In the following circuit, for a Twin-T notch filter, the author is using an additional inverting op-amp for the T-filter "feedback", that is connected to a potentiometer (pot).
Image credit: here
Why are they using this extra opamp instead of just the pot or fixed voltage divider circuit?
UPDATE:
I see there are some good info from the answers of this question:
Answer
As the pot is varied, the effective resistance 'seen' by the bottom of the twin T circuit will vary if the feedback amplifier is not present, changing the frequency response of the circuit.
Even for a fixed voltage divider, the analysis would be complicated by the effective resistance; using an amplifier means it does not have to be considered.
The amount of variation if the amplifier were not present will depend on the ratio of the effective feedback resistance to the resistors used in the main twin T section. A relatively small feedback resistance will cause a small variation, but to get the notch back to normal would require varying all the resistors to maintain the necessary ratios.
The use of a buffer amplifier means that the driving impedance from the feedback path will remain very low (and consistent) for all potentiometer settings.
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