Hi all,
Does anyone know the actual mechanics of how a Sallen Key Band pass achieves its unique response? The Sallen key design looks like:
**broken link removed**
As you can see it comes quoted with a formula to calculate its centre frequency, where R(eq) is the equivalent resistance R1||R2 and both capacitors are considered to have the same value. Everything I've read suggests that it's combination of low and high pass filters within it acting like a band pass. So I redrew the circuit below as (1) and then transformed the input side to its thevenin equivalent (2).
**broken link removed**
Now looking at the newly redrawn circuit (2) I do indeed begin to see a low pass filter (made up of R(equivalent) and C1) and a high pass filter made up of C2 and R3. So since both filters have their own individual cut off frequencies, I can work out their geometric mean (ie the centre frequency of a band pass filter made from two such filters) and compare it to the centre frequency formula given with the Sallen Key Band pass filter in the first diagram. I did the calculation and they're exactly the same (Shown on the right - both capacitors considered the same here too).
This is where I'm stuck as to how the circuit performs. I can guess that at really high and really low frequencies, no signal appears at the inverting input because it's blocked by at least one of the filters and so the op amp keeps the bottom rail grounded. Therefore the output of the filter is 0v for exceptionally high and low signals. But there's a particular centre frequency where the gain becomes -R3/2R1 and I'm not sure how this happens.
I even thought this could be described as some sort of oscillator where at a particular frequency the output of the op amp reinforces the input signal and hence you get a Q type response. However I don't know if this is correct as I cannot see how you'd get an additional 180 deg phase shift by going through the passive filter network back to the input which would help to reinforce the incoming signal. The inverting arrangement already provides the other 180 deg shift needed.
So I'm a bit stuck, maybe all of this is in the wrong direction, maybe I'm missing something, but I'd really like an idea of how the circuit works, especially around the centre frequency where the whole circuit seems to turn into just an inverting amplifier of gain R3/2R1 (It's as if R2, C1 and C2 either cancel out or disappear from the circuit!).
Any help or directions for further reading would be appreciated!
Thanks,
Megamox
Does anyone know the actual mechanics of how a Sallen Key Band pass achieves its unique response? The Sallen key design looks like:
**broken link removed**
As you can see it comes quoted with a formula to calculate its centre frequency, where R(eq) is the equivalent resistance R1||R2 and both capacitors are considered to have the same value. Everything I've read suggests that it's combination of low and high pass filters within it acting like a band pass. So I redrew the circuit below as (1) and then transformed the input side to its thevenin equivalent (2).
**broken link removed**
Now looking at the newly redrawn circuit (2) I do indeed begin to see a low pass filter (made up of R(equivalent) and C1) and a high pass filter made up of C2 and R3. So since both filters have their own individual cut off frequencies, I can work out their geometric mean (ie the centre frequency of a band pass filter made from two such filters) and compare it to the centre frequency formula given with the Sallen Key Band pass filter in the first diagram. I did the calculation and they're exactly the same (Shown on the right - both capacitors considered the same here too).
This is where I'm stuck as to how the circuit performs. I can guess that at really high and really low frequencies, no signal appears at the inverting input because it's blocked by at least one of the filters and so the op amp keeps the bottom rail grounded. Therefore the output of the filter is 0v for exceptionally high and low signals. But there's a particular centre frequency where the gain becomes -R3/2R1 and I'm not sure how this happens.
I even thought this could be described as some sort of oscillator where at a particular frequency the output of the op amp reinforces the input signal and hence you get a Q type response. However I don't know if this is correct as I cannot see how you'd get an additional 180 deg phase shift by going through the passive filter network back to the input which would help to reinforce the incoming signal. The inverting arrangement already provides the other 180 deg shift needed.
So I'm a bit stuck, maybe all of this is in the wrong direction, maybe I'm missing something, but I'd really like an idea of how the circuit works, especially around the centre frequency where the whole circuit seems to turn into just an inverting amplifier of gain R3/2R1 (It's as if R2, C1 and C2 either cancel out or disappear from the circuit!).
Any help or directions for further reading would be appreciated!
Thanks,
Megamox