This is a variable Q notch design with a bit of gain. (example below 1.2dB) Here you can adjust the BW(-3dB) from 240 Hz (Q<<1) down to 0.5 Hz at unity gain for fc=60 Hz with a Q=120.
This is what a variable Q notch looks like:
-3dB BW or Q can be increased significantly with positive feedback from the OpAmp to the return current, so it is negative feedback. This reduces the passband Bandwidth (BWp) while at the same time reducing the bandstop, BWs.
1st consider tolerances of the passive filter.
There are trade-offs between depth of Q and BW.
The result is that at one frequency, the signal on the HPF side cancels out only with perfectly matched parts on the LPF side. For example, if only 1 parts value changes 1%, the notch rises to -30dB and shifts the notch frequency slightly.
But worse, the attenuation starts long before and after the notch frequency, when the impedance of each cap matches the resistance as a voltage divider.
So while you might have a notch of -40 dB, the actual passband can be very wide. Using -3dB half-power as a reference, this filter has its passband between
4 - 253 Hz. Thus it appears to have a low Q passband but a deep notch.
2nd consider the positive feedback and non-inverting gain effects of the OpAmp and pot.
With a gain of
Av = 2 = 6 dB, the filter response is almost the same as the passive filter except with gain. As the gain is reduced, the -3dB passband BW is also reduced giving an apparent increase in Q or filter shape factor.
To optimize this filter, you must choose realistic pass
BWp(-3dB) and stop
BWs(-30dB) for a given center frequency. Expecting more requires more stages or tweaking of R.
Also note that:
- I only needed 1 OpAmp!
- To reduce OpAmp drive current, change all R's to kΩ and all C's from μF to nF. (This has no other effects, other than raising the input impedance.)