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Lecture 3 : Resistive Circuits & Nodal Analysis Nilsson 3.3, 3.4, 3.7, 4.1-4.4

Lecture 3 : Resistive Circuits & Nodal Analysis Nilsson 3.3, 3.4, 3.7, 4.1-4.4. ENG17 (Sec. 1): Circuits I Summer 1 2014. June 25, 2014. Overview. Voltage Divider Current Divider Voltage / Current Division Δ-to-Y Equivalent Circuits Node Voltage Method NVM w/Dependent Sources

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Lecture 3 : Resistive Circuits & Nodal Analysis Nilsson 3.3, 3.4, 3.7, 4.1-4.4

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  1. Lecture 3:Resistive Circuits & Nodal AnalysisNilsson 3.3, 3.4, 3.7, 4.1-4.4 ENG17 (Sec. 1): Circuits I Summer 1 2014 June 25, 2014

  2. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  3. Voltage Divider • One voltage supply, multiple voltage levels

  4. Load • RL = load = 1+ circuit elements that draw power from circuit • May alter voltage across parallel element • But not if RL >> R2

  5. Example

  6. Example • Wheatstone Bridge • 2 voltage dividers in parallel

  7. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  8. Current Divider • One current supply, multiple current levels

  9. Example

  10. Example • Similar analysis

  11. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  12. Voltage Division • Generalization of voltage divider circuit

  13. Current Division • Generalization of current divider circuit

  14. Example

  15. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  16. Unable to get Req • For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules • Must use circuit transformation

  17. Defining Delta/Pi and Y/T π Δ T Y

  18. Delta-to-Wye Circuit Transformation • Equivalent resistance between nodes • Note: resistor values are NOT THE SAME

  19. Apply to Wheatstone Bridge

  20. Recap • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  21. Planar Circuit Not Planar Planar Nodal good for either Mesh good for planar

  22. Identify • Node • Essential Node • Path • Branch • Essential Branch • Loop • Mesh

  23. Simultaneous Equations • How many unknown currents? • How many equations needed?

  24. Node Voltage Method – Setting Up • Identify essential nodes • Define reference node • Apply KCL to each non-reference node, express current in terms of node voltages • Solve simultaneous equations

  25. Node Equations

  26. Example

  27. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  28. Dependent Sources • Only need to add equation to describe relationship of the dependent source

  29. Example

  30. Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

  31. Source Between Essential Nodes

  32. w/Dependent Source

  33. Supernode

  34. Example

  35. Recap • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases

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