1. INC 112 Basic Circuit Analysis
Week 4
Mesh Analysis

2. Mesh Analysis (Loop Analysis)
Mesh = A closed loop path which has no smaller loops inside

3. Mesh Analysis Procedure
Count the number of meshes. Let the number equal N.
Define mesh current on each mesh. Let the values be I1, I2, I3, …
Use Kirchoff’s voltage law (KVL) on each mesh, generating N equations
Solve the equations

4. Example
Use mesh analysis to find the power consumption in the resistor 3 Ω I1 I2
Mesh current (loop current)

5. I1 I2
Loop 1
Equation 1
Loop 2
Equation 2
I1 = 6A, I2 = 4A, The current that pass through R 3Ω is 6-4 = 2A (downward)
Power = 12 W

6. Example
Use Mesh analysis to find Vx I1 I2 I3

7. I2
Equation 1 I1 I3
Equation 2
Equation 3
I1 = 3A, I2 = 2A, I3 = 3A
Vx = 3(I3-I2) = 3V

8. Supermesh
When there is a current source in the mesh path, we cannot use KVL because we do not know the voltage across the current source.
We have to use supermesh, which is a combination of 2 meshes to be a big mesh, and avoid the inclusion of the current source in the mesh path.

9. Example
Use Mesh analysis to find Vx I1 I2 I3

10. I1 I2 I3
Equation from 2nd loop

11. Supermesh I1 I2 I3
Equation 2
Equation 3

12. I1 = 9A
I2 = 2.5A
I3 = 2A
Vx = 3(I3-I2) = -1.5V

13. How to choose between Node and Mesh Analysis
The hardest part in analyzing circuits is solving equations. Solving 3 or more equations can be time consuming.
Normally, we will count the number of equations according to each method and select the method that have lesser equations.

14. Example From the previous example, if we want to use Nodal Analysis 7V

15. Example: Dependent Source
Find Vx I1 I2 I3

16. Equation 1 I1 I2 I3
Equation 2
Equation 3
Equation 4
I1=15A, I2=11A, I3=17A
Vx = 3(17-11) = 18V

17. Special Techniques Superposition Theorem Thevenin’s Theorem
Norton’s Theorem
Source Transformation

18. Superposition Theorem
In a linear circuit, we can calculate the value of current (or voltage) that is the result from each voltage source and current source independently.
Then, the real value is the sum of all current (or voltage) from the sources.

19. Linearity
V and I have linear relationship I V

20. Implementation
When calculating the effect of a source, the other sources will be set to zero.
For voltage sources, when set as 0V, it will be similar to short circuit
For current sources, when set as 0A, it will be similar to open circuit

21. Example
I1 = 1A
I2 = 2A
I total = 1+2 = 3A

22. Example
I1 = 1A
I2 = 0A
I total = 1+0 = 1A

23. Example
Find voltage Vx

27. Superposition and Dependent Source
Dependent sources cannot be used with superposition.
They have to be active all the time.

28. Example
Use superposition to find Ix

29. Find Ix by eliminating the current source 3A
KVL

30. Find Ix by eliminating the voltage source 10V
KVL outer loop