What are Thevenin and Norton equivalents?
1 Answer
Thevenin and Norton equivalents are two important concepts in electrical circuit analysis, particularly in the context of linear circuits. They are used to simplify complex circuits into simpler, equivalent circuits, which can make analysis and calculations easier.
Thevenin Equivalent:
The Thevenin equivalent represents a linear two-terminal circuit as an ideal voltage source in series with a resistor. It is named after the French physicist Léon Charles Thévenin. The idea behind the Thevenin equivalent is that any linear circuit can be represented by a single voltage source and a single series resistor.
The Thevenin equivalent circuit consists of the following two elements:
An ideal voltage source (Vth) that represents the open-circuit voltage across the terminals of the original circuit.
A series resistor (Rth) that represents the equivalent resistance of the original circuit as seen from the two terminals with all independent sources turned off (replaced by their internal resistances).
To find the Thevenin equivalent of a circuit, you need to follow these steps:
Disconnect the load connected to the terminals of the circuit.
Calculate the open-circuit voltage (Vth) across the terminals.
Calculate the equivalent resistance (Rth) seen from the terminals with all independent sources turned off.
The Thevenin equivalent circuit will be the ideal voltage source Vth in series with the resistor Rth.
Norton Equivalent:
The Norton equivalent is another way to represent a linear two-terminal circuit. It is named after the American engineer and mathematician Edward Lawry Norton. The Norton equivalent represents the original circuit as an ideal current source in parallel with a resistor.
The Norton equivalent circuit consists of the following two elements:
An ideal current source (In) that represents the short-circuit current across the terminals of the original circuit.
A parallel resistor (Rn) that represents the equivalent resistance of the original circuit as seen from the two terminals with all independent sources turned off (replaced by their internal resistances).
To find the Norton equivalent of a circuit, you need to follow these steps:
Disconnect the load connected to the terminals of the circuit.
Calculate the short-circuit current (In) flowing through the terminals.
Calculate the equivalent resistance (Rn) seen from the terminals with all independent sources turned off.
The Norton equivalent circuit will be the ideal current source In in parallel with the resistor Rn.
Both Thevenin and Norton equivalents are useful for simplifying circuits when you want to analyze how a load resistor affects the overall circuit behavior. By replacing a complex network with its Thevenin or Norton equivalent, you can significantly simplify calculations and analysis, especially in cases where the load may change or when connecting multiple circuits together.
Thevenin Equivalent:
The Thevenin equivalent represents a linear two-terminal circuit as an ideal voltage source in series with a resistor. It is named after the French physicist Léon Charles Thévenin. The idea behind the Thevenin equivalent is that any linear circuit can be represented by a single voltage source and a single series resistor.
The Thevenin equivalent circuit consists of the following two elements:
An ideal voltage source (Vth) that represents the open-circuit voltage across the terminals of the original circuit.
A series resistor (Rth) that represents the equivalent resistance of the original circuit as seen from the two terminals with all independent sources turned off (replaced by their internal resistances).
To find the Thevenin equivalent of a circuit, you need to follow these steps:
Disconnect the load connected to the terminals of the circuit.
Calculate the open-circuit voltage (Vth) across the terminals.
Calculate the equivalent resistance (Rth) seen from the terminals with all independent sources turned off.
The Thevenin equivalent circuit will be the ideal voltage source Vth in series with the resistor Rth.
Norton Equivalent:
The Norton equivalent is another way to represent a linear two-terminal circuit. It is named after the American engineer and mathematician Edward Lawry Norton. The Norton equivalent represents the original circuit as an ideal current source in parallel with a resistor.
The Norton equivalent circuit consists of the following two elements:
An ideal current source (In) that represents the short-circuit current across the terminals of the original circuit.
A parallel resistor (Rn) that represents the equivalent resistance of the original circuit as seen from the two terminals with all independent sources turned off (replaced by their internal resistances).
To find the Norton equivalent of a circuit, you need to follow these steps:
Disconnect the load connected to the terminals of the circuit.
Calculate the short-circuit current (In) flowing through the terminals.
Calculate the equivalent resistance (Rn) seen from the terminals with all independent sources turned off.
The Norton equivalent circuit will be the ideal current source In in parallel with the resistor Rn.
Both Thevenin and Norton equivalents are useful for simplifying circuits when you want to analyze how a load resistor affects the overall circuit behavior. By replacing a complex network with its Thevenin or Norton equivalent, you can significantly simplify calculations and analysis, especially in cases where the load may change or when connecting multiple circuits together.