Butterworth, Bessel, Linkwitz-Riley... What's the difference, & what's your favorite?

[Bricolo]

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

[Bricolo]

OH, BTW: what is a substractive crossover?

[Svante]

In short: Butterworth is for odd-order filters (1, 3, 5 etc) and Linkwitz-Riley for even-order filters. Bessel filters have nothing to do in crossovers.

[Mr Evil]

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.

[johnnyx]

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.

[Bricolo]

Originally posted by Mr Evil
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.

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

[Nelson Pass]

Originally posted by Bricolo
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

[5th element]

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.

[Bricolo]

If Bessel is 0.58, LR 0.49 and Butterworth 0.71

What is Tchebichev?

[Evan Shultz]

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.