10/6/10
Dr. Bruce McCann
1
Node Voltage Analysis
Node Voltage Analysis
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.
Node Voltage Analysis is the most important
technique we will cover in EE302.
It is essential that you master this method!
Example Circuit
To get the power we need
the voltage and current for
every element.
What if we use KVL, KCL and
Ohm’s Law to solve this?
How many unknowns?
1 current for the voltage
source.
2 voltages for the
current sources.
5 voltages or 5 currents
for the resistors.
We 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
+

How Many Equations?
We have 13 unknowns so we
need 13 equations:
We can write an Ohm’s
Law equation for each
resistor.
•
5 Equations.
We can write 3
independent KCL
equations.
We can write 5
independent KVL
equations.
Now we are 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!
The Easier Way
Systematic methods allow us
to solve circuits using the
minimum
number of equations.
Systematic methods allow us
to solve every
circuit in the
same manner.
We don’t have to be
clever.
We don’t have to see “the
trick.”
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 only:
2 Equations with 2 unknowns
Concept of Nodal Analysis
If I know all of the voltages in a circuit, then I
know everything!
Resistors
•
Current can be found via Ohm’s Law
•
Power can be calculated by V
2
/R
Current Sources
•
Power can be calculated once the voltage is known.
Voltage Sources
•
Finding the current through the voltage sources is harder –
often have to use KCL.
Nodal analysis is a systematic method for finding all of
the voltages in any circuit.
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10/6/10
Dr. Bruce McCann
2
Review of Definitions
What is a node?
A node is a point in the circuit where two or more elements are
connected
What is an extraordinary node?
An extraordinary node is a node where three or more elements
are connected.
4!
How many nodes are
there in this circuit?
How many extraordinary
nodes are there in
this circuit?
4!
R3
1 A
2 A
R1
R2
R4
R5
2 V
+

Finding Current from Voltages
Circuit
A
Circuit
B
+
V
a

+
V
b

How can we use Ohm’s Law to find the resistor current?
What is the voltage across the resistor (V
R
)?
+
V
R

V
R
= V
a
 V
b
I
R
= V
R
/R
R
What is the current through the resistor (I
R
)?
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 Fall '06
 MCCANN
 Volt, SEPTA Regional Rail, NODE VOLTAGE ANALYSIS

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