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

3.1 Terminology Planar and Nonplaner Circuits

Describing a Circuit The Vocabulary

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

The Systematic Approach An Illustration

3.2 Introduction to the Node-Voltage Method

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.

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.

3.4 The Node-Voltage Method Some Special Cases

3.4 The Node-Voltage Method The Concept of Supernode

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

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

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.

3.7 The Mesh-Current Method Some Special Cases

3.7 The Mesh-Current Method The Concept of Supermesh

3.8 Node-Voltage Versus Mesh-Current

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

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

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

Finding a Thevenin Equivalent 3.9 Thevenin and Norton Equivalents

3.9 Thevenin Equivalent Circuit Finding a Thevenin Equivalent

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

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

3.10 More on Deriving a Thevenin Equivalent

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

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.

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.

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.

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

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:

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

3.11 Maximum Power Transfer

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?

End of Chapter Three Basil Hamed