The easiest thing would be adding a emitter follower to the opamp. Also not that you need a supply voltage a bit higher than 12V, 15V would be adequate. The opamp should be set to a gain of 2.4 (=12/5)
Unfortunately, I only have 12V power supply and N-channel MOSFET...
I understand that I won't be able to reach 12V on my load. Is 10V doable ?
My OPAMPs are LM358. I can't fin a relation between Vcc and maximum output voltage in the datasheet.
What you are looking for is the parameter called output voltage swing. Its on the bottom of page 5 in this datasheet. http://www.ti.com/lit/ds/symlink/lm158-n.pdf.
I states Min 26v @ 30V supply voltage for Voh. Bipolar op amps have this behavior due to their technology. There are Rail to rail opamps that can swing within mV of supply voltage.
But those R-R outputs are not -really- R-R, as in they are not ideal components. They only get within a few tenths of a volt, and the more current drawn the further they get from the rail.
I am on my way to work, so I don't have time to sketch something up. A P channel MOSFET would work great, as the output of the LM358 would go -low- to cause the output to go high. You'd connect the feedback circuit from the output at the MOSFET drain to the -non-inverting input of the Op Amp, as the MOSFET is acting as an inverting amplifier.
There are a number of "power op amps" that deliver output currents in excess of 1 ampere. Many require dual power supplies but there are some single supply versions. For example, Power Amp Design's PAD117 can supply 15 amps with only a 1.5 volt drop from the power supply voltage. The PAD127 can do likewise with a 30 amp output. http://www.powerampdesign.net/
Here it is. You should put ferrite beads on the leads of the MOSFET. And it wouldn't be a bad idea to put a 10 ohm resistor between the Op Amp and the Gate, as close to the MOSFET as possible. These are to reduce the chances of oscillation.
This should take you right up to 12V, and be able to get down to 0V. Note that the Op Amp must run from the 12V supply.
Please note that, because the MOSFET is inverting, although the input is connected to the inverting input of the Op Amp, the entire circuit is noninverting. So 0V in is 0V out, and 5V in is 12V out.
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