Ill start by saying I know this has been flogged to death but I have been doing alot of reading across the filter types and designing them.
Problem :Â I need to construct a 48 db / Octave slope filter, LPF and HPF, without cascading the dB drop at the cuttoff frequency.
Things done :
1) Now from reading at a practical level it appears most filters are created from 2nd order filters. Using this as a basis I cascaded 4 x 2nd Order Butterworth Filters together in RackAFX. Now from the equations it shows a -3db at the cuttoff frequency but I am infact getting -3 * 4 = -12 dB at the cuttoff frequency fc. From the readings and youtube lectures  I have seen I only see the fc staying the same and the area around it rising to the idealised passband, NOT lowering. But I see all papers pointing to higher orders being designed by cascading 2nd orders.
2)Â I have read quite a few papers showing the creation of the elliptic filter and by setting certain values produces it to a Butterworth , Chebychev I && II and Bevel filters, otherwise it is a steeper roll off with ripples in the pass and stop bands.
This is obviously more complicated but is this something required to get more of a brickwall style cuttoff without cascading the fc with a -db * number of filters cascaded. I know this does come with a trade-offs of ripple but alas, is this how one would go about achieving this?Â
Questions (relating to numbers above) :Â
1)Â Is this a lack of understanding on my behalf or something that should not happen when cascading filters?Â
2) Is using an elliptic filter or chebychev I filter cascaded the way to cascade filters without cascading the fc db drop?Â
A) If this isn't something wrong above, I suppose I could come up with something in the behind the scenes using a normal 2nd Order L/H PF, with a Q value or shifted Fc with a higher order to compensate but this doesn't seem logical. A possible solution would be to run theÂ
Quick and easy reference:
If you're building a crossover then the Linkwitz-Riley approach is definitely the best choice.
I think the problem you're having is that,
2p BW + 2p BW + 2p BW + 2p BWÂ != 8p LRF
as 3db - 3db - 3db -3db != -6dbÂ Â /// instead its -12db
Definitely read the link below as it covers this exact question.
8p LRF = 4p BWF + 4p BWF
as -6db = -3db - 3dbÂ /// cascading two 4p BW's gives the response we want
4p BWF = 2p LPF + 2p LPFÂ Â //4p BW from two 2p LPs with different resonances
thus you'll need 4 separate instances of the 2p LPF object for each 8p LRF filter you're building.
8p LRF =Â 2p LPF + 2p LPF + 2p LPF + 2p LPFÂ Â Â // The four LPF's here act as a pair of BWs.
The resonance value for the first 2p LP is 0.54119610, for the second it's 1.3065630, the third is 0.54119610 and the fourth is 1.3065630.
Cutoff for all filters are identical.
Resonance values taken directly from the calculator on the linked site. Which also give orders up to 20, if you're ever itching to build a 40 pole crossover.
Hope that's helpful
This wasn't actually to do with the crossover but I think your explanation held the missing piece of information I have been looking for.
-> as 3db - 3db - 3db -3db != -6dbÂ Â /// instead its -12db <- is exactly my main problem with many filters when cascading!Â I didn't think of using different Q values for each cascaded filter. I thought you just utilised one master Q and pushed it back upwards.
Thank-you for this, I will save it as it is a very very lovely explanation! Thank-you for your time Jim!Â
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