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What's the difference between a Butterworth and Linkwitz-Reilly?

toxcrusadr

toxcrusadr

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What's the difference between a Butterworth and L-R crossover (assuming both are 2d order)?

I'm noodling around designing a simple small two-way speaker for the test bench using parts and cabinet materials I have laying around. I used the DIYAudio 2-way crossover designer:

http://www.diyaudioandvideo.com/Calculator/XOver/

This calculator allows selection of the type of filter, including both Butterworth and Linkwitz-Riley. The resulting schematics (for a 2d order crossover) look exactly the same - a cap in series with the tweeter, followed by an inductor in parallel with the tweeter; and the opposite arrangement on the woofer.

However the component values are different for the same inputs - every cap and inductor is different between the two designs. I used to know the difference but I don't remember. DIY Audio doesn't seem to think there is a difference in the arrangement, only the values.

If I just Google up "Butterworth crossover" or "Linkwitz-Riley crossover" I get a lot of curves and math, few crossover schematics. The simple ones still look identical; maybe there is only a difference when you get to higher orders?

Anybody wanna school me in crossover design?
 
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I hope you are joking! This is a doggone textbook with mathematical derivations. Unfortunately it never gives a schematic or a simple explanation of the design of the various types, nor does it answer the question in plain and simple language.
 
This is from wiki. I think this is as plain English as a topic like this gets.

A Linkwitz–Riley (L-R) filter is an infinite impulse response filter used in Linkwitz–Riley audio crossovers, named after its inventors Siegfried Linkwitz and Russ Riley, which was originally described in Active Crossover Networks for Noncoincident Drivers in JAES Volume 24 Issue 1 pp. 2-8; February 1976. It is also known as a Butterworth squared filter. An L-R crossover consists of a parallel combination of a low-pass and a high-pass L-R filter. The filters are usually designed by cascading two Butterworth filters, each of which has −3 dB gain at the cut-off frequency. The resulting Linkwitz–Riley filter has a −6 dB gain at the cutoff frequency. This means that summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response. This is the biggest advantage of L-R crossovers compared to Butterworth crossovers, whose summed output has a +3 dB peak around the crossover frequency. Since cascading two nth order Butterworth filters will give a 2nth order Linkwitz–Riley filter, theoretically any 2nth order Linkwitz–Riley crossover can be designed. However, crossovers of higher order than 4th may have less usability due to their increasing peak in group delay around crossover frequency and complexity.

Fourth-order Linkwitz–Riley crossovers (LR4) are probably today's most commonly used type of audio crossover. They are constructed by cascading two 2nd-order Butterworth filters. Their steepness is 24 dB/octave (80 dB/decade). The phase difference amounts to 360°, i.e. the two drives appear in phase, albeit with a full period time delay for the low-pass section.
 
Here's the Reader's Digest version, in bolded italics


L200B said:
This is from wiki. I think this is as plain English as a topic like this gets.

The resulting Linkwitz–Riley filter has a −6 dB gain at the cutoff frequency. This means that summing the low-pass and high-pass outputs, the gain at the crossover frequency will be 0 dB, so the crossover behaves like an all-pass filter, having a flat amplitude response with a smoothly changing phase response. This is the biggest advantage of L-R crossovers compared to Butterworth crossovers, whose summed output has a +3 dB peak around the crossover frequency.
Click to expand...
 
L200B said:
Fourth-order Linkwitz–Riley crossovers (LR4) are probably today's most commonly used type of audio crossover. They are constructed by cascading two 2nd-order Butterworth filters. Their steepness is 24 dB/octave (80 dB/decade). The phase difference amounts to 360°, i.e. the two drives appear in phase, albeit with a full period time delay for the low-pass section.
Click to expand...
At the risk of deviating too far off topic, if both drivers are subject to the same order high and low pass filters, are they not in phase? Granted, they'd be out of phase/timing with the terminals at the back of the amp, but I've never been able to hear those anyway.
 
A picture would be worth a thousand words here, unfortunately DIY Audio is offline right now so I'll have to do it later. I read the Wiki entry posted above, earlier. It appears what this is saying is that a Butterworth is basically a cap on the tweeter and an inductor on the woofer. Two components, right? Why does DIY Audio give you 4 components for this design?

It also sounds (from Wiki) like the L-R is two Butterworths cascaded, which would add an inductor to the tweeter and a cap to the woofer for 4 components total.

They show the IDENTICAL schematic for BOTH of these designs, given the same input. 4 components. But the values are different. I don't understand why.
 
toxcrusadr said:
I hope you are joking! This is a doggone textbook with mathematical derivations. Unfortunately it never gives a schematic or a simple explanation of the design of the various types, nor does it answer the question in plain and simple language.
Click to expand...


72afa6b98814ba6efa6a78de7ffd19c2.jpg

The values are different because how they cross is different. Picture from site I referenced.
 
So basically the L-R design gets rid of the "hump" at the crossover frequency right ? Sounds like a winner, especially if you're talking about a speaker that tends to have peaks in the frequency response. Maybe this is why I need to try out in those Bozak speakers that I'm not fond of.
 
