Reply by Jerry Avins May 20, 20092009-05-20
Vladimir Vassilevsky wrote:
> > > Jerry Avins wrote: >> Vladimir Vassilevsky wrote: >> >>> >>> >>> Greg Berchin wrote: >>> >>>> Let's create a generic Linkwitz-Riley 3-way crossover. The Lo band >>>> covers 0 Hz to "L" Hz, the Mid band covers "L" Hz to "H" Hz, and the >>>> Hi band covers "H" Hz upward. Name the filters "lpL" (lowpass-L), >>>> "hpL" (highpass-L), "lpH" (lowpass-H), and "hpH" (highpass-H). >>> >>> >>> [...] >>> >>>> Think that's complicated? You should see the 4-way configuration. >>> >>> >>> I am surprised to see the interest in that kind of sophistication. >>> Being involved with the design of the audio electronic for many >>> years, I was always told by the acoustic engineers that for crossover >>> filter you never actually need anything more complex then the >>> Butterworth of the 4th order; and I tend to agree with them. In the >>> most of cases, you can get by just the 2nd order filters. I've seen >>> the bizarre arrangements like Bessel lowpass + FIR highpass; the >>> sound was neither better or worse compared to the trivial Butterworth >>> filters. IMO that pre-ringing, linear phase, LinkwitzRiley and such >>> is the audiofoolery of the second kind (The first kind is about the >>> tubes and the silver wires). >> >> >> Linkwitz-Riley filters are about avoiding destructive interference in >> auditoriums (auditoria?) where the seats are on a sloping floor. The >> floors in my house are reasonably level. 'Nuff said? > > Oh, come on. Just take a microphone and make the phase/frequency > response measurement. Then move it couple of feet away and measure > again. The variation due to the crossover is barely visible compared to > the other irregularities.
The nulls can be quite deep in the vertical direction. Auditoriums with sloped floors are best served by a main lobe that matches the floor's slope. Linkwitz-Riley filters tend to do that. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by Vladimir Vassilevsky May 19, 20092009-05-19

Greg Berchin wrote:

> On Tue, 19 May 2009 10:19:23 -0500, Vladimir Vassilevsky > <antispam_bogus@hotmail.com> wrote: > > >>I am surprised to see the interest in that kind of sophistication. Being >>involved with the design of the audio electronic for many years, I was >>always told by the acoustic engineers that for crossover filter you >>never actually need anything more complex then the Butterworth of the >>4th order; and I tend to agree with them. In the most of cases, you can >>get by just the 2nd order filters. > > > Well, a Linkwitz-Riley 4th order is just the cascade of two > Butterworth 2nd orders, so I guess that covers both of your > assertions. :) > > >>I've seen the bizarre arrangements >>like Bessel lowpass + FIR highpass; the sound was neither better or >>worse compared to the trivial Butterworth filters. IMO that pre-ringing, >>linear phase, LinkwitzRiley and such is the audiofoolery of the second >>kind (The first kind is about the tubes and the silver wires). > > > To each his own. Having designed a whole class of Bessel-derived > matched-delay crossovers > (http://www.aes.org/e-lib/browse.cfm?elib=8170) that, to my ears, > sound better than the classical designs, I respectfully disagree but > refuse to argue about it. In many ways it's like arguing about what > flavor of ice cream is the best ... there is no answer. > > Oh, and I do have tubes in my system, but no silver wire.
It would be my pleasure to design the pinnacle of the audio DSP technology, however I have to look at that from the practical standpoint. It turns out that the customers are interested in the reliability and the low cost more then in the advanced features and the ultimate specmanship. Since nobody ever expressed considerable remarks about the audio performance, that simply means that the audio performance is sufficient and there is no point to improve it further. Nevertheless it is nice to know that somebody is willing to pay for the advanced crossovers, so I can only express my jealousy :) Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by Vladimir Vassilevsky May 19, 20092009-05-19

