrical and Electronics Engineering EEE 33 - p7 Example: Find the equivalent resistance across terminals AB. Ω = + + = 18 3 10 5 R 1 eq 4 Ω A B 5 Ω 3 Ω 3 Ω 12 Ω 1 Ω 1.5 Ω 10 Ω 2 Ω 9 Ω Starting from the right, we get for resistors in series 5 Ω 3 Ω 10 Ω Department of Electrical and Electronics Engineering EEE 33 - p8 Ω = + = 6 9 18 ) 9 )( 18 ( R 2 eq R eq1 is in parallel with the 9 Ω -resistor. R eq1 =18 Ω 9 Ω The resulting network becomes 4 Ω A B 3 Ω 12 Ω 1 Ω 1.5 Ω 2 Ω R eq2 =6 Ω
Department of Electrical and Electronics Engineering EEE 33 - p9 Convert wye into delta R a R c R b 3 Ω 1 Ω 1.5 Ω Ω = = + + = 6 5 . 1 9 5 . 1 ) 3 )( 5 . 1 ( ) 5 . 1 )( 1 ( ) 1 )( 3 ( R a Ω = = 3 3 9 R b Ω = = 9 1 9 R c Replace the wye with its delta equivalent and simplify. 4

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## This note was uploaded on 01/13/2011 for the course EEEI 33 taught by Professor Co during the Winter '10 term at University of the Philippines Diliman.

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Ch01 Analysis of Resistive Circuits 1s09 - Chapter 1 Topics...

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