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Unit 2: Node and Mesh Circuit Analysis
Unit 2.1 – Node Voltage Analysis
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Node Voltage Analysis
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In these lectures, you will learn:
±
The difficulty in using only KVL, KCL, and Ohm’s Law in
the analysis of large DC circuits.
±
How node voltage analysis simplifies the solution of large
DC circuits.
±
How to apply NodeVoltage Analysis.
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Example Circuit
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To get the power I need
the voltage and current for
every element.
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What if I was going to use
KVL, KCL and Ohm’s Law to
solve for this?
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How many unknowns?
±
1 current for the voltage
source.
±
2 voltages for the current
sources.
±
5 voltages or 5 currents
for the resistors.
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I need 13 equations!
Calculate the power associated
with each element in the circuit
below.
R3
1 A
2 A
R1
R2
R4
R5
2 V
+

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How Many Equations?
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I have 13 unknowns so I
need 13 equations:
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I can write an Ohm’s Law
equation for each resistor.
• 5 Equations.
±
I can write 3 independent
KCL equations.
±
I can write 5 independent
KVL equations.
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Now I am all done except
for the algebra.
Calculate the power associated
with each element in the circuit
below.
R3
1 A
2 A
R1
R2
R4
R5
2 V
+

There has got to be an
easier way!
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The Easier Way
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Systematic methods allow us
to solve circuits using the
minimum number of equations.
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Systematic methods allow us
solve every
circuit in the
same manner.
±
We don’t have to be clever.
±
We don’t have to see “the
trick”.
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We will learn two systematic
methods.
The first is
nodal
analysis
.
R3
1 A
2 A
R1
R2
R4
R5
2 V
+

With Nodal Analysis,
we need:
2 Equations and 2
unknowns
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Concept of Nodal Analysis
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If I know the voltage across each element in a
circuit, then I know everything.
±
Resistors
• Current can be found via Ohm’s Law
• Power can be calculated by V
2
/R
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Current Sources
• Power can be calculated once the voltage across it are
known
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Voltage Sources
• Finding the current through the voltage sources is a
bit harder – may have to use KCL.
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Nodal analysis is a systematic method for finding
all of the voltages in any circuit.
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Review of Definitions
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What is a node?
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A node is a point in the circuit where two or more elements are
connected
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What is an essential node?
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An essential node is a node where three or more elements are
connected. (This concept is not used in your text, but it greatly
simplifies the analysis.)
4!
How many nodes are
there in this circuit?
How many essential
nodes are there in
this circuit?
4!
R3
1 A
2 A
R1
R2
R4
R5
2 V
+

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Node Voltage
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What does a Node Voltage mean?
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We can define the value of a voltage at a node if we have
a point of reference.
Where are the nodes?
What if we say the voltage at
node A is 0 V…
What is the value at node B?
+

0 V
20 V
10 k
Ω
10 k
Ω
A
B
C
20 V
10 V
What is the value at node C?
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 Fall '08
 WilliamNeal
 Volt, SEPTA Regional Rail, Voltage source, NODE VOLTAGE ANALYSIS

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