INC 111 Basic Circuit Analysis

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INC 111 Basic Circuit Analysis

• Week 4
• Mesh Analysis

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Mesh Analysis (Loop Analysis)
Mesh A closed loop path which has no smaller
loops inside
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Mesh Analysis

• Procedure
• Count the number of meshes. Let the number equal
  N.
• Define mesh current on each mesh. Let the values
  be I1, I2, I3,
• Use Kirchoffs voltage law (KVL) on each mesh,
  generating N equations
• Solve the equations

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Example
Use mesh analysis to find the power consumption
in the resistor 3 ?
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I2
I1
Loop 1
Equation 1
Loop 2
Equation 2
I1 6A, I2 4A, The current that pass through R
3? is 6-4 2A (downward) Power 12 W
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Example
Use Mesh analysis to find Vx
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I2
Equation 1
I1
I3
Equation 2
Equation 3
I1 3A, I2 2A, I3 3A Vx 3(I3-I2) 3V
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Supermesh
When there is a current source in the mesh path,
we cannot use KVL because we do not know the
voltage across the current source. We have to
use supermesh, which is a combination of 2
meshes to be a big mesh, and avoid the inclusion
of the current source in the mesh path.
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Example
Use Mesh analysis to find Vx
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Equation from 2nd loop
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Equation 2
Equation 3
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I1 9A I2 2.5A I3 2A Vx 3(I3-I2)
-1.5V
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How to choose betweenNode and Mesh Analysis
The hardest part in analyzing circuits is solving
equations. Solving 3 or more equations can be
time consuming. Normally, we will count the
number of equations according to each method and
select the method that have lesser equations.
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Example
From the previous example, if we want to use
Nodal Analysis
7V
V2
V1
V3
0V
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Example Dependent Source
Find Vx
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Equation 1
Equation 2
Equation 3
Equation 4
I115A, I211A, I317A Vx 3(17-11) 18V
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Special Techniques

• Superposition Theorem
• Thevenins Theorem
• Nortons Theorem
• Source Transformation

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Superposition Theorem
In a linear circuit, we can calculate the value
of current (or voltage) that is the result from
each voltage source and current source
independently. Then, the real value is the sum of
all current (or voltage) from the sources.
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Linearity
V and I have linear relationship
I
V
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Implementation

• When calculating the effect of a source, the
  other sources will be set to zero.
• For voltage sources, when set as 0V, it will be
  similar to short circuit
• For current sources, when set as 0A, it will be
  similar to open circuit

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Example
I1 1A I2 2A I total 12 3A
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Example
I1 1A I2 0A I total 10 1A
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Example
Find voltage Vx
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Superposition andDependent Source
Dependent sources cannot be used with
superposition. They have to be active all the
time.
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Example
Use superposition to find Ix
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Find Ix by eliminating the current source 3A
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Find Ix by eliminating the voltage source 10V
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