Mesh Currents
2 February 2005
Mesh Current Analysis
ELEC 111
Loop Analysis
• A loop is a closed path that is drawn by starting at a
node and tracing a path back to that node without
passing through an intermediate node more than once
• In loop analysis there are not constraints on how we
assign loops. To perform loop analysis
– create a loop until all components are included in one loop.
• Do not make additional loops once all components have been
included
– A loop can include other loops within it
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Mesh Currents
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Mesh Current Analysis
• Mesh Analysis is a special case of Loop Analysis
– A Mesh is a loop that contains no other loops within it
• We use Mesh Current analysis when we have circuits:
– that contain multiple sources
– we wish to solve for currents
– where the number of independent Meshes (loops) is less than the number of
independent Nodes
• Since Mesh Currents is a special case of Loop Analysis, we will not
perform any examples of Loop Analysis as the procedure for writing KVL
equations is the same for both
• Mesh Current Analysis and Loop Analysis are the dual of Nodal Analysis
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Mesh Current Procedure
• We begin by
– Assigning simple clockwise meshes and mesh variables
– If a mesh contains a current source, we can use that source as the mesh current
keeping in mind the direction of the source current
– We may perform a source transformation if it simplifies the circuit
– Write a KVL equation for each mesh
• When you enter a dependent voltage or current source, the sign is written for a
voltage drop, not a dependent
– Collect terms for each mesh
– Solve the Simultaneous Linear Equations for unknown quantities using Ohm’s
Law, KVL, and KCL as appropriate
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Mesh Currents
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Mesh Currents 1
I1
I2
IR3 = I1 – I2
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Mesh Currents 1
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Mesh Currents
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Mesh Currents 2
I1
I2
IR3 = I1 – I2
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Mesh Currents 2
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Mesh Currents
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Mesh Currents 3
I1
I2
IX
IR4 = I1 – I2
IR5 = I2 – I3
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Mesh Currents 3
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Mesh Currents
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Mesh Currents with Supermesh
• A Supermesh exists when a current source is common to 2
meshes (IS2 in previous graphic)
• One method is
–
–
–
–
–
–
Write the KCL equation for the mesh with the current source
Create a Supermesh around the periphery of the two meshes
Write the KVL equation for the Supermesh
Write the remaining KVL equations
Substitute the KCL equation for one of the supermesh unknowns
Solve the Simultaneous Liner Equation
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Mesh Currents with a Supermesh I
NOTE: IS1 is a Supermesh
IS1
I1
I2
IR1 = IS1 – I1
IR3 = I1 – I2
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Mesh Currents
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Mesh Currents with a Supermesh I
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Mesh Currents with a Supermesh II
NOTE: IS1 is a Supermesh
IS1
I1
I2
IR1 = IS1 – I1
IR2 = I1 – I2
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Mesh Currents
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Mesh Currents with a Supermesh II
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Bridge Using Mesh Currents
I2
I1
I3
VS = 6V
R1 = 1k
R2 = 1k
R3 = 2k
R4 = 1.8k
RM = 2k
I M = I2 – I 3
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Mesh Currents
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Bridge Using Mesh Currents
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Mesh Currents 7
I2
I1
I3
IR3 = I1 – I2
IR4 = I2 – I3
IR5 = I1 – I5
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Mesh Currents
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Mesh Currents 7
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Mesh Currents 8
I3
I2
I1
IR2 = I1 – I3
IR4 = I1 – I2
IR3 = I3 – I2
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Mesh Currents
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Mesh Currents 8
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