Transcript Slide 1
SUMMARY ON NODAL AND MESH ANALYSIS • Both techniques provide systematic steps in solving electric circuit • Nodal applicable to all circuits, Mesh only applicable to planar circuit • NOT ALL circuits require nodal or mesh analysis to solve them. • If nodal or mesh analysis is required, choose the one which will give the fastest or simplest steps Nodal versus Mesh Analysis To select the method that results in the smaller number of equations. For example: :: Choose nodal analysis for circuit with fewer nodes than meshes. :: Choose mesh analysis for circuit with fewer meshes than nodes. :: Networks that contain many series connected elements, voltage sources, or supermeshes are more suitable for mesh analysis. :: Networks with parallel-connected elements, current sources, or supernodes are more suitable for nodal analysis. :: If node voltages are required, it may be expedient to apply nodal analysis :: If branch or mesh currents are required, it may be better to use mesh analysis. NODAL ANALYSIS Step 1 Determine the reference node: typically the one with the most branches Step 2 Assign the rest of the nodes with node voltages (referred to the reference node) Step 3 Write down equations using KCL for every non-reference node in terms of node voltages Step 4 Obtain the node voltages by solving the simultaneous equations in step 3 NODAL ANALYSIS va i1 vb R1 i1 va vb R1 NODAL ANALYSIS i2 va R1 i2 vb va R1 vb NODAL ANALYSIS i1 va R1 Vs i1 v a Vs R1 NODAL ANALYSIS i1 va R1 Vs R2 i1 v a Vs R1 R 2 NODAL ANALYSIS i1 va R1 Vs R2 i1 v a Vs R1 R 2 NODAL ANALYSIS va Vs v a Vs NODAL ANALYSIS i1 va Vs R1 i1 v a Vs v b R1 vb NODAL ANALYSIS i2 va Vs R1 i2 v b Vs v a R1 vb NODAL ANALYSIS SUPERNODE va Constraint equation: Vs v a v b Vs vb MESH ANALYSIS 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 i2 R1 Vs Mesh 1: i1 R2 i3 -Vs + R1(i1 – i2) + R2(i1 – i3) = 0 MESH ANALYSIS Is i2 i1 Mesh 2: i2 = I s i3 MESH ANALYSIS Is i2 i1 Mesh 2: i2 = I s i3 MESH ANALYSIS i2 SUPERMESH i1 Constraint equation : Is i3 i1 – i3 = Is