Butterworth, Bessel, Linkwitz-Riley... What's the difference, & what's your favorite?
Hi all!
After the "what's your favorite crossover slope?", here's the "what's your favorite crossover type?"
I was just wondering, what's the difference between all of them (if you know others, feel free to introduce them!), in terms of results/caracteristics, but also in the maths.
At first, I thought that the difference between them was the Q of the filter. But after reading some articles and threads, I have some doubts. Is this true?
Alex
Hi all!
After the "what's your favorite crossover slope?", here's the "what's your favorite crossover type?"
I was just wondering, what's the difference between all of them (if you know others, feel free to introduce them!), in terms of results/caracteristics, but also in the maths.
At first, I thought that the difference between them was the Q of the filter. But after reading some articles and threads, I have some doubts. Is this true?
Alex
Bessel (Q=0.58) has maximally flat delay. However you can't quite get a completely flat amplitude response. This is my favourite type.
Linkwitz-Riley (Q=0.49: critically damped) will have the best impulse response, if you like that sort of thing.
Butterworth (Q=0.71) is popular because it has the steepest slope you can get while retaining a flat amplitude response.
Yes, Q is the usual way of describing the difference between the different types of filter response.
A subtractive filter is one where you only have one filter section, then you derive the other by subtracting the filtered signal from a delayed version of the original. It has a few advantages, such as perfect impulse response, but a big disadvantage of shallow (6dB/octave) slope for the subtracted section.
Linkwitz-Riley (Q=0.49: critically damped) will have the best impulse response, if you like that sort of thing.
Butterworth (Q=0.71) is popular because it has the steepest slope you can get while retaining a flat amplitude response.
Yes, Q is the usual way of describing the difference between the different types of filter response.
A subtractive filter is one where you only have one filter section, then you derive the other by subtracting the filtered signal from a delayed version of the original. It has a few advantages, such as perfect impulse response, but a big disadvantage of shallow (6dB/octave) slope for the subtracted section.
I have a problem related to this; how do you change the Q of a passive crossover filter?
I am trying to "improve" a commercial speaker while replacing damaged woofers. The midrange frequency response looks like a two-hump camel (bactrian), so I thought to reduce the Q of the 2nd order filters, I change the ratio of L to C. So far I have found that everything increases the humps, rather than smooth them out. I want to slightly increase the high crossover frequency to better meet with the tweeter, but a reduction in inductance increases the hump.
So how does this talk of crossover slopes apply to passive networks?
I wish I could just go active.
I am trying to "improve" a commercial speaker while replacing damaged woofers. The midrange frequency response looks like a two-hump camel (bactrian), so I thought to reduce the Q of the 2nd order filters, I change the ratio of L to C. So far I have found that everything increases the humps, rather than smooth them out. I want to slightly increase the high crossover frequency to better meet with the tweeter, but a reduction in inductance increases the hump.
So how does this talk of crossover slopes apply to passive networks?
I wish I could just go active.
Mr Evil said:
That's odd, I read on another thread that classical XOs (not only 1st orders) are called substractive. Don't know why...
I started this thread because we started learning about filters, at school. L-R filters aren't mentionned (maybe they are specific to the audio use), but we saw tchebychev, butterworth and bessel.
One thing got my attention: the equations the teacher gave us were very different for all types. That's why I wondered if the difference was only the Q.
But that's maybe because the equations didn't explicitely show Q
Bricolo said:OH, BTW: what is a substractive crossover?
A subtractive crossover is there you have a filter which provides
one output (either high or low pass usually) and the other
output is provided by a differential amplifier that looks at the
difference between the input and output of that filter. As a
result the output of the differential amplifier represents the
complement of the filter. If the filter is a low pass, then the
complement is a high pass, and so on. If you sum the two
outputs you get the original wave, with no phase or amplitude
distortion, in other words, square wave in, square wave out.
There's an article posted in the archives at www.passlabs.com
With regards to preference on these things I usually find that what dictates what xover you use (in passive xovers anyway) is what slopes/orders give you the flat or desired on axis response AND a good cancellation with reversed polarity.
Its not as simple as just saying yes I will use a 4th order LWR at 2500hz to mate this woofer and tweeter. Most likely just getting the two drivers acoustic slopes to meet 4th O LWR wont yeild a pleasent reverse null. Thats when you start to fiddle with things!
In an active crossover its just as simple as adding a delay circuit to the tweeter, but in passive crossovers this is not easily and cheaply done.
Its not as simple as just saying yes I will use a 4th order LWR at 2500hz to mate this woofer and tweeter. Most likely just getting the two drivers acoustic slopes to meet 4th O LWR wont yeild a pleasent reverse null. Thats when you start to fiddle with things!
In an active crossover its just as simple as adding a delay circuit to the tweeter, but in passive crossovers this is not easily and cheaply done.
actually, many things can determine the filter type. Chebyshev really is any filter that is underdamped, Butterworth is a critically damped filter, and Bessel is any over damped filter. however, there are typical Q values associated with each filter.
the implementation of the filter also determines type. Sallen-Key filters have the filter type determined by many things including gain.
LR filters are simple an even number of Butterworth filter cascaded togther. therefore, there cannot be LR3 or LR5 filters, only LR2, LR4, LR6, etc. and, any even number of Butterworth filter should be a LR, not just a Butterworth.
