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

[Bricolo]

Yep me too. Being the stubborn guy I am I had to build 'em in LspCAD and see for myself.

In the pic, the top one is a real 100Hz LR4 and the bottom one is a .5 + 1 kludge. They are pretty close but there are small differences of a dB or so in the shoulder region below Fc.

I had always thought the Q values Linkwitz picked for his stacked filters were arbitrary but I guess we'd better stick to the Q values on his web page for building LR filters of orders up to 10. Thanks for the heads up, guys.

http://www.linkwitzlab.com/filters.htm#2

could you also show us the phase of both, please?
maybe something more interesting is happening there

 

[catapult]

could you also show us the phase of both, please?

Not with the demo copy of LspCAD I have. But simple lowpass filters like that are minimum phase so a Hilbert-Bode transform of the amplitude will give you the phase. They don't become non minimum phase until you mix in a highpass.

 

[tocs100]

Building a guitar eq

Okay crossover/filter buffs, I want a low frequency contour for my electric guitar (in a small eq box). I want it to cascade like this: 1kHz -6dB & 250Hz -6dB & 60Hz -12dB. What's the fancy Q equation so I can convince my engineer-friend to build it?

 

[ctviggen]

If you can take two cascaded first order filters and get a second order filter, then what's the difference between a quasi-second order filter and a second order filter? Further, isn't the "order" of a filter defined by the number of poles and not the slope (i.e., that the first order filter has a 6db slope is happenstance)?

 

[tocs100]

By "quasi 2nd order" do you mean "why a pole at 1kHz and another at 250Hz instead of just two at 250Hz?" I've tried a 2-pole at 250Hz and the cutoff sounds too abrupt. I want a g-e-n-t-l-e bass rolloff. (I'm a newbie, too, so don't laugh!)

 

[forr]

Currently, I think there are two challenging active crossovers to the LR :
- the Le Cleac'h 18 dB/o or the Brooke 18 dB/o, -5 dB at Xover frequency (he called it a quasi LR)
- and the Hardman, of elliptic kind.
After having read this
http://www.diyaudio.com/forums/showthread.php?s=&threadid=6655&highlight=
I built a two ways stereo Hardman at 1500 Hz. First listening tests were in agreement with what is said in the mentionned thread. I am very satisfied with the results. I have just finished to design a stereo three ways board.

~~~~~~~ Forr

§§§

 

[tocs100]

Thanks forr, that's neat stuff, but I'm not prototyping a crossover at the moment. What I need is a high pass tone control to reduce bass on my guitar. What values do I need to know to place a 1-pole filter at 1kHz, a 1-pole filter at 250Hz, and a 2-pole filter at 60Hz?

Or how about this as a toggle-switch option:
1-pole filter at 500kHz, and 3-pole filter at 30Hz?

 

[AudioEngineer]

Butterworth Filter has a flat power response

Hi, Correct me if I am wrong but the linkwitz riley filter has a serious flaw because it has a dip of 50% in its power response at the crossover frequency. The butterworth filter power response is almost flat at the crossover frequency. Therefore wouldn't a butterworth filter be a better filter for audio use?

 

[john k...]

It's not that simple. To start, and crossover that yields flat on axis response and uniform polar response will have flat power response. The behavior of the polar response depends on what the crossover frequency is and the driver separation. The driver separation will determine whether there are off axis nulls in the power response. If there are such nulls, then Butterwort crossovers will still have flat power response because in addition tot he nulls, there will be off axis peaks that result in maintaining flat power response. With a Linkwitz crossover the off axis nulls are not countered by peaks at other positions, thus the power response can dip through the crossover region. These results assume that both sources radiate omnidirectional. Once directionality is introduced typically power response will be a function of a number of factors and no general conclusion can be stated.

One thing to remember is that the radiated power is not the sum of the power radiated by each source separately. It is the power computed by the sum of the radiated pressure response.

Basically, at low frequency, where the driver separation is much less than a wave length, any crossover that yields flat response will yield flat power response, given that the sources are omnidirectional.

 

[steveu]

The only analog crossovers that provide "flat response" are 1st order and "subtractive". Higher order crossovers have too much phase shift to sum together without producing a notch at cross-over. Unless they are wired inverted and then you get an abrupt phase inversion.

Digital crossovers can avoid the phase shift by using future as well as past samples, ie causing an overall delay.

But the whole issue is academic because drivers have peaks and valleys that dwarf any crossover errors. A good passive crossover is actually a carefully tuned equalizer, ie the result of a lot of measurements and tweaking.

Passive crossover Q is determined by the loading. A passive crossover has an impedance as well as a frequency. If you use a 16 Ohm driver on a 8 Ohm crossover, the crossover will resonate and peek at the crossover frequency rather than be -3dB down, IE the Q depends on loading.

 

[john k...]

The only analog crossovers that provide "flat response" are 1st order and "subtractive". Higher order crossovers have too much phase shift to sum together without producing a notch at cross-over. Unless they are wired inverted and then you get an abrupt phase inversion.

Compete nonsense.