Th venin 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

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Thévenin’s and Norton’s Theorem

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Th venin s and norton s theorem

Thévenin’s and Norton’s Theorem


Objective of lecture

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.


Th venin s theorem

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.


Circuit schematic th venin s theorem

Circuit Schematic:Thévenin’s Theorem


Definitions for th venin 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 th venin s theorem1

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 th venin s theorem2

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 v th and r th

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

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

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 theorem1

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 i n and r n

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

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

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

Example #1


Example 1 con t

Example #1 (con’t)

Find IN and RN


Example 1 con t1

Example #1 (con’t)

  • Calculation for IN

  • Look at current divider equation:

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


Why chose r th r n

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

Source Transformation

Equations for Thévenin/Norton Transformations

VTh = IN RTh

IN = VTh/RTh

RTh= RN


Alternative approach example 1

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

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

Example #2

Simplification through Transformation


Example 2 con t

Example #2 (con’t)


Example 2 con t1

Example #2 (con’t)

Current Source to Voltage Source


Example 2 con t2

Example #2 (con’t)

Current Source to Voltage Source

RTh = 3W

VTh = 0.1A (3W) = 0.3V

0.3V


Example 2 con t3

Example #2 (con’t)

0.3V


Example 2 con t4

Example #2 (con’t)

Voltage Source to Current Source

RTh = 2W

IN = 3V/2W = 1.5A


Example 2 solution 1

Example #2 - Solution 1

  • Simplify to Minimum Number of Current Sources

0.3V


Example 2 con t5

Example #2 (con’t)

Voltage Source to Current Source

RTh = 6W

IN = 0.3V/6W = 50.0mA

0.3V


Example 2 con t6

Example #2 (con’t)


Example 2 con t7

Example #2 (con’t)

Current Sources in Parallel Add


Example 2 solution 2

Example #2 - Solution 2

  • Simplify to Minimum Number of Voltage Sources

0.3V


Example 2 con t8

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

PSpice


Example 2 solution 11

Example #2 - Solution 1


Example 2 solution 21

Example #2 – Solution 2


Summary

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.


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