• Nodal analysis

• Nodal analysis with Voltage Sources

• Mesh Analysis

• Mesh Analysis with Current Sources

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis (1)

• It is based on systematic application of

Kirchhoff’s current law (KCL)

• It is using node voltages as circuit variables

• In nodal analysis we are interested in finding the node voltages

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis (2)

Steps to determine the node voltages:

1. Select a node as the reference node. Assign voltages v1,v2,…,vn-1 to the remaining n-1 nodes. The voltages are referenced with respect to the reference node.

2. Apply KCL to each of the n-1 non-reference nodes. Use

Ohm’s law to express the branch currents in terms of node voltages.

3. Solve the resulting simultaneous equations to obtain the unknown node voltages.

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis (3)

Example:

Node 1:

Node 2:

Current flows from a higher potential to a lower potential in a resistor 4

Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis

Example (3.1):

Obtain the node voltages:

Solution 3.1:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis with Voltage

Sources

There are 2 cases:

1. If a voltage source is connected between the reference node and a nonreference node, then we simply set the voltage at the nonreference node equal to the voltage of the voltage source. 2. If the voltage source (dependent or independent) is connected between two nonreference nodes, the two nonreference nodes form a generalized node or supernode; we apply both KCL and KYL to determine the node voltages.

A supernode is formed by enclosing a (dependent or independent) voltage source connected between two nonreference nodes and any elements connected in parallel with it.

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Example:

v1 = 10V

Now we apply KVL to supernode:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis with Voltage

Sources

Example (3.3):

Find v and i

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Solution 3.1:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Nodal Analysis with Voltage

Sources

Example (3.4):

Find v1,v2,v3:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Solution 3.4:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Mesh Analysis (1)

1. Mesh analysis provides another general procedure for analyzing circuits using mesh currents as the circuit variables.

2. Nodal analysis applies KCL to find unknown voltages in a given circuit, while mesh analysis applies KVL to find unknown currents.

3. A mesh is a loop which does not contain any other loops within it.

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Mesh Analysis (2)

Steps to determine the mesh currents:

1. Assign mesh currents i1, i2, …, in to the n meshes.

2. Apply KVL to each of the n meshes. Use Ohm’s law to express the voltages in terms of the mesh currents.

3. Solve the resulting n simultaneous equations to get the mesh currents.

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Mesh Analysis (3)

Example

Mesh 1:

Mesh 2:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Mesh Analysis

Example (3.5):

Calculate mesh currents i1 and i2

Solution 3.5:

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Alexander and Sadiku, Fundamentals of Electric Circuits, Third Edition. McGraw-Hill

Mesh Analysis

Example