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METHODS OF ANALYSIS
Mesh Analysis
Nodal analysis
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Nodal Analysis 2
Supernode
Determine v 1 , v 2
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
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Nodal Analysis 2
Supernode
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
Step 1
Determine the reference node
Step 2
Assign the rest of the nodes with node voltages
v 1 v 2
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Nodal Analysis 2
Supernode
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
v 1 v 2
Step 3
Write down equations using KCL for every non-reference node in terms of nodevoltages
We cannot write equation for current with branch containing 2V voltage source !
To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE
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Nodal Analysis 2
Supernode
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
v 1 v 2
To avoid this, we will combine nodes 1 and 2 to form a SUPERNODE
supernode
We will use KCL to sum all current going out of supernode:
074
v
2
v2
21!
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Nodal Analysis 2
Supernode
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
v 1 v 2
supernode
074
v
2
v2
21!
We need another equation in order to solve v 1 and v 2
Applying KVL for the loop, 2
vv12!
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Nodal Analysis 2
Supernode
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
v 1 v 2
074
v
2
v2
21! 2vv
12!
Step 4
Obtain the node voltages by solving the simultaneous equations in step 3
and
V333.7v1
! V333.5v2
!
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Nodal Analysis 2
Supernode
To summarize «.We form a su pernode when there is a voltage source in
between 2 non-reference nodes
For example: Supernode needed since V s in
between non-reference node
+
+
V s
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+
+
v b
v a
Nodal Analysis 2
Supernode
To summarize «.
For example:
v 1 v 2 v 3
Supernode needed since v a in between
non-reference node
We don¶t need to formsupernode.
Also note that v 1 = V b
We form a su pernode when there is a voltage source in
between 2 non-reference nodes
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Nodal Analysis 2
Supernode
To summarize «.
For example:
We form a su pernode when there is a voltage source in
between 2 non-reference nodes
+
3i o +
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Nodal Analysis 2
Supernode
To summarize «.We form a su pernode when there is a voltage source in
between 2 non-reference nodes
Since we have combined two nodes, we lost 1 equation to
solve the circuit. @ we need one more equation to solve thecircuit
We write an equation (using KVL) that defines the voltage
relationship between the two non-reference nodes that forms
the supernodes
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Nodal Analysis 2
Verification with Pspice
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
v 1 v 2
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Nodal Analysis 2
+
v 1
+
v 2 2; 4;
10;
+
2V
2A 7A
Mark reference node with 0.
Mark the rest of the nodes
with other than 0
0
1 2
Write the NETLIST for the
circuit ans save it with .cir
extension, e.g. example1.cir
EXAMPLE 1
I1 0 1 DC 2
I2 2 0 DC 7
V1 2 1 DC 2R1 1 0 2
R2 1 2 10
R3 2 0 4
.END
Verification with Pspice