Well, I THOUGHT I had it for a minute there, but now I'm lost again... Wait, which Bozak speaker?

On the L/R, which way does the 6dB-per-step downslope go? On the way UP (as in woofer/mid/tweeter)? Or on the way down (as in tweeter/mid/woofer)? I might as well learn something here.

Somehow, this all reminds me of Steve Martin back in the day, telling that plumber's joke.

“Ok, I don’t like to gear my material to the audience but I’d like to make an exception because I was told that there is a convention of plumbers in San Francisco this week – I understand about 30 of them came down to the show tonight – so before I came out I worked-up a joke especially for the plumbers. Those of you who aren’t plumbers probably won’t get this and won’t think it’s funny, but I think those of you who are plumbers will really enjoy this…

This lawn supervisor was out on a sprinkler maintenance job, and he started working on a Finley sprinkler head with a Langstrom 7-inch gangley wrench. His apprentice laughed and said, “You can’t work on a Finley sprocket with a Langstrom 7-inch wrench!” Well, this infuriated the supervisor, so he went and got Volume 14 of the Kinsley Manual. He opened it to page 214 and read, “A 7-inch Langstrom wrench is compatible with a Finley sprocket”. Just then the little apprentice leaned over and said, “It says sprocket, not socket!”

*SILENCE*

Were those plumbers supposed to be HERE this evening?"
 
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The two schematics are likely identical because the first one is 2 butterworth filters. One for the woofer and one for the tweeter. And the second one is the same thing except the two are working together to satisfy different conditions. These classifications are greater then just the pictures.
 
L200B said:
The two schematics are likely identical because the first one is 2 butterworth filters. One for the woofer and one for the tweeter. And the second one is the same thing except the two are working together to satisfy different conditions. These classifications are greater then just the pictures.
Click to expand...

I must assume then that even though the schematic looks the same, DIY is using different mathematical models to calculate the values.

bhunter said:
This article may help:

http://www.rane.com/note160.html
Click to expand...

I got all excited when Fig. 8 showed a 2d order Butterworth, so I looked farther down hoping to find an equivalent L-R. It says only:

Referring to Figure 8 all that is required is to add a buffer amplifier (to avoid interaction between cascaded filter components) to each of these two outputs and then add another resistor/capacitor network identical to the first. We now have a 2nd-order Linkwitz-Riley crossover.
Click to expand...

A buffer amplifier? :scratch2:
 
Actually, I answered my own question about models.

http://www.diyaudioandvideo.com/Calculator/XOver/Help.aspx

If you scroll down to the 2d Order chart it has 4 columns (Butterworth, L-R and two more) and the table gives the ratios for the C and L components which are different for the various crossover types.

I guess I was just assuming the schematic would look different, but based on this and what some of you all are saying above, it's more complicated than that.

Thanks for the help and sorry for being so dense. Long week. :bash:
 
Tox,

Sorry to raise such an old thread, but have been wondering the same thing lately.

My Optimus 1000s use a 2nd order on the tweeter, and a band pass on the mid. Tweeter is using a 2.2uF cap and 4ohm resistor in series, with .4mH coil in parallel. 5” mid is using a 3.9uF cap and .56mH coil in series. 15” woofer is wired direct, no coil or cap.

My questions are; with the ratios you mentioned, it LOOKS like the tweeter network is L-R? If it IS, do I need to wire it out of phase? New to the whole “phase shift” thing with different type and order networks.

Original drivers were all wired in phase, if I recall. Replaced the 3” cone tweet with a dipole though, and still working out the blending.

Thanks!

Joe
 
dc270 said:
How does Cheby Chev fit into this soup?
DC
Click to expand...

I'm assuming you mean Chebyshev, right?

One of the main differences in the 4 usual crossover types are their "Q" factor. Chebyshev has a Q of 1.0, Butterworth .707, Bessell .58 and Linkwitz-Riley .49. The Chebyshev is rarely used as it has a 0db crossover point but +6db amplitude gain and adds ripple in the passband (which is not good). I tinkered with these some back in my car audio days with drivers that were farther apart versus being right there together and I needed that gain between the mid and tweeter. In home speakers, I can't think of any manufacturer that has stated they use it. At least none that I ever sold at the retail sales level or when I was a Rep.
 
avguytx said:
I'm assuming you mean Chebyshev, right?

One of the main differences in the 4 usual crossover types are their "Q" factor. Chebyshev has a Q of 1.0, Butterworth .707, Bessell .58 and Linkwitz-Riley .49. The Chebyshev is rarely used as it has a 0db crossover point but +6db amplitude gain and adds ripple in the passband (which is not good). I tinkered with these some back in my car audio days with drivers that were farther apart versus being right there together and I needed that gain between the mid and tweeter. In home speakers, I can't think of any manufacturer that has stated they use it. At least none that I ever sold at the retail sales level or when I was a Rep.
Click to expand...

Sorry for the spelling, I was trying to be quick about the question and forced the typo into play!
Thanks for the "Q" informations, that helps a lot to know!
DC
 
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