I have a power source that has an internal resistance. I want to connect it to a battery but in order to get maximum power output, I need to match the internal resistance of the power source with the load resistance. As a rule, when load matched, the open circuit voltage should be double the load voltage.
In order to acheive this I want to read the open circuit voltage of the power source and apply a variable resistance (using a junction FET) so that the loaded voltage is half the open circuit voltage.
Is the next step forward to read the OC voltage, then apply a voltage to the gate of the JFET so that the load voltage is 0.5Voc. Hold this for 5 seconds and then re-read the Voc?
Also I am trying to use minium power in load matching. Preferrably I want the max power to go into the battery so the less power consumed in load matching the better. Can anybody suggest a better method?
What is this "power source" you speak of? Sources rarely have constant internal resistance over their entire current range.
Why do you want maximum power output? Apart from being an interesting theoretical value, charging a battery has nothing to do with maximum power transfer but everything to do with properly following a battery's recommended charging profile.
Let's get these out of the way first and consider your other questions later
Be RB the internal resistance of the battery (not constant, beut depending on the charge level!) to be charged, then the current IB has to limited so that
IBIBRB does not exceed a certain value, because much of it will be converted into heat. Some chargers try to measure the temparature to learn whether they are still on the safe side... Some use current pulses to allow a cool-down. This does not change anything to the fact, the the current is limited, and so the voltage to be applied is
UB = RB*IB
There is no further degree of freedom in this process....
The current source of course can be designed to be "most efficient" in providing UB @IB. This will mean that its "natural" internal resistance should be the same as that of the battery to be charged.
The power source is a thermoelectric module. It's internal resistance varies with temperature difference. In order to get maximum power from the thermoelectric module you must match the internal resistance to the load resistance. In our case the load is a battery plus a circuit. This circuit will be variable in resistance in order to match the internal resistance of the module.
Sorry this seems to be over my head.....
You generally model a "real source" by an ideal voltage source and an internal resistor Ri. (You can also model a current source...)
When you draw current from that source the terminal voltage sadly drops down (to zero in case of a shortcut). Maximum power (=IV = II*Ri) is sucked when the terminal voltage is half of the OCV. This is a consequence of the "I square" in the formula, given that Ri is a constant.
Though this is the maximum does not necessarily mean that this is an "optimum" in a more comprehensive context.... You generally want to have current at the best possible voltage (or voltage at the best possible current).....
To add dissipating resistance (by FET or whatever) seems a foolish act at the first glance...
To add dissipating resistance (by FET or whatever) seems a foolish act at the first glance...
And second, and third, and...
Indeed, the point is (usually) not to create the condition for which the rate of transfer of energy is maximum. See Footnote.
We (usually) want the application circuit to suck energy out of the battery until it can't give any more. That is, until its output voltage falls below our minimum requirements.
Unless the object is to heat the environment, dissipating energy with an external resistor, FET, or whatever, reduces the amount that is available for use by the real application device. In other words, we want to reduce the resistance in the leads (and connectors, etc.) going to the device to minimize the amount of energy is wasted in heating stuff up. We certainly don't want to put an additional external dissipative device anywhere.
Regards,
Dave
Footnote:
One application that might lead us to want maximum energy transfer rate is if we want to discharge the battery as fast as possible. An "active load" could sense the battery voltage and current and use that to continuously adjust itself to present an effective resistance that is equal to the (changing) internal resistance of the battery. I don't know if it would be worth it (compared with just attaching some big dissipative load), but it might be possible.
I mean I think it could be done, but I believe that typical active-load battery testers (used to characterize a battery's charge/discharge performance) don't try to achieve maximum energy transfer rate; they adjust their active load to maintain a constant current as the battery decreases during the discharge cycle.
Since most applications do not want to discharge the battery as fast as possible...well, I hope you get the point.
This circuit will be variable in resistance in order to match the internal resistance of the module.
If this variability is just burning off the excess power then you are not really optimising anything, let alone getting the maximum power from your generator.