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Thévenin’s and Norton’s Theorem PowerPoint PPT Presentation

Thévenin’s and Norton’s Theorem. Objective of Lecture. State Thévenin’s and Norton Theorems. Chapter 4.5 and 4.6 Fundamentals of Electric Circuits

Thévenin’s and Norton’s Theorem

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Thévenin’s and Norton’s Theorem

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 ca 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 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

+

Voc

_

Open-circuit voltage Voc is the voltage, V, when the load is an open circuit (i.e., RL = ∞W).

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).

Steps to Determine VTh and RTh

• Identify the load, which may be a resistor or a part of the circuit.

• Replace the load with an open circuit .

• Calculate VOC. This is VTh.

• Turn off all independent voltage and currents sources.

• 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 originial circuit.

Norton’s Theorem

• A linear two-terminal circuit can be replaced with an equivalent circuit of an ideal current source, IN, in series 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 are turned off.

Definitions for Norton’s Theorem

Open-circuit voltage Isc is the current, i, when the load is a short circuit (i.e., RL = 0W).

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).

Steps to Determine IN and RN

• Identify the load, which may be a resistor or a part of the circuit.

• Replace the load with a short circuit .

• Calculate ISC. This is IN.

• Turn off all independent voltage and currents sources.

• Calculate the equivalent resistance of the circuit. This is RTH.

• The current through and voltage across the load in parallel with IN and RN is the load’s actual current and voltage in the originial 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.

Find IN and RN

Example #1 (con’t)

• Calculation for IN

• Look at current divider equation:

If RTh = RN= 1kW, then IN = 6mA

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 Transformation

Equations for Thévenin/Norton Transformations

VTh = IN RTh

IN = VTh/RTh

RTh= RN

Alternative Approach: Example #1

IN is the current that flows when a short circuit is used as the load with a voltage source

IN = VTh/RTh = 6mA

Alternative Approach

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

Example #2

Simplification through Transformation

Example #2 (con’t)

Current Source to Voltage Source

Example #2 (con’t)

Current Source to Voltage Source

RTh = 3W

VTh = 0.1A (3W) = 0.3V

0.3V

0.3V

Example #2 (con’t)

Voltage Source to Current Source

RTh = 2W

IN = 3V/2W = 1.5A

Example #2 - Solution 1

• Simplify to Minimum Number of Current Sources

0.3V

Example #2 (con’t)

Voltage Source to Current Source

RTh = 6W

IN = 0.3V/6W = 50.0mA

0.3V

Example #2 - Solution 2

• Simplify 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.

Summary

• Thévenin and Norton transformations are performed to:

• Simplify a circuit for analysis

• Allow engineers to use a voltage source when a current source is called out in the circuit schematic

• Enable an engineer to determine the value of the load resistor for maximum power transfer/impedance matching.