And had some ideas. First, I don't think a microcontroller is the best way to go. Reason is, resolution * time are fixed: for PWM, to get more resolution, you need to chop the pulse period into more divisions, which forces you to lower the pulse frequency. At some point it will be too low. At least it will make the settling time of the feedback loop way too long. Most microcontrollers don't have a D/A at all, and those that do, it isn't likely to be better than 12 bits. I have seen 14, but it's rare.
That schematic is a nice beginning, but I think the current mirror is a good idea, for the stated reason. If the resistance of the coil changes in the current design, the calibration will go to hell. My only complaint about a current mirror is that the one shown probably doesn't have a high enough output resistance to support a 16 or 24 bit range, plus it will have base current error (due to it being made out of bipolar transistors). I would recommend an op-amp current pump (schematic later, I promise), degenerated by a high-precision, temperature compensated resistor. Such things can be bought or found. Maybe I can break out my Pease and see how an easy one might be constructed. It all depends how far you want to go. And anyway, why not go all out and close the feedback loop in analog? I am certain it will be better and more accurate than any digital implementation. I've been thinking about how to do this for a while. Probably the easiest way would bee to mount a small LED on the scale end (too heavy?) and have two photodiodes, one above, one below. Then make a voltage divider reference, and put them as the inputs to an op-amp. Maybe one op-amp could do the transimpedance and current driving, I would use 2. That would be a dual package, still cheap...and then...use a chopper and feed it to your computer's sound card or something. *heh* That would be awfully interesting way of doing DAQ. This is probably too confusing...I will try to figure a way of drawing a schematic for everybody...sorry, electronics can be hard in words...
And here is one last idea for you: If you buy some wire, say very pure metal, or metal of known composition (nichrome), you should be able to calculate its resistivity (ohms per cm^3). Then, if you measure the resistance of a precisely measured, looooong piece (wire, for example), you should be able to calculate very accurately its diameter, and thus, its mass. This, without a micrometer. So a little math can substitute for a little expensive equipment. Just make sure that wire is uniform...
Hope this helps