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I have understood that there are both input and output parasitic capacitances in real op-amps, but I am trying to understand why they are there.

As for the input capacitance, there are two types:

  • Differential: it is the parasitic capacitance between the inverting and non-inverting pins of an op amp
  • Common-mode: it is the parasitic capacitance between each input pin and ground.

    1. Is that right?
    2. For the output capacitance, I don't know where it comes from.
    3. Also, I understand that this capacitances are almost always neglected, but they may affect our circuit if the frequency becomes extremely large, right?
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Common-mode: it is the parasitic capacitance between each input pin and ground.

Is that right?

Yes.

All insulators, regardless of distance and composition, will impart some capacitance to a conductor (even in a vacuum.)

Any two conductors will have some capacitance between them, even in a vacuum. Insulators other than a vacuum result in more capacitance. Very, very slightly more in the case of air, significantly more in the case of plastics and such like (several times more). The ratio to that of a vacuum is often called the dielectric constant but better called the relative permittivity \$\epsilon_r\$.

Also, I understand that this capacitances are almost always neglected, but they may affect our circuit if the frequency becomes extremely large, right?

Not correct. Input capacitance can affect the circuit even at low frequencies, if the feedback resistance is high enough. For example, an input capacitance of 10pF with a 10M\$\Omega\$ feedback resistor has a pole at 1.6kHz, so it's pretty easy to make an op-amp amplifier oscillate when there is a high-value feedback resistor.

This is a common issue in circuits designed to work from very low current, and is compounded by some op-amp designs that use scores of interdigitated input MOSFETs in parallel to minimize Vos.

Output capacitances are part of the transistor structure and also caused by the geometry of the IC package and the conductors on the PCB etc. Too much output capacitance on an op-amp output can cause oscillation. Most op-amps are specified for phase margin with some reasonable amount of output load capacitance (in addition to whatever is internal to the IC), but excessive added capacitance (such as driving a few meters of cable without series resistance) can result in oscillation. The oscillation may be relatively high frequency (since the output resistance of the op-amp is generally in the 100-1000\$\Omega\$ range) but your amplifier circuit may only be designed for low frequencies or even DC.

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