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Page 1: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

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THEVENIN’S THEOREMThevenin’s theorem states that a linear two-

terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTh in series with a resistor RTh,

Where VTh is the open-circuit voltage at the terminals

And RTh is the input or equivalent resistance at the terminals when the independent sources are turned off.

Page 3: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 4: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

A particular element in a circuit is variable (usually called the load) while other elements are fixed.

As a typical example, a household outlet terminal may be connected to different appliances constituting a variable load.

Each time the variable element is changed, the entire circuit has to be analyzed all over again.

To avoid this problem, Thevenin’s theorem provides a technique by which the fixed part of the circuit is replaced by an equivalent circuit.

Page 5: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

According to Thevenin’s theorem, the linear circuit in Fig. 4.23(a) can be replaced by that in Fig. 4.23(b).

(The load in Fig. 4.23 may be a single resistor or another circuit.)

The circuit to the left of the terminals a-b in Fig. 4.23(b) is known as the Thevenin equivalent circuit.

It was developed in 1883 by M. Leon Thevenin (1857–1926), a French telegraph engineer.

Page 6: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 7: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Finding RthTo apply this idea in finding the Thevenin

resistance RTh, we need to consider two cases.

Page 8: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 9: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

It often occurs that RTh takes a negative value. In this case, the negative resistance (v = −iR) implies that the circuit is supplying power.

A linear circuit with a variable load can be replaced by the Thevenin equivalent, exclusive of the load.

The equivalent network behaves the same way externally as the original circuit.

Page 10: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 11: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Load Voltage and Current

Page 12: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

MAXIMUM POWER TRANSFERMaximum power is transferred to the load

when the load resistance equals the Thevenin resistance as seen from the load (RL = RTh).

Page 13: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

NORTON’S THEOREMNorton’s theorem states that a linear two-

terminal circuit can be replaced by An equivalent circuit consisting of a current

source In in parallel with a resistor Rn, where In is the short-circuit current through

the terminals and Rn is the input or equivalent resistance at

the terminals when the independent sources are turned off.

Page 14: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 15: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

The Thevenin and Norton equivalent circuits arerelated by a source transformation.

Page 16: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 17: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

Page 18: THEVENIN’S THEOREM Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source

The End

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