Thevenin Norton MaxPower

Principles of Electric Circuits - Floyd

Chapter 8Chapter 8 1

Apr 27, 2023

Chapter 8


Chapter 8Chapter 8 2SummarySummary

Thevenin’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:

Thevenin’s theorem

V T H

R T H



VTH is defined as


RTH is defined as

the open circuit voltage between the two output terminals of a circuit. the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.

V T H

R T H




R

R

1

R 2R 2 L

V SV S

1 2 V1 0 k

6 8 k 2 7 k

Output terminals

What is the Thevenin voltage for the circuit? 8.76 V

What is the Thevenin resistance for the circuit? 7.30 k

Remember, the load resistor has no affect on the Thevenin parameters.



Thevenizing from two different sets of terminals



Thevenizing a portion of a circuit




Thevenin’s theorem is useful for solving the Wheatstone bridge. One way to Thevenize the bridge is to create two Thevenin circuits from A to ground and from B to ground. The thevinin’s resistance between point A and ground is R1||R3 and the resistance from B to ground is R2||R4. The voltage on each side of the bridge is found using the voltage divider rule.

R3 R4

R2

RL

R1VS

-

+A B



Norton’s theorem states that any two-terminal, resistive circuit can be replaced with a simple equivalent circuit when viewed from two output terminals. The equivalent circuit is:

Norton’s theorem

RNIN



Norton’s theorem

the output current when the output terminals are shorted. the total resistance appearing between the two output terminals when all sources have been replaced by their internal resistances.

IN is defined as

RN is defined as

RNIN



Norton’s theorem

Output terminals

What is the Norton current for the circuit? 17.9 mAWhat is the Norton resistance for the circuit? 359

R2

R1

RL

VS +10 V

560

820 1.0 k

The Norton circuit is shown on the following slide.



Norton’s theorem

RNIN17.9 mA 359

The Norton circuit (without the load) is:



Maximum power transfer

The maximum power is transferred from a source to a load when the load resistance is equal to the internal source resistance.

The maximum power transfer theorem assumes the source voltage and resistance are fixed.

RS

RL

VS +



Maximum power transfer

What is the power delivered to the matching load?

The voltage to the load is 5.0 V. The power delivered is

RS

RL

VS + 50

50 10 V

22

LL

5.0 V= 0.5 W

50 VPR



-to-Y and Y-to- conversion

The -to-Y and Y-to- conversion formulas allow a three terminal resistive network to be replaced with an equivalent network.

For the -to-Y conversion, each resistor in the Y is equal to the product of the resistors in the two adjacent branches divided by the sum of all three resistors.

RC

RA RB

R1 R2

R3



RC

RA RB

R1 R2

R3



-to-Y and Y-to- conversion

The -to-Y and Y-to- conversion formulas allow a three terminal resistive network to be replaced with an equivalent network.

For the Y-to- conversion, each resistor in the is equal to the sum of all products of Y resistors, taken two at a time divided by the opposite Y resistor.

RC

RA RBR1 R2

R3



RC

RA RB

R1 R2

R3

Thevenin Norton MaxPower

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