Maximum Power Transfer Theory for Circuit Example

[Ratchit]

You're working on a fixed value for R2. If R2 changes so must the voltage across it.

OK, then you can make the power transferred anything you want by changing R2. But, then you cannot say that there is particular value of R2 that transfers maximum power.

Ratch

 

[ACharnley]

I may have it.

 

[ACharnley]

Wishful thinking.

 

[Ratchit]

I may have it.

Can't do that. Thevenin's theorem relies on linearity. Power is not linear. Solving by the current division theorem I get greatest power of 45 W at R = 5 ohms.

Ratch

 

[crutschow]

that is true enough though irrelevant for the course of computation. It is best to forget the current source and work with the LCR impedance.

No it's not. It's totally relevant.
Do you not understand what has been said about a current source?
You can't "forget the current source" in that circuit.

Since you seem to think you know the answers than stop wasting our time asking questions from the rest of us who do know the answers but you refuse to believe them.

 

[ACharnley]

I don't know the answer, I have provided the data and hope someone with knowledge of max power transfer theory can assist. I know for a fact it is possible.

If you know the answer - state it.

 

[ACharnley]

Have a read.

 

[The Electrician]

Have a read.

The circuit in this zip file does have a maximum power delivered to the load, because its source is a voltage source, not a current source. This makes all the difference. The circuit you showed in the first post has a current source, not a voltage source. Because of this, there is no maximum of delivered power. The larger the load resistance, the larger the power. There is never a value of load resistor above which the power decreases. As long as the load resistor gets larger, the delivered power gets larger. This is a consequence of the fact that the source in post #1 is a current source.

 

[ACharnley]

It is NOT a voltage source. It is a dynamo, fixed current with voltage varying by frequency.

 

[The Electrician]

It is NOT a voltage source. It is a dynamo, fixed current with voltage varying by frequency.

In Figure 6 of that zip file, a symbol labeled Vg is shown; that is the symbol for an ideal voltage source. In post #1 you have a symbol labeled V3 which in post #3 you said is a current source.

 

[ACharnley]

It does, though voltage is dependant on frequency and impedence, impedence being relatively constant (other than eddies) so that voltage is directly related to frequency. So for the two equations that matter, Vg would have to be determined for a given frequency.

The second equation has removed the source current/voltage, it must be using the maximum power transfer theory. I have all those values and if I could get the thing to work (I have tried and retried) then knowing current is fixed, the ideal Rl equivalent duty cycle could be determined.

Notice how it's missing right hand brackets, does that mean default them to the EOL?

 

[The Electrician]

The circuit shown in Figure 7a does have an optimum RL (because Vg is a voltage source, not a current source) which will result in maximum power delivered to RL.

If we calculate the Thevenin impedance (Rth) seen by RL in Figure 7a, we will find that it is a complex value. The maximum power theorem says that for maximum power transfer, the load impedance must be the conjugate of Rth. But in this case RL is not an impedance with both a real and an imaginary part--it is a pure real impedance, just a resistance.

The maximum power transfer theorem also says that if the load impedance must be pure real, its value for maximum power transfer (in this pure real load case) is equal to the magnitude of the Thevenin impedance. The magnitude of the Thevenin impedance is given by the square root of the sum of the squares of the real and imaginary parts of the Thevenin impedance. That is what equation 6 is trying to show, but as you have noticed, it's not all there.

The result I get is:

 

[ACharnley]

Coffee made, about to get on it - should be interesting making it work with the PIC16!

Re: 7a I don't know how/why it's possible to use the current source as a voltage source, at a guess knowing the impedance at a given frequency it's derived from that? (I would have expected it to form part of that equation though).

Any chance you can explain how you derived that final equation? It will probably help with the below...

My fragmented understanding

"The maximum power transfer theorem also says that if the load impedance must be pure real, its value for maximum power transfer (in this pure real load case) is equal to the magnitude of the Thevenin impedance"

Which is saying for maximum transfer the impedence of LCR (which I've worked out in the spreadsheet) is equal to the real value of Rl?

 

[ACharnley]

What's L and Lg (same thing?)

 

[The Electrician]

What's L and Lg (same thing?)

What L are you referring to? If you mean the L in CL, I just was too lazy to use a subscripted L in CL, where CL is the capacitor in Figure 7a

 

[The Electrician]

Coffee made, about to get on it - should be interesting making it work with the PIC16!

Re: 7a I don't know how/why it's possible to use the current source as a voltage source, at a guess knowing the impedance at a given frequency it's derived from that? (I would have expected it to form part of that equation though).

Any chance you can explain how you derived that final equation? It will probably help with the below...

For this to work, Vg must be a voltage source. Even though the current at a given frequency and value of RL is fixed, the general expression for the optimum load resistance can only be derived by assuming Vg is a voltage source during the calculation.

My fragmented understanding

"The maximum power transfer theorem also says that if the load impedance must be pure real, its value for maximum power transfer (in this pure real load case) is equal to the magnitude of the Thevenin impedance"

Which is saying for maximum transfer the impedence of LCR (which I've worked out in the spreadsheet) is equal to the real value of Rl?

Yes

 

[ACharnley]

It appears to be working (ignore the wattage column which I don't believe I can calculate).

I'll need another coffee tomorrow morning, then it's being implemented in the PIC without floats.

I'll write more tomorrow, and I'm going to PM you for sending over some beer tokens.