1. Methods of Analysis EE 2010: Fundamentals of Electric Circuits Mujahed AlDhaifallah

2. Nodal Analysis Identify the nodes in the circuit. Pick a reference node (usually the ground) Define node voltages with respect to the reference for all nodes. Apply KCL at all nodes. Solve the resulting linear equations.

3. Example

4. Nodal Analysis with Dependent Sources Dependent sources are handled the same way we handled independent sources The node voltage equations must be supplemented with an additional equation resulting from the dependent source Observations from visual inspection don’t apply for circuits containing dependent sources

5. Examples

6. Nodal Analysis with Voltage Sources 3 cases: The voltage source connects one of the nodes and the ground The voltage source lies between two nonreference nodes The voltage source has a series resistor

7. Nodal Analysis with Voltage Sources (I) The voltage source connects one of the nodes and the ground: Solution: node voltage = voltage of the voltage source

8. Nodal Analysis with Voltage Sources (II) The voltage source is connected between two nonreference nodes: Problem: the current through the voltage source is unknown Solution: form a “supernode” and apply KCL+KVL to the supernode

9. Nodal Analysis with Voltage Sources (III)

10. Bridge Circuits

11. Bridge Circuit Planar / Non–planar circuits?

12. Planar vs. Non-planar

13. Bridge Circuits Symmetrical Lattice Network if  R1 = R4 and R2 = R3

14. Y - Δ Conversions

15. Y-∆ (T- π) and ∆ -Y (π -T) Conversions Circuit configurations are encountered in which the resistors do not appear to be in series or parallel; it may be necessary to convert the circuit from one form to another to solve for the unknown quantities if mesh and nodal analysis are not applied.  Two circuit configurations that often account for these difficulties are the wye (Y) and delta (∆) configurations.  They are also referred to as tee (T) and the pi (π) configurations.

16. Y-∆ (T- π) and ∆ -Y (π -T) Conversions

17. 1) ∆ -Y (π -T) Conversion Note that each resistor of the Y is equal to the product of the resistors in the two closest branches of the ∆ divided by the sum of the resistors in the ∆.

19. EXAMPLE Find the total resistance of the network shown in the Fig., where RA = 3, RB = 3, and RC = 6.

20. Another Example