Rane has a great app note on LR filters and their advantages. they are excellent for audio applications in many cases.
the 'best' type of rolloff has more to do with enclosure and drivers than anything else. the filter must match and complement the driver's response to achieve whatever freq response the speaker needs. normally, underdamped filters are avoided in audio because they produce amplitude fluctuations in the passband which is sonically undesirable. overdamped filters have a slow rolloff which usually doesn't match well with speaker acoustic rolloff. BW/LR are a typical choice because they have flat amplitude response in the passband (sounds good) and sharp rolloffs. however, because the critically damped is such a finite value there are very few filters that are exactly BW or LR. acheiving the desired freq response for the speaker will push the filter type around a bit, but most filters hang around the BW/LR area, or else a smidge toward Bessel.
Also, something to keep in mind is that I believe that the damping changes with filter order.
the implementation of the filter also determines type. Sallen-Key filters have the filter type determined by many things including gain.
LR filters are simple an even number of Butterworth filter cascaded togther. therefore, there cannot be LR3 or LR5 filters, only LR2, LR4, LR6, etc. and, any even number of Butterworth filter should be a LR, not just a Butterworth.
Rane has a great app note on LR filters and their advantages. they are excellent for audio applications in many cases.
the 'best' type of rolloff has more to do with enclosure and drivers than anything else. the filter must match and complement the driver's response to achieve whatever freq response the speaker needs. normally, underdamped filters are avoided in audio because they produce amplitude fluctuations in the passband which is sonically undesirable. overdamped filters have a slow rolloff which usually doesn't match well with speaker acoustic rolloff. BW/LR are a typical choice because they have flat amplitude response in the passband (sounds good) and sharp rolloffs. however, because the critically damped is such a finite value there are very few filters that are exactly BW or LR. acheiving the desired freq response for the speaker will push the filter type around a bit, but most filters hang around the BW/LR area, or else a smidge toward Bessel.
Also, something to keep in mind is that I believe that the damping changes with filter order.
Chebyshev has Q=1. For most audio use I wouldn't recommend going outside a range of 0.49-0.71. Lower has too soft a cuttoff without offering any particular advantages. Higher will have lumpy frequency response. If you need the sharper cuttoff, better to use a higher order rather than higher Q.
I expect that Google would be able to find a site listing the various filter responses.
I expect that Google would be able to find a site listing the various filter responses.
If this isn't a confusing thread, I don't know what is. Everyone is saying something different than everyone else. Jeez.
My only knowledge of Chebeschev (sic) and Bessel come from my mathematics education, but not applied to crossovers and filters. Can someone define Q definitively for me? I guess I should not be so lazy and look it up.
My only knowledge of Chebeschev (sic) and Bessel come from my mathematics education, but not applied to crossovers and filters. Can someone define Q definitively for me? I guess I should not be so lazy and look it up.
Actually we are all saying pretty much the same thing.
What even said here
is probably the best thing said here and what I do others probably do when designing a filter.
You dont tend to have exact filter types used in a loudspeaker. Its more what give you what you are after. Most speakers will use as even said from bessel to butterworth, many inbetween and most of the time maybe even none of the predetermined names given to set "Q's" for filters.
You may have a 0.65 Q high pass on the tweeter and a 0.57 Q lowpass on the woofer, all of these coming together to get you a flat response whilst maintaining good phase for symetrical and deep notch when the polarity is reversed.
What even said here
is probably the best thing said here and what I do others probably do when designing a filter.
You dont tend to have exact filter types used in a loudspeaker. Its more what give you what you are after. Most speakers will use as even said from bessel to butterworth, many inbetween and most of the time maybe even none of the predetermined names given to set "Q's" for filters.
You may have a 0.65 Q high pass on the tweeter and a 0.57 Q lowpass on the woofer, all of these coming together to get you a flat response whilst maintaining good phase for symetrical and deep notch when the polarity is reversed.
Since someone mentionned Sallen Key filters,
How do we set the Q? Only with the 2 resistors making a divider bridge between -in, out, and ground?
By looking rapidly on the S-K schematic, I thought that those resistors were here to set the gain (and only the gain)
And, how can I set the Q with a follower? (not an opamp, a buffer, emitter follower...)
But that's maybe for another thread
How do we set the Q? Only with the 2 resistors making a divider bridge between -in, out, and ground?
By looking rapidly on the S-K schematic, I thought that those resistors were here to set the gain (and only the gain)
And, how can I set the Q with a follower? (not an opamp, a buffer, emitter follower...)
But that's maybe for another thread
this link has been posted several times on this forum:
http://beis.de/Elektronik/Filter/ActiveLPFilter.html#SallenKey
are the calculations correct?
I learnt at scool that Chebycheff filters had ripple in theyr passband (and not only a peak before the rolloff)
Spice and the values given by the online calculator don't result with a filter having ripples, even when 3dB chebycheff is chosen
http://beis.de/Elektronik/Filter/ActiveLPFilter.html#SallenKey
are the calculations correct?
I learnt at scool that Chebycheff filters had ripple in theyr passband (and not only a peak before the rolloff)
Spice and the values given by the online calculator don't result with a filter having ripples, even when 3dB chebycheff is chosen
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.