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ECE 3144 Lecture 7

In Lecture 7 of ECE 3144, Dr. Rose Q. Hu discusses advanced techniques for analyzing resistor networks, focusing on the Wye-Delta transformation. Students learn how to simplify complex circuits into manageable series-parallel combinations. The lecture covers the importance of maintaining terminal characteristics during transformations and introduces problem-solving strategies for circuits with dependent sources. Homework assignments provide practical examples to reinforce understanding. Relevant circuit examples illustrate the application of these concepts in real-world electrical engineering scenarios.

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ECE 3144 Lecture 7

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  1. ECE 3144 Lecture 7 Dr. Rose Q. Hu Electrical and Computer Engineering Department Mississippi State University

  2. Reminder for Lecture 6 • Resistors in parallel • Current divider • Current sources in parallel or

  3. Problem solving strategy Find RAB in the circuit given

  4. + - Wye  Delta Transform I1 R1 R2 V1 R3 • We have learned how to simplify the network with series parallel resistors combination. • In the circuit network given, nowhere is the resistor in series or parallel with another. • Techniques learned so far do not apply here. • We can replace one portion of the network with the equivalent network. The conversion will reduce the network to series parallel combination of resistors, which we are already familiar with. • One conversion technique we are learning here is wye-to-delta or delta-to-wye transformation. R4 R5 R6

  5. a Ra Rc Rb c b Figure (2) Wye  Delta Transform a R1 R2 R3 • Notice that resistors figure (1) forms a  (delta) and resistors in figure (2) forms a Y (wye). • Both of these two configurations are connected to the same terminals a, b,c • It is possible to relate these two networks to each other such that terminal characteristics are the same. The relationship is called wye-delta (Y- ) transformation. • The transformation must keep terminal characteristics the same. At each corresponding pair of terminals, the resistance at the corresponding terminals must be the same. b c Figure (1)

  6. Wye  Delta Transform

  7. Wye  Delta Transform Special case: suppose the delta-connected load is balanced, that is, R1=R2=R3=R. The equivalent wye-connected load is also balanced, so Ra=Rb=Rc=RY. Then we have

  8. Wye  Delta Transform I1 R1 R2 V1 + - R3 R4 R5 R6 Ra Rb Rc V1 + - R4 R5 R6 • Rc and R4 are in series => Rc4 • Rb and R5 are in series => Rb5 • Rc4 and Rb5 are in parallel => Rc4b5 • Rc4b5 and Ra are in series =>Rc4b5a

  9. Is + + - - Rc =2 k Rb=3 k 12 V 4 k 9 k Example Is Ra=6k R1=12 k R2=18 k R3 12 V 6 k 4 k 9 k

  10. Circuits with dependent sources • When writing the KVL and/or KCL equations for the network, treat the dependent source as though it were an independent source. • Write the equations that specifies the relationship of the dependent source to the controlling parameters. • Solve the equations for the unknowns. Be sure that number of linearly independent equations matches the number of the unknowns.

  11. + - Example Determine the voltageVo in the circuit VA = 2000 I1 3 k I1 - + + Vo 12 V 5 k -

  12. + 2 k 3 k 4 I0 10 mA + Vs 4 k V0 I0 - - Example Given the network, find voltage V0

  13. Homework for Lecture 7 • Problems 2.57, 2.64,2.65,2.69, 2.71, 2.72, 2.73, 2.75, 2.77

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