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ECE 3301 General Electrical Engineering Section 19 Maximum Power Transfer Theorem 1 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. RS VS IL RL 2 Maximum Power Transfer • The current through the load resistance is: VS IL = RS + RL RS VS IL RL 3 Maximum Power Transfer • The power dissipated in the load resistance is : VS2RL PL = (RS + RL)2 RS VS IL RL 4 Maximum Power Transfer • When RL = 0, there is zero power dissipated in the load. All of the power available is dissipated in the source resistance. VS2RL PL = (RS + RL)2 RS VS IL RL 5 Maximum Power Transfer • When RL = , IL = 0 and There is again zero power dissipated in the load resistance. VS IL = , RS + RL PL = IL2 RL RS VS IL RL 6 Power Dissipated in Load Resistance Maximum Power Transfer Load Resistance • For what value of RL is maximum power delivered to RL? 7 Maximum Power Transfer • The power dissipated in the load resistance is: VS2RL 2 –2 PL = 2 = VS RL(RS + RL) (RS + RL) 8 Maximum Power Transfer • To find the maximum power transferred, the derivative of this quantity with respect to RL is placed equal to zero. dPL = VS2 [RL(– 2)(RS + RL) – 3 + (RS + RL) – 2] = 0 dRL 9 Maximum Power Transfer • The quantity in brackets is set equal to zero: 2RL(RS + RL) –3 = (RS + RL) –2 • Solving for RL reveals 2RL = RS + RL RL = RS 10 Maximum Power Transfer • Maximum Power is transferred when the Load Resistances matches the Source Resistance. RS VS IL RL = RS 11 Power Dissipated in Load Resistance Maximum Power Transfer Load Resistance RS = RL 12