It is exactly the combined feedback approach that made this video so useful to me: it simply hadn't occurred to me before, but now makes very much sense.
I consider the one on the input side as the "outer" opamp, and the one on the output side as the "inner" opamp, to intuitively understand how the feedback works, and what the limitations of the combined system are.
As a first approximation for the entire system, the "outer" opamp's noise and accuracy/drift dominates the combined system, but is "supported" by the "inner" opamp especially in slew rate and amplification (by taking part of the burden from the "outer" one).
Even if one uses ideal opamp models in spice (KiCAD/ngspice has a OPAMP model in the Simulation_SPICE section), modeling noise using input and output referred voltage signals, shows directly how the outer input-referred noise gets amplified by both opamps, but outer output-referred and inner input-referred noise only by the inner opamp, giving a rough idea how amplification should be divided between the two opamps. Of course, real-world properties, especially noise (not being purely input- or output-referred) and gain-bandwidth product, affects that somewhat so simulation with appropriate models will yield much better results; point being that even super-simplifying the situation one gets pretty good starting points: no black magic here.
I'm particularly interested in the case of using opamp output to control the gate or base of a transistor, with feedback across both the transistor and the opamp. In that case, the "inner" one is a transistor "amplifier" instead of an opamp, but the same intuitive model still applies just fine.
In the Art of Electronics, figure 4.29 shows a feedback voltage regulator using this scheme, but I'm even more interested in voltage-controlled constant current sources (in the 0-120mA range) with PWM/PDM capability for flicker-free display backlight LEDs. (This allows one to choose between constant current-controlled LED drive which can affect the color at lower currents, and PWM/PDM at specific current designed to optimize color output and backlight lifetime, at run time, with just microcontroller firmware changes.)
Manipulating the feedback, or the transistor base/gate, seem both workable options for this. I haven't simulated this yet, because I'm still looking at components I can both obtain easily but also use in KiCAD/ngspice simulations, but it definitely opened up an easy way to approach the underlying problem at a conceptual level without just copying suggested schematics and trying to understand how they work.
Attached is a Burr-brown Application note on Composite amplifiers.
Thanks! Figures 1 to 4 confirm to me my new understanding is correct to at least the first approximation, while showing how much the exact details affect the combined system –– that is, that modeling and practical experimentation is necessary to verify and optimize the first approximation.
Stability/oscillations is always a bit of an issue in feedback-based systems, but to me, a hobbyist, grasping the basic feedback path makes it much less scary, more like an issue to watch for.
Compare to e.g. linear voltage regulators that require a specific load and capacitance to not oscillate. To me,
those are black boxes. I basically have to estimate the minimum and maximum load and capacitance of the rest of my system. All those supply bypass capacitors do add up quickly even in relatively simple microcontroller projects; and then their spiky or pwm/pdm-like current draw –– switching noise in MCUs and OLED displays being worst offenders –– means someone like me without enough practical experience cannot ever be sure before testing and measuring the worst case conditions in practice.
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