Hi everyone, I've been looking for a reference or an article about formulas and calculations on the 6th order Sallen-Key Butterworth high-pass filter in "two stages" but I couldn't find anything. As you can see this is the Rod Elliott's 6th order Sallen-Key design but there is no explanation on how the calculations are. I've also checked out the Doug Self's book and found nothing. Any help will be appreciated.
I do not think this is actually a Butterworth filter, but rather a "Butterworth Squared" filter or better known as a "Linkwitz-Riley" filter, of order 6.
What the schematic shows is two third order filters in series (cascaded). The B6 cannot be made in this way - it has no real poles (the first order sections formed by R1C1 and R4C4). This is why I suspect it's an LR6 filter. You (or anyone) can check this by seeing if each stage corresponds to a B3 filter.
If you DO want to make a Butterworth 6th order filter you will need to make it using three second order stages instead, each with the same corner frequency, and having Q values of 0.52, 0.707, and 1.93. You should be able to find how to design second order filters around an op-amp pretty easily. Cascade the three in the order given for the Q values to limit overloading.
What the schematic shows is two third order filters in series (cascaded). The B6 cannot be made in this way - it has no real poles (the first order sections formed by R1C1 and R4C4). This is why I suspect it's an LR6 filter. You (or anyone) can check this by seeing if each stage corresponds to a B3 filter.
If you DO want to make a Butterworth 6th order filter you will need to make it using three second order stages instead, each with the same corner frequency, and having Q values of 0.52, 0.707, and 1.93. You should be able to find how to design second order filters around an op-amp pretty easily. Cascade the three in the order given for the Q values to limit overloading.
That WOULD be possible, if one stage is 4th order and the other is 2nd order, but that is NOT what the circuit in the schematic is showing.
The schematic is from here:
https://sound-au.com/project99.htm
It says right on the page:
Also:
EACH half of the filter is a Butterworth 3rd order filter. That does NOT make a Butterworth filter overall. It makes an LR6 filter.
https://sound-au.com/project99.htm
It says right on the page:
Also:
EACH half of the filter is a Butterworth 3rd order filter. That does NOT make a Butterworth filter overall. It makes an LR6 filter.
The Q of the complex pole pair of a third-order Butterworth filter or of the two complex pole pairs of a sixth-order Linkwitz-Riley filter is 1 rather than 0.707.
Anyway, CharlieLaub is correct, this can't possibly be a sixth-order Butterworth filter or be changed into a sixth-order Butterworth filter by changing component values.
Anyway, CharlieLaub is correct, this can't possibly be a sixth-order Butterworth filter or be changed into a sixth-order Butterworth filter by changing component values.
I found this as well: https://www.edn.com/design-second-and-third-order-sallen-key-filters-with-one-op-amp/
If the response shape is useful (it need not fit an ideal form), then leave the resistors alone and scale all the capacitors smaller to move the frequency higher. It really is that simple.
If you want an intense education on the filters useful in audio, you want Don Lancaster's Active Filter Handbook, 1975-1995 and now posted on the author's website on www.tinaja.com
"leave the resistors alone and scale all the capacitors smaller to move the frequency higher. It really is that simple."
It really is that simple. I've used this circuit and it works great. I even made my own board.
It must be driven by a low impedance source at all times. It cannot be used on the input of a preamp or audio device without a buffer. When testing on the bench, short the inputs. If powered up with the inputs open it will oscillate.
It really is that simple. I've used this circuit and it works great. I even made my own board.
It must be driven by a low impedance source at all times. It cannot be used on the input of a preamp or audio device without a buffer. When testing on the bench, short the inputs. If powered up with the inputs open it will oscillate.
Use these capacitors. https://www.mouser.com/ProductDetail/WIMA/MKP2C031501H00MN00?qs=iPPgFPFs9PNjgSXnqrG9ng==
Some references on how to scale circuit values:
https://ecstudiosystems.com/discove...nics/filters/frequency-and-impedance-scaling/
https://wiraelectrical.com/magnitude-and-frequency-scaling/
https://ecstudiosystems.com/discove...nics/filters/frequency-and-impedance-scaling/
https://wiraelectrical.com/magnitude-and-frequency-scaling/