Lecture 6
- 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,