Post History
The low-pass MFB filter can be a little tricky to analyse so, if you are only interested in the result skip to the end. The MFB low-pass filter: - The first thing to do is convert impedances to ...
#3: Post edited
by
Andy aka
·
2026-04-13T17:20:51Z (5 months ago)
#2: Post edited
by
Andy aka
·
2026-02-02T15:19:57Z (8 months ago)
The low-pass MFB filter can be a little tricky to analyse but, if you are only interested in the result skip to the end. The MFB low-pass filter: -- 
- The first thing to do is convert impedances to functional blocks using circuit theorems: -
- 
- The stages above should all be fairly clear. In the centre stage the integrating op-amp, R3 and C2 are converted to a functional block but, R3 still acts as impedance to ground because of the op-amp's virtual ground. Stage 3 mops up things a bit more leaving two remaining impedances. We are trying to get rid of impedances because they simultaneously have a loading effect and, shape functional blocks. We just want to make functional blocks.
- We can convert the two remaining impedances to functional blocks using superposition theorem: -
- 
- From this point onwards it can be a math problem but, I choose to solve this by keeping an image of the overall functional transfer function so that it's clear what's happening: -
- 
- 
- 
- 
- We can now put the above in standard form: -
- 
- That's it and remember that some derivations swap the positions of R2 and R3 so, watch out for that if you are double checking my post.
- The low-pass MFB filter can be a little tricky to analyse so, if you are only interested in the result skip to the end. The MFB low-pass filter: -
- 
- The first thing to do is convert impedances to functional blocks using circuit theorems: -
- 
- The stages above should all be fairly clear. In the centre stage the integrating op-amp, R3 and C2 are converted to a functional block but, R3 still acts as impedance to ground because of the op-amp's virtual ground. Stage 3 mops up things a bit more leaving two remaining impedances. We are trying to get rid of impedances because they simultaneously have a loading effect and, shape functional blocks. We just want to make functional blocks.
- We can convert the two remaining impedances to functional blocks using superposition theorem: -
- 
- From this point onwards it can be a math problem but, I choose to solve this by keeping an image of the overall functional transfer function so that it's clear what's happening: -
- 
- 
- 
- 
- We can now put the above in standard form: -
- 
- That's it and remember that some derivations swap the positions of R2 and R3 so, watch out for that if you are double checking my post.
#1: Initial revision
by
Andy aka
·
2026-02-02T15:18:27Z (8 months ago)
MFB low-pass filter transfer function derivation
The low-pass MFB filter can be a little tricky to analyse but, if you are only interested in the result skip to the end. The MFB low-pass filter: -  The first thing to do is convert impedances to functional blocks using circuit theorems: -  The stages above should all be fairly clear. In the centre stage the integrating op-amp, R3 and C2 are converted to a functional block but, R3 still acts as impedance to ground because of the op-amp's virtual ground. Stage 3 mops up things a bit more leaving two remaining impedances. We are trying to get rid of impedances because they simultaneously have a loading effect and, shape functional blocks. We just want to make functional blocks. We can convert the two remaining impedances to functional blocks using superposition theorem: -  From this point onwards it can be a math problem but, I choose to solve this by keeping an image of the overall functional transfer function so that it's clear what's happening: -     We can now put the above in standard form: -  That's it and remember that some derivations swap the positions of R2 and R3 so, watch out for that if you are double checking my post.