Maximum Power Transfer Theorem: Statement: Maximum Power Transfer Theorem states that “maximum...

Maximum Power Transfer Theorem:

Statement: Maximum Power Transfer Theorem states that “maximum power is transferred from the source to the load when the load resistance is equal to the Thevenin’s equivalent resistance”.

i.e, RL = RTH

Proof:

1...............

,

LTH

TH

RR

VI

Here

and

2.................2LRIP

Substitute the value of I,

2

22

)( LTH

LTHL

LTH

TH

RR

RVR

RR

VP

For max power,

4

222

)(

)(2)(0

LTH

LTHLTHTHLTH

L RR

RRRVVRR

dR

dP

0)(

)(2)(

4

222

LTH

LTHLTHTHLTH

L RR

RRRVVRR

dR

dPor

THL

LLTH

LTHLTHTHLTH

RRor

RRR

RRRVVRRor

2)(

)(2)( 222

Now, maximum power transfer is given by

)(max

2

2

22

LL

LTHL

LTH

TH

RR

RVR

RR

VP

inputting

L

TH

R

V

4

2

Output power=I2RL

Input power= I2RTh

η = o/p power / (o/p power+i/p power)

=I2RL / I2(RL+RTh)

For max efficiency RL=RTh

Hence efficiency η = RL/(2RL)*100= 50%

Example

3Ω

2Ω

10V

10Ω

RL

2Ω

Evaluate RL for maximum power transfer and find the power

Note: To solve a question for maximum power transfer, the thevenin equivalent needs to be calculated.

Vth = VA - VB = 6V

Rth=(2 3׀׀ )+ 10+2=13.2 Ω

Rth

2

3

2

10

Calculation of Vth and Rth:

13.2

6V RL

Thevenin’s equivalent circuit

RL should be set to 13.2Ω to get max. power transfer

Max. power is WRth

Vth68.0

2.13*4

)6(

4

22

Example: Evaluate RL for maximum power transfer and find the power

Calculation of RTH :

RL = RTH =6Ω

Calculation of VTH :

• RL must equal to RTh = 6 ohms• The maximum power transferred=

6*4

8.64

4

22

L

Th

R

V