adding two 12 bit dacs does not give you 24 bits ...
Adding DAC + DAC, no. Using a voltage divider yes. The fine DAC does the same range as one step on the course DAC. You end up with for example 256 steps per each of the 256 steps resulting in 65536 or 16 bits from two 8 bit DAC's. Alignment appears to be a bitch however.
besides why do you need so many bits ? shall we take a look at the absurdity ?
10 bit is 1024 steps so 12 bits 4096 steps. Assuming you make a supply that does 0 to 20 volts this gives you 5 millivolt per step. You'll have to have a killer regulation system to get the output noise of the supply be below 10mV peak/peak under all load and line conditions... so your step size is already below the noise band. useless...
Even if you were to do a weighted system using two dacs /.. how do you handle the non-monotonicity of the DAC (INL/DNL). any attempt to 'jiggle' between steps will create random behavior. So this approach fails as well.
Mostly because it's interesting to be able to do so. The analog portion has proven very clean and stable. Linear of course which sits around 1mv with a light load. For the jitter you have to use a latched synchronous update DAC or in this case two DAC's in one chip. The voltages present themselves to the divider at the same time. Well close enough not to matter. I agree if you updated one DAC and then the other you'll have lots of jitter.
You use an Lt431 as reference ? that's not a reference .... if you want any kind of precision from your adc or dac start looking at real reference chips.
Without a doubt, amazingly I've been able to get a few of these shunt regulators to maintain the last digit on my 3457 for hours on end. 98% of them however don't. Long term, no they are complete junk.
As for the ADC. get a microcontroller like an ADuC8xx series or a Silabs 900 series. Those come with 24 bit ADC's on board... and matching references. These micros are relatively cheap and have differential input stages so you can sense where it matters.
I've been working with PIC's for too long to change up now. External components will need to do. Keep in mind also that this is an exercise in being cheap, not one of precision. It's getting more then you normally would out of little or no extra money.
Now, here is the same problem as with the DAC : the noise band of the PSU ...
Agreed, any extra resolution will just end up adding to the noise band offsetting the net average. It's all linear, so at least it has a fighting chance. In the end it's all gravy and interesting none the less. Now picture the same supply slowing charging a large cap through a resistor, would the extra 1uV of voltage show up ? Hmm.
Jeff