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NODAL ANALYSIS

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by

afnee aziz

on 19 December 2013

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Transcript of NODAL ANALYSIS

GROUP MEMBERS NAME
1) SITI NOOR FATIHAH BT AHMAD
AE 130033

2) RATHY-SHRY A/P VELOO
AE130287

3) NURUL AFNEE BT ABDUL AZIZ
AE130066

INTRODUCTION
In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage between "nodes" in an electrical circuit in terms of the branch currents.
1) Every circuit has n nodes with one of the nodes being
designated as a reference node.
2) We designate the remaining n – 1 nodes as voltage nodes
and give each node a unique name, vi.
3) At each node we write Kirchhoff’s current law in terms
of the node voltages.
4) We form n-1 linear equations at the n-1 nodes
in terms of the node voltages and solve the equation by making the calculation.
v1-v2
R2
+
v1-v3
R3
=
I
1
v2-v1
R3
+
v2
R4
+
v2
R5+R6
=
0
v1
R1+R2
+
v1-v2
R3
=
I1
v2-v1
R3
+
v2
R4
+
v2
R5+R6
=
0
Steps 1 and 2 have already been applied. To apply step 3:
In this case there is only one unknown, vb. Plugging in numbers and solving the circuit we get
EXAMPLE 1
EXAMPLE 2
The first part of the problem involved obtaining these equations:
I'm going to solve this problem using Cranmer's Rule, but either the Gauss elimination method or matrix inversion will work equally as well.
So, the two node voltages are:
Now, we set this up in matrix form:
So. the answer will be:
Based on the analysis of the circuit, we have these two nodal equations.
Put into a matrix gives:
Solved using Cranmer's method.
So, the node voltages are:
Looking at the circuit again, v can be found simply by subtracting node 2 from node 1
EXAMPLE 3
Lecturer Muhammad Shukri bin Ahmad
NODAL ANALYSIS
BASIC CIRCUIT: THE CONCEPT
Full transcript