Phase diagrams + OpAmp phase shift specs / phase margin are what you need to predict instability.
-------
EDIT: IMO it's also a lot easier to explain in the frequency domain. At 180-degree phase shift, all your negative feedback turns into positive feedback, causing instability. You need your amplifier to stay as far away from 180-degree phase shift as possible.
I get that what the author was trying to get to with the 'Tape Delay OpAmp' example. But it should be double downed upon and the starting point of the discussion rather than something brought up later IMO.
That said, I agree that if you're used to thinking about things in the frequency domain it makes sense to explain it in those terms. Myself, as a young EE in college found thinking about things in the frequency domain to be useless, in part because I didn't understand the math, and in part because I didn't really understand sinusoidal waveforms. It wasn't until I started diving into SDRs and really unpacking the FFT and how it worked and why did I manage to connect a lot of dots that retroactively gave me a better insight into what my control systems professor was trying to teach me back in the day.
Phase Margin (How far away you are from 180 Phase Shift) is a critical parameter used whenever designing any kind of feedback loop and testing for stability.
This is very to measure at the 0dB gain he pointed out, but lacked the phase diagram to show this shift.
Nonlinear systems responses to a sine signal are in general not just a change in phase and amplitude.
It works if the perturbation stays small and within a linearised version of the dynamics.
Here’s my attempt in a couple of sentences.
It takes time for the signal to propagate from input to output in any real circuit. If that time is a substantial fraction of the period under consideration then the input of the amplifier, which includes the feedback signal, cannot effect the output before it has moved. And if the delay through the amplifier is just wrong relative to the signal period one can end up in a dog chasing its own tail situation and the output oscillates.
The rest is just math. :)
P.S. this explanation also explains why we use phase and not seconds to measure the delay of the circuit. Because everything is relative to the input signal period and if we use phase we get that for free. No extra divide.
When I see people asking questions about op-amps and doing "deep dives" into op-amps, I'm left wondering what's so deep about these things we do in week 2 of EE 101.
I've forgotten almost everything from that class though, so maybe it was just a bad class? I switched majors and never took another EE class.
Part core concept, part outdated nonsense that's taught due to tradition.
If you've got components that can halve a voltage, then by putting that in a feedback loop you can double a voltage.
And you can make an accurate amplifier even if some of your components - like the op-amp's gain - are inaccurate. So long as your voltage-halving components are accurate, your voltage doubler will be accurate whether your op-amp's gain is 10000x or 20000x
You can chuck other components into the feedback loop too - want a higher current output from your voltage doubler? Have the op-amp control a high-power transistor.
You know how a feedback loop can turn a voltage-halver into a voltage-doubler? It can invert other mathematical functions too. Put a capacitor into your op-amp circuit and you can integrator or differentiate. There are even op-amp circuits for summing inputs!
You now understand feedback loops, precise gains, power output stages, integration and differentiation. You can now make a PID controller - a key concept in control theory! Just what you need to position control a robot's joints.
Except making PID controllers out of op-amps is obsolete; they're all done in software these days.
There are entire books about op amps and their uses. They're a cornerstone of analog design.
We started with transistors (BJT and FET) analyzed many types of designs, and only then moved on to op-amps.
You have to appreciate the reason it was invented in Bell Labs: analog computers, which primary applications at that time were in military applications for computing artillery solutions.
Now, as a professional EE, I still think fondly of them, even though I know well about their real life limitations. My advice is to try to stay first at ideal OPAMP abstraction level to appreciate the mathematical usefulness of that abstract construct. This is almost entirely how professionals use them.
I can only lament the educational system, which invariably makes the students miss the forrest for the trees by not presenting well the power of ideal opamp
For those who are not related to the field, what the reported subject here (and destabilizing effect of the negative feedback) is fixed by Black to remedy amp ringing, led to Bell labs, develop frequency domain techniques later analyzed by Nyquist and Bode (also seniors in Bell labs) then made western control theory kick off (then united with the Soviet techniques) and today everybody losing their mind about boosters coming back to base with SpaceX (which was already done a few times historically decades ago).
You will hear the effects of this in many hard clipping distortion circuits, though, where the amplifier gain factor will far exceed the voltage rails and be pushed into undefined clipping territory. Behaviors in this range can be an important part of the sound, e.g. the Proco Rat and the infamous LM308 op amp with its slow slew rate. Some like the TL072 exhibit a really nasty phase inversion that results in a pretty horrific (usually undesired) distortion.
It's a balancing act, though; search "op amp motorboating" in any DIY stompbox forum and you'll find thread after thread of people trying to keep op amp gain stages from oscillating. I know more than a few noisier artists who enjoy when designs can be tortured into doing that, though :)
There's a lot of constraints that either remain due to the restrictive power supply requirements on top of tradition or people building off designs from the 90s that were hand assembled and took BOM golf to the next level.
The op-amp oscillation the article is talking about occurs in the radio frequency range. Tiny parasitic capacitances induce 180° phase shift at some very high frequency where the op-amp's open loop gain has dropped to unity.
You can't hear this directly since it's not in the audio range. It brings about distortion. The amp may pass audio signal, but the oscillation prevents it from performing properly.
I wasn't trying to assert anything about the article, just responding to a comment about desired op amp imperfections in guitar effects. It's fairly common practice to bandwidth limit high gain op amp stages to avoid the issues discussed in the article, amongst other things.
Same with numerical methods. Zero sense of why we had to learn, and I failed spectacularly.
But notice that the Gartner hype cycle is full of unjustifiable hidden assumptions (like the fact that the thing being hyped is useful at all) so it has no predictive power. It only happens that some times people act like that.
Also, there's no guarantee that the society's response to a change will be stable.
0. Any transfer function higher than 2nd order overshoots.
1. Society is super complex, has a ton of internal feedback loops and would easily be higher than 2nd order.
2. So of course it overshoots all the time.
I haven't been able to actually "use" it for anything but it does describe a lot of what we see every day in society.
That's false. Any LTI system higher than first order might overshoot. But it's easy to design high-order systems that don't overshoot. Consider for example a cascade of first-order sections. Related terms: Bessel filter, complex vs real poles, overdamped system.
The above mentioned FM upgrade to VHS, called HI-Fi VHS I believe, had excellent audio recording capabilities. I used it to archive albums back in the day, and when I play some of the warped ones back today, the speaker cone can be seen moving where it would playing the original vinyl.
The way I have always come to understand this boils down to what modulation actually is. DC is not modulation. Anything above DC can be, or maybe technically is and must be managed or accounted for. Frequency drift might be one example.
DC is basically continuous wave and the signaling, if any is intended, is basically limited to turning the wave on or off, or the wave just being present.
The VCR was basically reproducing very low frequency waves. One could see the cones moving in and out with the rotation of the 33 RPM vinyl.
The only other analog device that did something similar was an old vacuum tube reel to reel running a very high tape speed. And the effect was not as dramatic.
Both of those devices could basically archive a CD respectably. The VCR added about 3db and the reel a bit more that I was not in a position to measure.
The most striking things about that ancient reel to reel device were that it was rack mounted with some other gear, EQ, pre-amp, amp, and some other things, and how much better it could really do when using pretty great tape at crazy speeds. The highs would start to roll off pretty high, 18khz or so. The usual was 10 to 12.
That was a very fun old piece of gear. Left over relic from the 60's available for curious high schoolers to tinker with.
A metaphor should be referring to something common, not something that can be made in theory to fit a different set of requirements, but does not really exist.