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The ideal op-amp in open loop, has a frequency response with infinite bandwidth. What about an ideal op amp in closed loop (inverting, non-inverting etc.) configuration? Does it (still being an ideal op amp although now in closed loop) also have a frequency response with infinite bandwidth?

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Yes, if the other components are ideal too and there is no parasitic capacitance, series inductance, etc. With these effects, every resistor has a non-flat frequency response. Since your feedback path will contain resistors, the frequency response will likewise be non-flat.

Then there are other considerations depending on how obsessive you want to get. Regardless of how ideal the opamp may be, there will be some finite propagation time of the feedback signal back to a opamp input. This represents a different phase shift at different frequencies, which will again make the frequency response non-flat and can make the whole system unstable.

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The following answer considers practical aspects only (and neglects parasitic influences like signal delay, propagation time, node capacitances, etc.):

  • If the opamp unit is considered to be ideal (infinite open-loop gain with infinite bandwidth), also the closed-loop gain has an infinite bandwidth. For real circuits, of course, this is not the case.
  • However, in many cases the following approach gives good results with sufficient accuracy: For closed-loop gain calculations the open-loop gain is considered to be infinite. However, this approach applies up to a certain frequency limit fc only. This limit is set by the real gain-bandwidth product (GBW) which is given in the data sheets. For most opamp types (unity-gain stable) this figure is identical with the frequency (transit frequency ft) for which the open-loop gain Aol of the opamp is unity (0 dB).
  • This frequency limit fc (3dB cut-off frequency of the closed-loop gain Acl) is determined by the mentioned GBW figure: fc=GBW/Acl=ft/Acl
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