UCLA
E
LECTRICAL
E
NGINEERING
D
EPARTMENT
:
EE
10:
C
IRCUIT
A
NALYSIS
1
L
ECTURE
6
LECTURE NOTES: OCT 24, 2007
OUTLINE
REVIEW
1.
Dependent Sources
2.
Node Voltage Methods for Circuits with Dependent Sources
SIMPLIFIED NODE VOLTAGE SOLUTIONS FOR SPECIAL CIRCUIT STRUCTURES
•
Certain arrangement of dependent and independent voltage and current sources reduces
the complexity of the circuit solution.
•
If a source is connected between two Essential Nodes, then one less equation is required
to specify the circuit, than would otherwise be required.
•
We will develop a new rule:
o
When a voltage source is connected between two Essential Nodes
, then
this node can be replaced with a “
supernode
” for the purposes of computing
currents for the KCL sum.
o
The currents that arrive at
each node of the voltage source
are treated as if
the voltage source is
one node.
4.8A
2.5
Ω
12V
10
Ω
1
Ω
i
x
+
v = i
x
7.5
Ω
2.5
Ω
+
v
1

+

Figure 1.
Example Problem
•
First, lets write down the Node Voltage Equations in the normal way.
1)
List the information that is requested by the problem.
1
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E
LECTRICAL
E
NGINEERING
D
EPARTMENT
:
EE
10:
C
IRCUIT
A
NALYSIS
1
L
ECTURE
6
lution
2)
Examine the circuit to determine the approach for a so
3)
Determine if a circuit simplification may be accomplished using an equivalent circuit, for
example, a parallel, series, delta, or Y, circuit structure.
4)
List known values of circuit variables
5)
Identify and label the N
E
Essential Nodes
6)
Choose one Essential Node and label it with a Reference Potential Symbol. The choice of
this node will determine the level of simplicity of the calculation.
However,
any
choice of
an Essential Node will yield the same problem results.
You should select in the circuit,
that Essential Node that is connected to the most branches.
7)
Identify and label the nonreference node voltages.
8)
Each nonreference node voltage is labeled as positive.
9)
Use KCL to write down an equation for each nonreference node, writing the equations
in terms of the resistances, and node voltages.
10)
Write down N
E
– 1 equations.
11)
Solve the set of equations.
1)
Information requested: Find
v
2
de voltage method
es
ssential Nodes.
These are b, and c, e,
6)
e and label it with a Reference Potential Symbol. The choice of
•
No
.
This is clearly the proper
)
Identify and label the nonreference node voltages.
a
is
not an independent node.
8)
E
9)
ve three steps and they are shown in Figure 6.
2)
Determine approach:
Simple no
3)
No circuit simplification is attempted
4)
List known values: 4.8A and 12V sourc
5)
For this step, we must label the circuit E
and d, shown in Figure 3.
Choose one Essential Nod
this node will determine the level of simplicity of the calculation.
However,
any
choice of
an Essential Node will yield the same problem results.
You should select in the circuit,
that Essential Node that is connected to the most branches.
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 Fall '07
 Chang
 Volt, Mesh Analysis, Kirchhoff's circuit laws, Electrical Engineering Department, UCLA Electrical Engineering Department, UCLA ELECTRICAL ENGINEERING

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