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E E 1205. Lecture 08 -Mesh Current Analysis. Introduction to Mesh Current Method. More direct than branch equations Fewer equations to solve Express all variables in terms of mesh currents Solution is set of mesh currents Solution completely defines the circuit

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e e 1205

E E 1205

Lecture 08 -Mesh Current Analysis

introduction to mesh current method
Introduction to Mesh Current Method
  • More direct than branch equations
  • Fewer equations to solve
  • Express all variables in terms of mesh currents
  • Solution is set of mesh currents
  • Solution completely defines the circuit
  • Most Convenient Method to Model Magnetic Coupling (E E 2446 Topic)
mesh current example 1 1 2
Mesh Current Example 1 (1/2)

KVL at Mesh 1:

KVL at Mesh 2:

Using Ohm’s Law:

mesh current example 1 2 2
Mesh Current Example 1 (2/2)

Above linear equations can be solved for

mesh currents I1 and I2.

mesh current example 1a 1 2
Mesh Current Example 1a (1/2)

KVL at Mesh 1:

KVL at Mesh 2:

Solve:

forced mesh 1 2
Forced Mesh (1/2)
  • No KVL equation possible for mesh 2
  • But I2 is known: I2 = Is
forced mesh 2 2
Forced Mesh (2/2)

KVL for mesh 1:

Substitute and Solve:

forced mesh example 3a
Forced Mesh Example 3a

KVL for mesh 1:

Substitute and Solve:

supermesh example 1 5
Supermesh Example (1/5)
  • No KVL possible for meshes 1 or 2
  • Use Supermesh (dotted loop) for KVL
supermesh example 2 5
Supermesh Example (2/5)

Supermesh KVL:

Mesh 3 KVL:

supermesh example 3 5
Supermesh Example (3/5)

Also:

Subst for I2:

supermesh example 4 5
Supermesh Example (4/5)

And:

Rearranging the equations: