Nodal vs. Mesh
• In nodal analysis, circuit variables are node voltages
• Nodal analysis applies KCL to find unknown voltages
Mesh Analysis
• In mesh analysis, circuit variables are mesh currents
• Mesh analysis applies KVL to find unknown currents
• Both methods result in a system of linear equations
• Mesh analysis is only applicable to a circuit that is planar
Planar vs. Non-planar
• Planar circuit: it can be drawn on a plane surface
where no element cross any other element
• Non-planar circuit: there is no way to redraw it and
avoid the branches crossing
What is a mesh/mesh current?
• A mesh is a loop that does not contain any other
loops within it
• The current through a mesh is known as mesh
current
C
a
b
c
d
C
e
1
C
Steps of Mesh Analysis
Example
1. Assign a mesh current to each mesh.
2. Apply KVL to each mesh
--- express voltages in terms of mesh currents.
3. Solve the resulting linear equations.
R1
Va
Example
(only for circuits containing resistors and
independent voltage sources)
− Diagonal terms is the sum of resistances in the
related mesh
− Off-diagonal terms are the negatives of the
resistances common to the meshes.
• Right-hand side:
− Algebraic sum of voltage rises of all independent
voltage sources in the related mesh
Vb
R3
Mesh Equations by Visual Inspection
• Left-hand side:
R2
12 V
1Ω
2Ω
3Ω
4Ω
1Ω
18 V
6V
24 V
1Ω
2Ω
2
Mesh Analysis with Current
Sources
Two cases:
• a current source exists only in one mesh
• a current source exists between two meshes
Mesh Analysis with Current
Sources (I)
Find Vo
4 mA
o
+
2 kΩ
6 kΩ
4 kΩ
Vo
2 mA
3V
4 kΩ
o
Mesh Analysis with Current
Sources (II)
6Ω
Mesh Analysis with Current
Sources (II)
Find I1, I2.
10 Ω
-+
2Ω
20 V
8Ω
4Ω
I2
2I2
40 Ω
I1
6A
5A
80 Ω
2.5I1
64 V
3