I'm investigating maximum power transfer in a AC circuit

[djstar]

Hi,

I'm investigating maximum power transfer in a AC circuit. I understand that for maximum power transfer the reactance both cancel each other out and the value of the source resistance and load resistance have to be equal. I have also found some formulas to prove this.

what i would like to know is why when either the source inductance or load capacitance is increased the value for the maximum power transfer is different. I have produced some graphs from a simulation. with Xl=Xc, Xl doubled and Xc doubled.

when Xl=Xc the maximum power is when the resistors are the same. If I keep the resistors the same and double either of the reactance the maximum power is less and happens at a higher resistance. why is this?

many thanks

 

[Ratch]

djstar,

I understand that for maximum power transfer the reactance both cancel each other out and the value of the source resistance and load resistance have to be equal.

For a unchangable source generator, the max power transfer occurs when the load immitance is the conjugate of the generator immitance. If a conjugate match cannot be attained, the highest power transfer occurs when the magnitude of the load immitance equals the magnitude of the source immitance.

what i would like to know is why when either the source inductance or load capacitance is increased the value for the maximum power transfer is different. I have produced some graphs from a simulation. with Xl=Xc, Xl doubled and Xc doubled.

Power transfer is determined by how much the voltage and current are in phase with each other. The reactance of the circuit determines the phase between the voltage and current. Therefore, the reactance also determines the power transferred.

when Xl=Xc the maximum power is when the resistors are the same. If I keep the resistors the same and double either of the reactance the maximum power is less and happens at a higher resistance. why is this?

See above. The conjugates of the source generator and the load do not match. Therefore the power transferred will be lower.


A higher max power transfer will be attained if the source immitance can be lowered.

Ratch

 

[djstar]

Hi Ratch,

Thanks for the quick reply. Its all starting to make sense now. i understand the maximum power is a lot less because the current and voltage is out of phase. However the only thing I'm still unclear on is that the maximum power is transferred when the source resistor is 1k ohm and the load resistor is 1.3k ohm? i know it must be with the doubling of the reactance but is there any formula I could use to find out what load resistor i would need.?

 

[Carl Pugh]

Are you aware that when maximum power transfer occurs, the efficiency is only 50%?
For good efficiency the source resistance should be less than the load resistance.

 

[Ratch]

djstar,


Define symbolically load reactance as Xl, source reactance as Xs, source resistance as Rs, and load resistance as Rl.

The maximum power transfer occurs when the load is the conjugate of the source. This is called a conjugate match.

If Rl is fixed, then the max power transfer occurs at jXl = (jXs)* , where "*" means the conjugate. This is called a reactance conjugate match, and is the second highest power transfer that can be attained.

If Xl is fixed, but Rl can be changed, then the max power transfer occurs when Rl = |Rs+j(Xs+Xl)| . This is called a magnitude match, and is the third highest power transfer that can be attained.

Ratch