How to properly compensate a composite OP that aims for high open loop gain?

[Echo88]

Im trying to increase the open loop gain and therefore decrease the dc gain error of a unity gain buffer, in this case i want more open loop gain from a OPA140 (126dB, i aim for more than 140dB -> G=1, DC-error <0.1ppm).
But so far i fail to properly compensate this unity gain composite amplifier as i only could find ressource that deal with inverting/noninverting amplifiers like for example: https://www.renesas.com/en/document/apn/r13an0002-composite-amplifier-design-high-gain-applications-read2302-and-isl28134
How is it done properly with a unity gain buffer when the input OP is for example a OPA140?
I could of course use the ADA4625-1 (which is included in LTSpice and therefore used here for simplicity instead of the OPA140) with its better specs, but then i wont learn how to properly compensate said composite amplifier for future projects.
Attached are some tests in LTSpice that i did to get more familiar with it.

[magic]

Dunno, something like that perhaps? At high frequencies, U1 is simply an inverting amplifier, driving the noninverting input of U2, which runs open loop. At low frequencies it's an integrator, adding extra loop gain.

First, set the ratio R2/R1 so that overall forward gain falls below unity earlier than phase response deteriorates unacceptably. I suppose it should be doable? Then insert C1 and tweak it to get the most gain at low frequencies without compromising stability.

Note that performance will never be better than U1 input stage. For OPA140, this means up to 120μV offset and up to 1μV/°C drift, which may easily cause more DC error than a deficit of loop gain

If you switch to a chopper, you will usually get more than 140dB DC gain for free and no need for tricks.

[Kleinstein]

The open loop gain is only one limitation to a buffer. There is also the limited CMRR.

To improve on both, bootstrapping the supply can be a way to go. This could be true bootstrapping from the output side for lowest input current or a more feed forward driven supply from the input for a bit easier stability and often better bandwidth.
For the case with gain an additional 3rd OP-amps like in a compound configuration allows for the full swing at the output.

An AZ amplifier can indeed be the simpler solution.

[magic]

Dunno, something like that perhaps? At high frequencies, U1 is simply an inverting amplifier, driving the noninverting input of U2, which runs open loop. At low frequencies it's an integrator, adding extra loop gain.

Sorry, forget it. I tried actually running this simulation - it doesn't really work as advertised and I'm not sure how to fix.

[David Hess]

magic shows how it can be done, although I would configure U2 for a fixed gain.

Bootstrapping to improve common mode rejection of a follower helps, like Kleinstein suggests.

Low frequency open loop gain is limited by thermal feedback from the output stage to the input stage, so an easy way to improve it is to unload the output of the operational amplifier with a separate buffer, which could be as simple as an emitter follower.  Sometimes a JFET is used to lower the change in the output current even further.

[magic]

No, I showed how to shoot yourself in the foot

Problem is that the midpoint between U1 and U2 is effectively a virtual ground, so R2+C1 load the feedback resistor R1, resulting in more than unity closed loop gain at high frequencies where C1 impedance is comparatively low. That's not exactly a voltage follower anymore.

It can be fixed by "bootstrapping" the midpoint, by connecting U2 IN- to the input signal, but then U1 has to produce the same swing as U2 and requires the same error voltage at its inputs, hence open loop gain is no longer improved over the baseline single opamp case. But this scheme still appears to improve correction of U2 output stage errors, so perhaps it could have some value for audio and such.

This is all because I tried to be clever and use feedback to control U1's contribution to overall loop gain. People actually build high-gain composites, but they usually use passive RC networks between the opamps to shape frequency response. Maybe for good reason. Look up Samuel Groner's "Low-Distortion, Low-Noise Composite Operational Amplifier" for an example of that.

edit
OK, let's switch the roles and put low-frequency integrator / high-frequency follower feedback network around U2 while running U1 open loop. This appears to be better, at least in sim.
Any ideas if something may still be wrong with it?