Differences between notch filter designs - use of op-amps

Question

I have a question about notch filter designs using op-amps and I hope that you can help.

Following this tutorial https://www.electronics-tutorials.ws/filter/band-stop-filter.html, they give examples of different notch filter designs. I'm interested in the designs using 1 and 2 op-amps:

Circuit 1:

Circuit 2:

Besides the fact that values for the resistors and capacitors have been introduced in circuit 2, what is the difference between having one and two op-amps connected in this fashion? What does A2 add to the circuit? It has something to do with the feedback, but I'm not sure how it's affecting the circuit.

As a note, I'd like to know more about these circuit elements and be able to figure these things out on my own. So if you have any litterature suggestions, please feel free to share :).

Answer 1

This configuration is called "Bootstrapped Twin T Filter". This filter is an active notch filter. A1 OpAmp is a simple voltage follower which will reduce output impedance. A2 is an another voltage follower used for the feedback. The usage of the voltage follower at the feedback is, it won't draw much current from the voltage divider feedback circuit and simply supply a feedback voltage to the filter. This will make the response is more oriented around our target frequency.

Texas instruments has a very good explanation about this design here.

If you are going to use this design to build a circuit, I strongly suggest to use this. I have used this circuit to build a EEG circuit and had fabulous results!

Hope this helps :-)

Answer 2

The opamp A1 is the main amplifier which provides positive feedback (providing a low-resistive output is a secondary nice effect). If you compare the transfer functions for both circuits you will notice that the the filter function for the 1st circuit looks much more complicated (it contains the elements R3 and R4) - if compared with the function for the 2nd circuit. It is the purpose of the amplifier A2 to decouple the resistors R3 and R4 from the rest of the feedback elements. Hence, only the RATIO of these two resistors enters the transfer function (the real values play no role).

Hence, a simplified transfer function allows a simpler design procedure (fixing all elements for the desired notch frequency).

Comment: Note, however, that there are other notch filter topologies which have better properties. One of the main disadvantages of this Twin-T structure is the following: The notch frequency and - in particular - the depth of the notch (maximum damping)is extremely sensitive to parameter tolerances (tolerances of the passive elements). This restriction is somewhat relaxed for other notch topologies.