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In a voltage follower circuit with negative feedback like the one below:

enter image description here

How would the transient response of Vout look? My guess would be that if Vout is initially at 0V, when Vin is applied to the non-inverting terminal, the output voltage would spike and this would be fed back into the inverting terminal leading to a large negative voltage voltage at the output and this will be fed back again and this pattern will keep happening until the output voltage reaches steady state. So the output will oscillate for a short period of time before stabilizing? Is this how a voltage follower circuit would work in real life?

Is the way to counteract this effect to use a capacitor at the output?

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So the output will oscillate for a short period of time before stabilizing? Is this how a voltage follower circuit would work in real life?

Some op-amps will and some won't. It depends on the internal compensation inside the op-amp. It also depends on the loading of the output, the values of any feedback resistors and parasitic capacitance around the pins.

Any op-amp data sheet worth its salt will have transient response curves showing what you might get for your money.

Is the way to counteract this effect to use a capacitor at the output?

No, absolutely not - that will likely make things worse and push the op-amp to turn into an oscillator. OK some need only a few pF of loading capacitance for this to happen and some need several nano farads. Pretty much all of them will behave once the loading capacitance has reach into the micro farad region but, by then the op-amp is as slow as mud.

Any op-amp data sheet worth its salt will have details about maximum loading capacitance showing what you might get for your money.

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