ECE 211 Workshop: Nodal and Loop Analysis, Slides of Electrical Engineering

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ECE 211 WORKSHOP: NODAL AND

LOOP ANALYSIS

Tutor: Asad Akram

AGENDA

 Background: KCL and KVL.

 Nodal Analysis:

 Independent Sources and relating problems,

 Dependent Sources and relating problems.

 Loop (Mesh Analysis):

 Independent Sources and relating problems,

 Dependent Sources and relating problems.

 Practice Problems and solutions.

KCL AND KVL EXAMPLE

 Find I and Vbd in the following circuit?

 Solution:

Using KCL we know that only 1 current I flows in the loop. Then we apply Ohm’s law to find the current I. Lastly, we use KVL in the single loop to evaluate the voltage Vbd. We therefore see how KCL and KVL can used as simple analysis tools.

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NODAL ANALYSIS

 Nodal Analysis of electronic circuits is based on

assigning Nodal voltages at various nodes of the circuit with respect to a reference and then finding these nodal voltages to analyze the circuit.

Simple representation of Nodal Voltages shown below:

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As shown in Figure, a node is a point in a circuit where two or more wires meet. At these nodes one can assign a nodal voltage with respect to the reference ground shown.

In this example we write the KCL equations at the nodes as Shown, then solve them to find The respected nodal voltages.

NODAL ANALYSIS: INDEPENDENT SOURCES ONLY

NODAL ANALYSIS: INDEPENDENT SOURCES ONLY

Example2 (Ind. Voltage Sources Only):

For this Problem, we first make the main KCL equation at the only node 1. Current is taken to be coming out of the node as positive. We solve this equation to find The nodal voltage V1. Once this is determined, Io is simply found by using Ohm’s law at the sole resistor of 3KOhm.

NODAL ANALYSIS: DEPENDENT SOURCES

After setting up the Nodal Eqn. For dependent Circuits, on has To make the Controlling eqn. This equation is made using the Dependent source. Using the Controlling equation we solve For the nodal voltages.

NODAL ANALYSIS: DEPENDENT SOURCES

Using KCL at nodes 2 and Forming a controlling equation At node 1 we can simplify the Problem into simple equations. Current entering the node is Summed at the node to form The equations.

Find Io in the circuit using Nodal Analysis?

MESH ANALYSIS

 Mesh Analysis involves solving electronic circuits

via finding mesh or loop currents of the circuit. This is done by forming KVL equations for respected loops and solving the equations to find individual mesh currents.

We simply assume clockwise current flow in All the loops and find them to analyze the circuit. Also any independent current source in a loop Becomes the loop current as current in series is Same.

MESH ANALYSIS: INDEPENDENT SOURCES

Find Vo in the circuit? Using KVL at loops 1 and 2, we form KVL equations using the current and Components in the loops in terms of The loop currents. Important thing to look at it the Subtraction of the opposing loop Current in the shared section of the Loop.

MESH ANALYSIS: DEPENDENT SOURCES

Find Vo in the circuit using Mesh Analysis? Simplify the circuit using the Independent sources by assigning Them to the mesh currents for The specific loop.

MESH ANALYSIS: DEPENDENT SOURCES

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Form KVL in Main loop 3.

Simplify Using Vx and I2.

PRACTICE PROBLEMS

PRACTICE PROBLEMS