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SUMMARY ON NODAL AND MESH ANALYSIS
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Both techniques provide systematic steps in solving electric circuit
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Nodal applicable to all circuits, Mesh only applicable to planar circuit
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NOT ALL circuits require nodal or mesh analysis to solve them.
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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
va  vb
i1 
R1
NODAL ANALYSIS
i2
va
vb
R1
vb  va
i2 
R1
NODAL ANALYSIS
i1
va
R1
Vs
v a  Vs
i1 
R1
NODAL ANALYSIS
i1
va
R1
Vs
R2
v a  Vs
i1 
R1  R 2
NODAL ANALYSIS
i1
va
R1
Vs
R2
v a  Vs
i1 
R1  R 2
NODAL ANALYSIS
va
Vs
v a  Vs
NODAL ANALYSIS
i1
va
Vs
R1
v a  Vs  v b
i1 
R1
vb
NODAL ANALYSIS
i2
va
Vs
R1
v b  Vs  v a
i2 
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