1. ENG17 (Sec. 1): Circuits I Summer 1 2014
Lecture 3: Resistive Circuits & Nodal Analysis Nilsson 3.3, 3.4, 3.7,
ENG17 (Sec. 1): Circuits I
Summer
June 25, 2014
Notes are here

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/Tπ 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