In various places, e.g. this tutorial video by ti, a circuit like the following is being recommended to drive the analog input of a SAR A/D converter:
The general intention is to ensure that the sampling capacitor of the ADC will be charged with sufficient accuracy by the end of the sampling period. If the source has a sufficiently low impedance, it can be connected directly to the analog input, but otherwise this circuit should be used.
I understand the use of the buffer amplifier, and that it has to be fast enough to settle to the required accuracy within the sampling period. I also understand how to choose the values for the extra RC filter, but I'm not entirely sure about its purpose. So why is it there? And as part of that, why is the recommended value for C1 10x to 20x the value of the sampling capacitor?