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I suppose, this is a continuation of this question: Parallelizing opamps for higher precision

For the moment I'm leaning towards cascading opamps by implementing a Composite Amplifier, albeit a lazy one at it:

enter image description here

While it lands me smack at the intended \$V_{IN}\$, once I lower the resistance of the load to really low values, the opamps starts oscillating:

enter image description here

I suppose this is exactly how the opamps resolves the right \$V_{gate}\$ to have the proper \$I_D = \frac{V_{IN}}{R_{LOAD}}\$; going up & down.

My question is, what exactly is the mathematical function that describes what it happening? I'll figure out how to mitigate this.

In the amplifier, would it be something like (pseudocode, definitely wrong):

\$if \quad V_{IN1} < V_{IN2}:\$

\$ \quad \quad V_{A\_OUT} = V_{IN1} - V_{IN2}\$

\$else \quad if \quad V_{IN1} > V_{IN2}\$:

\$ \quad \quad V_{A\_OUT} = V_{IN1} + V_{IN2}\$

\$else:\$

\$ \quad \quad V_{A\_OUT} = last \quad V_{A\_OUT}\$ (hysteresis)

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    \$\begingroup\$ Maybe learn to build an amplifier with one op-amp before worrying about cascading them. It does not appear as if you know what you are actually trying to do. It looks like you are just chaining outputs to inputs and hoping something happens. It does not appear as though you even understand how an op-amp buffer works. \$\endgroup\$
    – DKNguyen
    Jul 31 at 2:08
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    \$\begingroup\$ Why do you want to use more than one op-amp? A single op-amp can give you far better accuracy than likely need (ppm) especially without special considerations regarding the source resistor. As far as stability, even a single op-amp can easily oscillate in this configuration with such a low R11 and the gate capacitive loading. \$\endgroup\$ Jul 31 at 2:13
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    \$\begingroup\$ You are not building anything, just playing with spice. Getting usable results out of spice when ppm-level precision is your goal requires lots of hard core understanding, and even experts find it somewhat tedious. Put together some actual circuits and get the T&M equipment needed to measure things. The questions you pose are a veritable Quixotic pursuit: you're fighting imaginary dragons that are just windmills. Actual op-amps in real precision circuits don't have the problems you imagine they do. \$\endgroup\$ Jul 31 at 3:49
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    \$\begingroup\$ With a decent precision op-amp, on a properly laid out circuit on a PCB (no, breadboards won't do the trick unless you're super careful) you'll need a 6.5 digit voltmeter just to measure the errors in the non-composite circuit. Right now you're just guessing at imaginary errors. For driving 6A into a 1 ohm load, the IRF530 mosfet is the wrong part as well - its output resistance degrades the dynamic response and cuts the usable bandwidth. For precision and good transient response in such a circuit, you want the output resistance to be in the <10mohm range. \$\endgroup\$ Jul 31 at 3:53
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    \$\begingroup\$ You've also not shown what model of the op-amp you're using in the spice model. It's sorta-kinda the most important thing to even begin to figure out what's going on here. Most likely you've just chosen an entirely wrong op-amp for the job, and are trying to work around its limitations. You'll have much better luck using a part that's designed for the job and precision level you have in mind. And even fairly "lousy" decades-old op-amps would work in a non-composite circuit, or perhaps one with just a modest fixed 2nd gain stage - say 10 to 100. \$\endgroup\$ Jul 31 at 3:55

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1 microvolt on an output voltage range of 10V is 0.1ppm. That's firmly in the 7.5-digit voltmeter territory. Whatever you're getting from SPICE for such requirements is pure fantasy, since in an actual circuit all the parasitic effects will play a major role, and you are modelling none of them. Just thermal gradients alone will kill the performance if you're not careful, even if you had an ideal op-amp.

To explore this area, you want to head to the volt-nuts mailing list and its archives, and spend a couple weeks-months of evenings doing serious reading to get some idea of what even is involved just to measure that sort of performance. If you can't measure it, then any efforts at designing will be mostly pointless, since you won't have any idea if your design does the right thing. Yes, SPICE modelling of precision circuits in the 0.1ppm territory is possible, but it requires lots of work, and good working understanding of SPICE modelling. And a very good understanding of the physical implementation circuit being modelled. For a beginner it's not any easier than putting together an actual physical circuit - in fact, it's much, much harder.

I think you are simply misunderstanding where the problems are. They are not in the op-amp. They are, for example, in the expensive interconnect hardware needed to even accurately measure voltages to 0.1ppm level accurately and reproducibly. Just the metrological technique needed to get the same result every time you measure is a skill in itself.

The heat the mosfet will be giving off, and the thermal gradients it generates in the enclosure, will be enough to make 0.1ppm a fantasy, even 1ppm would be a fantasy.

Making such a circuit actually work will require lots of learning for you, and it's not an easy task, and definitely not something I'd suggest a beginner undertake. It's like someone who never played any keyboard instrument wanting to start by playing Chopin's Revolutionary Etude. Sure, you can get there eventually, it's possible after all, but it will take years of work.

So, any idea that you have identified a problem that needs fixing, is also fantastic at the moment. If you want to know where the actual problems that need fixing are, read publications by people and institutions doing research on the Volt standard and related metrology.

Try and get something physical - not a SPICE simulation - that works to 1mV precision over +/-10V output range. That's one-in-20,000 or 50ppm precision. Learn to measure its performance across typical operating temperature range, say 0-50C or something like that. Ensure your results are reproducible, and that you know where all the errors come from, and that you can measure their contributions individually - or at least at some finer level of detail than just "the voltmeter is off by 0.5mV" observation. Then you can try for 10ppm. Once you got that figured out and it is robust, go for 1ppm. And only then even start thinking about 0.1ppm.

To measure voltages down to 0.1ppm, it will be expensive no matter what. Just the cables and interconnect hardware. And you'll need an air-conditioned space with a stable temperature. An underground karst cavern where temperature is fairly stable at 12C may work well if an above-ground location is not available, although bringing a lab down into a cavern is not cheap either... But at least you could bring a car battery, an inverter, a precision voltmeter, interconnects, and the device-under-test, and do stable measurements. Given the temperature difference from above-ground/indoors, the equipment will need a week+ to stabilize at least. Everything will drift like crazy in the first days... And also, if the cavern is not open to the public, forget about going into one without training and equipment needed to do it safely (PPE, gas detectors, etc. - none of it cheap).

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