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ECA Thevanin Norton
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Objective of LectureState Thévenin’s and Norton Theorems.
Chapter 4.5 and 4.6 Fundamentals of Electric Circuits
Demonstrate how Thévenin’s and Norton theorems can be used to simplify a circuit to one that contains three components: a power source, equivalent resistor, and load.
Thévenin’s TheoremA linear two-terminal circuit can be replaced
with an equivalent circuit of an ideal voltage source, VTh, in series with a resistor, RTh.VTh is equal to the open-circuit voltage at the
terminals.RTh is the equivalent or input resistance when
the independent sources in the linear circuit are turned off.
Circuit Schematic:Thévenin’s Theorem
Definitions for Thévenin’s Theorem
Linear circuit is a circuit where the voltage is directly proportional to the current (i.e., Ohm’s Law is followed).
Two terminals are the 2 nodes/2 wires that can make a connection between the circuit to the load.
Definitions for Thévenin’s Theorem
Open-circuit voltage Voc is the voltage, V, when the load is an open circuit (i.e., RL = ∞).
+Voc
_
ThOC VV
Definitions for Thévenin’s TheoremInput resistance is the resistance seen by
the load when VTh = 0V.
It is also the resistance of the linear circuit when the load is a short circuit (RL = 0).
SCThThin iVRR
Steps to Determine VTh and RTh1. Identify the load, which may be a resistor or a
part of the circuit.2. Replace the load with an open circuit .3. Calculate VOC. This is VTh.4. Turn off all independent voltage and currents
sources in the linear 2-terminal circuit.5. Calculate the equivalent resistance of the
circuit. This is RTh. The current through and voltage across the load
in series with VTh and RTh is the load’s actual current and voltage in the original circuit.
Norton’s TheoremA linear two-terminal circuit can be replaced
with an equivalent circuit of an ideal current source, IN, in parallel with a resistor, RN.IN is equal to the short-circuit current at the
terminals.RN is the equivalent or input resistance when
the independent sources in the linear circuit are turned off.
Circuit Schematic:Norton’s Theorem
Definitions for Norton’s Theorem
Short-circuit current Isc is the current, i, when the load is a short circuit (i.e., RL = 0).
NSC II
Definitions for Norton’s TheoremInput resistance is the resistance seen by
the load when IN = 0A.
It is also the resistance of the linear circuit when the load is an open circuit (RL = ∞).
NOCNin IVRR
Steps to Determine IN and RN1. Identify the load, which may be a resistor or a
part of the circuit.2. Replace the load with a short circuit .3. Calculate ISC. This is IN.4. Turn off all independent voltage and currents
sources in the linear 2-terminal circuit.5. Calculate the equivalent resistance of the
circuit. This is RN. The current through and voltage across the load
in parallel with IN and RN is the load’s actual current and voltage in the original circuit.
Source ConversionA Thévenin equivalent circuit can easily be
transformed to a Norton equivalent circuit (or visa versa).If RTh = RN, then VTh = RNIN and IN = VTh/RTh
Voltage Polarity and Current Flow
Value of TheoremsSimplification of complex circuits.
Used to predict the current through and voltage across any load attached to the two terminals.
Provides information to users of the circuit.
Example #1
Example #1 (con’t)Find IN and RN
Example #1 (con’t)Calculation for IN
Look at current divider equation:
If RTh = RN= 1k, then IN = 6mA
NN
N
NloadNload
NloadN
load
eqload
IRk
RmA
IRRR
RRI
R
RI
22
1
Why chose RTh = RN?Suppose VTh = 0V and IN = 0mA
Replace the voltage source with a short circuit.Replace the current source with an open
circuit.
Looking towards the source, both circuits have the identical resistance (1k).
Source TransformationEquations for Thévenin/Norton
Transformations
VTh = IN RTh
IN = VTh/RTh
RTh= RN
Example #1: Norton’s Theorem IN is the current that flows when a short circuit
is used as the load with a voltage source
IN = VTh/RTh = 6mA
Example #1: Norton’s TheoremRN is the resistance of the linear circuit when the power sources in the original circuit are turned off (VTh is replaced with a short circuit).
Example #1: Norton’s TheoremThe Norton equivalent circuit is:
Check: Thévenin Theorem VTh is the voltage across the load when an open
short circuit is used as the load with a current source
VTh = IN RTh = 6V
Check: Iload and Vload
VV
kmAV
mAI
mAkk
kI
load
load
load
load
4
)2(2
2
621
1
Example #2Simplification through Transformation
Example #2 (con’t)
Example #2 (con’t)Find Req to obtain a Norton equivalent circuit
Example #2 (con’t)
RTh = 3
VTh = 0.1A (3) = 0.3V
0.3V
Current Source to Voltage Source
Example #2 (con’t)
0.3V
Example #2 (con’t)
RTh = 2
IN = 3V/2 = 1.5A
Voltage Source to Current Source
0.3V
Example #2 - Solution 1Simplify to Minimum Number of Current
Sources
RTh = 6
IN = 0.3V/6 = 50.0mA
0.3V
Voltage Source to Current Source
Example #2 (con’t)
Current Sources in Parallel Add
Example #2 - Solution 2Simplify to Minimum Number of Voltage
Sources
0.3V
Example #2 (con’t)Transform solution for Norton circuit to Thévenin circuit to obtain single voltage source/single equivalent resistor in series with load.
PSpice
Example #2 - Solution 1
Example #2 – Solution 2
SummaryThévenin and Norton transfomrations are
performed to simplify a circuit for analysis and design. Two techniques were described.
Examples using the source transformation technique were given.
