Here is example of an active waveform-inverting low-pass-filter with a stop-band problem; notice the input pulse appears (initially) as part of the output waveform, not what we expect from a low-pass-filter. The initial pulse-leakage into Output Wave is 240 milliVolts.
Here is the circuit: the OpAmp is slow, only 1MHz UGBW by default (we'll later return to this menu and edit UGBW to 10MHz), and the OpAmp has a high Rout of 1,000 Ohms (typical values are 100 ohms). Notice at lower left, the C1 is not enabled.
What is going on? At the higher frequencies, the opAmp is unable to control Vout, because charge passing through the "Cf" path is stronger than the opamp.
What is cure? (1) Turn on (in the simulator) the very first capacitor, the C1 at junction of the first 2 resistors. (2) Use a faster opamp.
Here is the benefit of C1 in place. The initial pulse-leakage is 13 milliVolts.
What if we use a faster OpAmp (almost guaranteed to consume more power)?
Here is 10x faster OpAmp, with C1 turned off.
Here is that same fast OpAmp, with C1 on, and Rout reduced to 100 Ohms; notice the pulse-leakage is "invisible":
Here is the frequency response for Fast OpAmp, C1 enabled, Rout of 100 Ohms; see how the BODE rolloff is very very close to perfect 1_pole rolloff (that is, straight line fit to 6dB/octave once past 1Mhz; there is a tiny rise at 100MHz, but only a couple db, quite unlike the 20dB rise in the prior BODE):
We encountered this "noise reduction" challenge some years back, for a client's touchscreen product. The column-drivers were magnetically coupling into the top 1/4 of the Y-axis pickup loops. The signal conditioning already had a good GND plane and bypass caps. Turns out the cure was to split the Rin into 2 resistors and add that "T" cap (C1) to keep the very fast transient energy off the Virtual Gnd node of the OpAmp LPF. The solution was so useful, we included it as 1 of the 13 Examples in the tool.