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Objective of Lecture State 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 Theorem A 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.
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 = ∞W).
+
Voc
_
ThOC VV
Definitions for Thévenin’s Theorem Input 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 = 0W).
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 Theorem A 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.
Definitions for Norton’s Theorem
Short-circuit current Isc is the current, i, when the load is a short circuit
(i.e., RL = 0W).
NSC II
Definitions for Norton’s Theorem Input 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 = ∞W).
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 Conversion A 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
Value of Theorems Simplification 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 (con’t) Calculation for IN
Look at current divider equation:
If RTh = RN= 1kW, then IN = 6mA
N
N
N
N
loadNload
NloadN
load
eq
load
IRk
RmA
IRRR
RRI
R
RI
W
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 (1kW).
Source TransformationEquations for Thévenin/Norton Transformations
VTh = IN RTh
IN = VTh/RTh
RTh= RN
Example #1: Norton’s TheoremIN 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).
Check: Thévenin TheoremVTh is the voltage across the load when an open short circuit is used as the load with a current source
VTh = IN RTh = 6V
Example #2 (con’t)Transform solution for Norton circuit to Thévenin circuit to obtain single voltage source/single equivalent resistor in series with load.