1. Electric Circuits (EELE 2312)
Chapter 3 Techniques of Circuit Analysis
Dr. Basil Hamed

2. 3.1 Terminology Planar and Nonplaner Circuits

3. Describing a Circuit The Vocabulary

4. Example 3-1 Identifying Node, Branch, Mesh and Loop
For the figure shown identify:
All nodes and all essential nodes
All branches and all essential branches
All meshes
Two paths that are not loops or essential branches
Two loops that are not meshes

5. The Systematic Approach An Illustration

6. 3.2 Introduction to the Node-Voltage Method

7. Example 3.2 Using the Node-Voltage Method
Use the node-voltage method to find the branch currents ia, ib, and ic
Find the power associated with each source and state whether the source is delivering or absorbing power.

8. Example 3.3 Node-Voltage Method with Dependent Sources
Use the node-voltage method to find the power dissipated in the 5Ω resistor in the circuit.

9. 3.4 The Node-Voltage Method Some Special Cases

10. 3.4 The Node-Voltage Method The Concept of Supernode

11. 3.5 Introduction to the Mesh-Current Method
Unknowns currents=3
be=3 ne=2
1 current equation
2 voltage equations
Number of Mesh Equations=be-(ne-1)
Number of Mesh Equations=7-(4-1)=4

12. Example 3.4 Using the Mesh-Current Method
Use the mesh-current method to determine the power associated with each voltage source.
Calculate the voltage across the 8Ω resistor

13. 3.6 Mesh-Current Method with Dependent Sources Example 3.5
Use the mesh-current method to determine the power dissipated in the 4Ω resistor.

14. 3.7 The Mesh-Current Method Some Special Cases

15. 3.7 The Mesh-Current Method The Concept of Supermesh

16. 3.8 Node-Voltage Versus Mesh-Current

17. Example 3.6 Understanding Node-Voltage/Mesh-Current Method
Find the power dissipated in the 300Ω resistor in the circuit shown.

18. Example 3.7 Comparing Node-Voltage & Mesh-Current Methods
Find the voltage vo in the circuit shown.

19. 3.9 Thevenin and Norton Equivalents
a Thevenin equivalent circuit is an independent voltage source VTh in series with a resistor RTh, which replaces an interconnection of sources and resistors. This series combination of VTh and RTh, T is equivalent to the original circuit in the sense that, if we connect the same load across the terminals a,b of each circuit, we get the same voltage and current at the terminals of the load. This equivalence holds for all possible values of load resistance

20. Finding a Thevenin Equivalent
3.9 Thevenin and Norton Equivalents

21. 3.9 Thevenin Equivalent Circuit Finding a Thevenin Equivalent

22. 3.9 Norton Equivalent Circuit
A Norton equivalent circuit consists of an independent current source in parallel with the Norton equivalent resistance, We can derive it from a Thevenin equivalent circuit simply by making a source transformation.
Using Source Transformation

23. Example 3.8 Thevenin Equivalent with Dependent Source
Find the Thevenin equivalent for the circuit containing dependent sources.

24. 3.10 More on Deriving a Thevenin Equivalent

25. Example 3.9 Thevenin Equivalent Using a Test Source
Find the Thevenin resistance RTh for the circuit shown.

26. 3.11 Maximum Power Transfer
Circuit analysis plays an important role in the analysis of systems designed to transfer power from a source to a load.
We discuss power transfer in terms of two basic types of systems.
The first emphasizes the efficiency of the power transfer (Power utility systems)
The second basic type of system emphasizes the amount of power transferred.

27. 3.11 Maximum Power Transfer
Maximum power transfer can best be described with the aid of the circuit shown in Fig.
We assume a resistive network containing independent and dependent sources and a designated pair of terminals, a,b, to which a load, RL, is to be connected.

28. 3.11 Maximum Power Transfer
The problem is to determine the value of RL that permits maximum power delivery to RL
The first step in this process is to recognize that a resistive network can always be replaced by its Thevenin equivalent.

29. 3.11 Maximum Power Transfer
Replacing the original network by its Thevenin equivalent greatly simplifies the task of finding RL

30. 3.11 Maximum Power Transfer
Next, we recognize that for a given circuit, VTh and RTh will be fixed. Therefore the power dissipated is a function of the single variable RL, To find the value of RL that maximizes the power, we use elementary calculus. We begin by writing an equation for the derivative of p with respect to RL:

31. 3.11 Maximum Power Transfer
The derivative is zero and p is maximized when
Solving above eq. yields
To find the maximum power delivered to RL

32. 3.11 Maximum Power Transfer

33. Example 3.10 Condition for Maximum Power Transfer
For the circuit shown, find the value of RL that results in maximum power being transferred to RL.
Calculate the maximum power delivered to RL.
When RL is adjusted for maximum power transfer, what percentage of the power delivered by the 360 V source reaches RL?

34. End of Chapter Three
Basil Hamed