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Thévenin’s and Norton’s Theorem

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Thévenin’s and Norton’s Theorem

- 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.

- 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.

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.

+

Voc

_

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

- 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).

- 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.

- 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.

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

- 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).

- 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.

- 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

- 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

- Calculation for IN
- Look at current divider equation:
If RTh = RN= 1kW, then IN = 6mA

- 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).

Equations for Thévenin/Norton Transformations

VTh = IN RTh

IN = VTh/RTh

RTh= RN

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

IN = VTh/RTh = 6mA

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

Simplification through Transformation

Current Source to Voltage Source

Current Source to Voltage Source

RTh = 3W

VTh = 0.1A (3W) = 0.3V

0.3V

0.3V

Voltage Source to Current Source

RTh = 2W

IN = 3V/2W = 1.5A

- Simplify to Minimum Number of Current Sources

0.3V

Voltage Source to Current Source

RTh = 6W

IN = 0.3V/6W = 50.0mA

0.3V

Current Sources in Parallel Add

- Simplify to Minimum Number of Voltage Sources

0.3V

Transform solution for Norton circuit to Thévenin circuit to obtain single voltage source/single equivalent resistor in series with load.

- 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.