The document discusses the mesh-current method (also called loop analysis) for solving circuits. It describes mesh-current analysis as applying Kirchhoff's voltage law around loops (meshes) in a circuit to obtain equations relating the mesh currents. The key steps are to identify the meshes, assign a current to each mesh, write KVL equations for each mesh, and solve the resulting system of linear equations for the unknown currents. Examples are provided to illustrate mesh analysis for circuits with current sources between meshes or dependent sources.

1. 1
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Mesh-Current Method (Loop Analysis)
• Nodal analysis was developed by applying KCL at each non-reference
node.
• Mesh-Current method is developed by applying KVL around
meshes in the circuit.
• A mesh is a loop which doesn't contain any other loops within it.
• Loop (mesh) analysis results in a system of linear equations which
must be solved for unknown currents.
• Reduces the number of required equations to the number of meshes
• Can be done systematically with little thinking
• As usual, be careful writing mesh equations – follow sign convention.

2. 2
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
•Powerful analysis method which applies KVL to find unknown currents.
•It is applicable to a circuit with no branches crossing each other.
no branches
Crossing

3. 3
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Definitions
+
-
ig
A
B C i3
i1
i2
i4
i5
A mesh is a loop which does not contain any other loops within it.

4. 4
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Steps of Mesh Analysis
Step1
Identify the number of
basic meshes.
Step 2
Assign a current to each mesh.

5. 5
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Step 4
Solve the resulting system of linear equations.
As an example
V1 + I1 R1 + (I1 - I2) R3 = 0
I2 R2 + V2 + (I2-I1) R3 = 0
Step 3
Apply KVL around each loop to get
an equation in terms of the loop currents.

6. 6
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Example
Use mesh analysis to find the current io
Solution
We apply KVL to the three meshes
For mesh 1
For mesh 2
Divide by 2
Divide by 2

7. 7
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
For mesh 3
at node A
Divide by 2
By Substitution

8. 8
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
For Loop 1
-10 + 4i1 + 6(i1-i2) = 0
For Loop 2
(No need to write a loop equation)
Cases to be considered for Mesh Analysis
Case I
A current source exists only in one mesh
set i2 = −5A and write a mesh equation for the other
mesh
i2 = - 5A

9. 9
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Case II
A current source exists between two meshes
Exclude this part

10. 10
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
a supermesh was created by
excluding the current source and any
elements connected in series with it,
A supermesh results when two meshes have a (dependent
or independent) current source in common.
Because mesh analysis applies KVL—we do not know the
voltage across a current source in advance.
Why???

11. 11
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Applying KVL to the supermesh
i1 i2
Apply KCL to a node in the branch where the two meshes intersect.

12. 12
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
-75 + 5i1 + 20(i1-i2) = 0
10ix + 20(i2-i1) + 4i2 = 0
-75 + 5i1 + 20(i1-i2) = 0 …………………(1)
10(i1-i2) + 20(i2-i1) + 4i2 = 0 …………….(2)
i2 = 5A
i1 = 7A
Case III
Mesh with Dependent Sources
Solve for Ix
ix = i1 - i2
Solve the two equations
then

13. 13
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Example:
Use the mesh-current method to find io

14. 14
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Solution
meshes 1 and 2 form a supermesh
meshes 2 and 3 form a supermesh

15. 15
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Applying KVL to the larger supermesh,

16. 16
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
For the independent current source, we apply KCL to node P

17. 17
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
For the dependent current source, we apply KCL to node Q:

18. 18
Dr.-Eng. Hisham El-Sherif
Electronics and Electrical Engineering Department
ELCT608, Electrical Engineering
Applying KVL in mesh 4,