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EE 2315

EE 2315. Lecture 04 - Wye/Delta & Delta/Wye Conversions and Node Voltage Analysis. Wye/Delta Conversion (1/2). Wye. Delta. Wye/Delta Conversion (2/2). Delta/Wye Conversion. Effects of D -Y & Y- D Conversions. D -Y Conversion eliminates a loop but adds a node.

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EE 2315

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  1. EE 2315 Lecture 04 - Wye/Delta & Delta/Wye Conversions and Node Voltage Analysis

  2. Wye/Delta Conversion (1/2) Wye Delta

  3. Wye/Delta Conversion (2/2)

  4. Delta/Wye Conversion

  5. Effects of D-Y & Y-D Conversions • D-Y Conversion eliminates a loop but adds a node. • Y-D Conversion eliminates a node but adds a loop.

  6. Y-D Conversion Example Find Rab Several Methods: We choose to eliminate node c, then simplify.

  7. Y-D Conversion Calculations

  8. New Circuit

  9. Further Simplifications

  10. Introduction to Node Voltage Method • More direct than branch equations • Fewer equations to solve • Choose one node as reference • Express all variables in terms of node voltages • Solution is set of node voltages w.r.t. chosen reference node • Solution completely defines the circuit

  11. Node Voltage Example 1 (1/4) Apply KCL at Node 1: Use Ohm’s Law:

  12. Node Voltage Example 1 (2/4) Apply KCL at Node 2: Use Ohm’s Law:

  13. Node Voltage Example 1 (3/4) KCL for Node 1: KCL for Node 2:

  14. Node Voltage Example 1 (4/4)

  15. Node Voltage Example 1a (1/2)

  16. Node Voltage Example 1a (2/2)

  17. Node Voltage Example 2 (1/2) KCL for Node 1: KCL for Node 2:

  18. Node Voltage Example 2 (2/2) Substitute: into KCL equations Node 1: Node 2:

  19. Node Voltage Example 2a (1/2) Substituting for ix:

  20. Node Voltage Example 2a (2/2)

  21. Node Voltage Example 3 (1/2) KCL for Node 1: KCL for Node 2:

  22. Node Voltage Example 3 (2/2) Substitute: into KCL equations Node 1: Node 2:

  23. Node Voltage Example 3a (1/2) After Substitution:

  24. Node Voltage Example 3a (2/2) Substitute and solve:

  25. Node Voltage Example 4 (1/3) No KCL equation possible at node 1 or at node 2. KCL can be applied at the supernode.

  26. Node Voltage Example 4 (2/3) KCL @ Supernode: Other relationships: and

  27. Node Voltage Example 4 (3/3)

  28. Node Voltage Example 4a (1/2)

  29. Node Voltage Example 4a (2/2) Substitute and solve:

  30. Alternative to Supernode (1/2) KCL @ Node 1: KCL @ Node 2:

  31. Alternative to Supernode (2/2) Use Ix to get same info as Supernode:

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