1 ECE 3301 General Electrical Engineering Section 19 Maximum Power Transfer Theorem.

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Presentation transcript:

1 ECE 3301 General Electrical Engineering Section 19 Maximum Power Transfer Theorem

2 Maximum Power Transfer It is often desired to transfer maximum power out of a network into a load resistance. Since a Thevenin Equivalent Circuit may be found for any network we may consider a voltage source in series with a resistance.

3 Maximum Power Transfer The current through the load resistance is:

4 Maximum Power Transfer The power dissipated in the load resistance is :

5 Maximum Power Transfer When R L = 0, there is zero power dissipated in the load. All of the power available is dissipated in the source resistance.

6 Maximum Power Transfer When R L = , I L = 0 and There is again zero power dissipated in the load resistance.

7 Maximum Power Transfer For what value of R L is maximum power delivered to R L ?

8 Maximum Power Transfer The power dissipated in the load resistance is:

9 Maximum Power Transfer To find the maximum power transferred, the derivative of this quantity with respect to R L is placed equal to zero.

10 Maximum Power Transfer The quantity in brackets is set equal to zero: Solving for R L reveals 2R L = R S + R L R L = R S

11 Maximum Power Transfer Maximum Power is transferred when the Load Resistances matches the Source Resistance.

12 Maximum Power Transfer R S = R L