METHODS OF ANALYSIS Nodal analysis Mesh Analysis Mesh

METHODS OF ANALYSIS • Nodal analysis • Mesh Analysis

Mesh Analysis An analysis technique to solve electrical circuit where the mesh currents are used as the circuit variables A loop which does not contain any other loops within it R 1 V 1 R 2 R 3 meshes V 2

Mesh Analysis An analysis technique to solve electrical circuit where the mesh currents are used as the circuit variables A loop which does not contain any other loops within it It involves systematic steps with an objective to solve the mesh currents mesh current is not branch current ! If all mesh currents are known, the circuit can be solved V 1 R 2 + v 1 + v 2 i 1 + v 3 R 3 i 2 io i 1 & i 2 are mesh currents v 1 = R 1 i 1 V 2 v 2 = R 2 io = (i 1 - i 2) v 3 = R 3(i 1 - i 2)

Mesh Analysis Mesh analysis only applicable to planar circuit Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing Planar circuit

Mesh Analysis Mesh analysis only applicable to planar circuit Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing nonplanar circuit

Mesh Analysis Mesh analysis only applicable to planar circuit Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing ?

Mesh Analysis Mesh analysis only applicable to planar circuit Mesh analysis cannot be applied to nonplanar circuit Note: Nodal analysis is applicable to planar and nonplanar circuit Planar circuit: A circuit that can be drawn on a plane with no branches crossing ?

Mesh Analysis 36 V 2 9 i 1 i 2 4 12 24 V 3 Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents Step 3 Solve mesh currents in equations obtained in step 2, simultaneously

Mesh Analysis 4 k Example 2 i 1 6 V 6 k + 9 k i 2 3 k i 3 12 k Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents Step 3 Solve mesh currents in equations obtained in step 2, simultaneously

Mesh Analysis Verification using Pspice 4 k Example 2 1 6 V + 9 k 2 3 k 0 Netlist: Mesh example 2 R 1 0 1 9000 V 1 2 1 DC 6 R 2 2 0 3000 R 3 1 3 4000 R 4 2 3 6000 R 5 3 0 12000. DC V 1 6 6 6. PRINT DC I(R 1) I(R 3), I(R 5). END 6 k 3 12 k

Mesh Analysis Example 2 Verification using Pspice

Mesh Analysis Example 3 6 V 4 k + + 2 k i 1 i 2 + 3 V 6 k Using mesh analysis, solve vo vo Step 1 Assign mesh currents to the meshes Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents Step 3 Solve mesh currents in equations obtained in step 2, simultaneously

Mesh Analysis 5 A Example 4 i 3 8 Using mesh analysis, solve i 1, i 2 2 1 i 1 40 V + 4 i 2 + 20 V Step 1 Assign mesh currents to the meshes i 3 is already solved i. e. i 3 = 5 A Step 2 For every mesh, apply KVL – Using Ohm’s law, write down the equations in terms of mesh currents Step 3 Solve mesh currents in equations obtained in step 2, simultaneously