Jerry Avins wrote:
> Vladimir Vassilevsky wrote: > >> >> >> Greg Berchin wrote: >> >>> Let's create a generic Linkwitz-Riley 3-way crossover. The Lo band >>> covers 0 Hz to "L" Hz, the Mid band covers "L" Hz to "H" Hz, and the >>> Hi band covers "H" Hz upward. Name the filters "lpL" (lowpass-L), >>> "hpL" (highpass-L), "lpH" (lowpass-H), and "hpH" (highpass-H). >> >> >> [...] >> >>> Think that's complicated? You should see the 4-way configuration. >> >> >> I am surprised to see the interest in that kind of sophistication. >> Being involved with the design of the audio electronic for many years, >> I was always told by the acoustic engineers that for crossover filter >> you never actually need anything more complex then the Butterworth of >> the 4th order; and I tend to agree with them. In the most of cases, >> you can get by just the 2nd order filters. I've seen the bizarre >> arrangements like Bessel lowpass + FIR highpass; the sound was neither >> better or worse compared to the trivial Butterworth filters. IMO that >> pre-ringing, linear phase, LinkwitzRiley and such is the audiofoolery >> of the second kind (The first kind is about the tubes and the silver >> wires). > > > Linkwitz-Riley filters are about avoiding destructive interference in > auditoriums (auditoria?) where the seats are on a sloping floor. The > floors in my house are reasonably level. 'Nuff said?
Oh, come on. Just take a microphone and make the phase/frequency response measurement. Then move it couple of feet away and measure again. The variation due to the crossover is barely visible compared to the other irregularities. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by Jerry Avins May 19, 20092009-05-19
Greg Berchin wrote:

   ...

> Oh, and I do have tubes in my system, but no silver wire.
My first decent hi-fi amplifier had Invar (or some such) wire in it. I had a friend studying EE in Columbia back when I did odd jobs around the neighborhood. One of his fraternity brothers had built a 20-watt Heathkit that turned out to have a hum problem that nobody in the fraternity or willing faculty could track down. I traded him my 10-watt Bogen PA amplifier for it, way overextending my meager abilities. There was a spool component in it covered with yellow tape and some pen indication I couldn't read. Laborious tracing revealed that it was an unbypassed cathode resister, and when I unsoldered it for a better look, it read, "100 ohm 0.1%". I replaced it with a 100-ohm composition Allen-Bradley and the hum went away. The wirewound, evidently a swiped replacement for the lost original component, was near the power transformer. Somewhere, I still have it. When is a resistor not a resistor? When it is the secondary of a transformer! :-) That was a sturdy circuit. Once, with the speaker accidentally disconnected, I heard faint sound anyway. The first clue was a bit of arcing in the 6L6 output tubes. The sound was the plates vibrating due to electrostatic forces. I turned the volume down, reconnected the speaker, and nothing was the worse for it. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Greg Berchin May 19, 20092009-05-19
On Tue, 19 May 2009 11:38:25 -0400, Jerry Avins <jya@ieee.org> wrote:

>Linkwitz-Riley filters are about avoiding destructive interference in >auditoriums (auditoria?) where the seats are on a sloping floor.
As I understand it, that's close but not exactly correct. With Linkwitz-Riley crossovers, the lowpass section and the highpass section are in-phase at all frequencies. In large venues, where the audience is in the far-field, phase differences between the lowpass and the highpass sections can lead to lobes that cause frequency response variations between sections of the audience. I can intuit the effect that the slope of the floor would have upon this, but overall the most important thing is the off-axis angle and thus the degree to which any interference, destructive or constructive, might occur. Greg
Reply by Greg Berchin May 19, 20092009-05-19
On Tue, 19 May 2009 10:19:23 -0500, Vladimir Vassilevsky
<antispam_bogus@hotmail.com> wrote:

>I am surprised to see the interest in that kind of sophistication. Being >involved with the design of the audio electronic for many years, I was >always told by the acoustic engineers that for crossover filter you >never actually need anything more complex then the Butterworth of the >4th order; and I tend to agree with them. In the most of cases, you can >get by just the 2nd order filters.
Well, a Linkwitz-Riley 4th order is just the cascade of two Butterworth 2nd orders, so I guess that covers both of your assertions. :)
>I've seen the bizarre arrangements >like Bessel lowpass + FIR highpass; the sound was neither better or >worse compared to the trivial Butterworth filters. IMO that pre-ringing, >linear phase, LinkwitzRiley and such is the audiofoolery of the second >kind (The first kind is about the tubes and the silver wires).
To each his own. Having designed a whole class of Bessel-derived matched-delay crossovers (http://www.aes.org/e-lib/browse.cfm?elib=8170) that, to my ears, sound better than the classical designs, I respectfully disagree but refuse to argue about it. In many ways it's like arguing about what flavor of ice cream is the best ... there is no answer. Oh, and I do have tubes in my system, but no silver wire. Greg
Reply by Jerry Avins May 19, 20092009-05-19
Vladimir Vassilevsky wrote:
> > > Greg Berchin wrote: > >> Let's create a generic Linkwitz-Riley 3-way crossover. The Lo band >> covers 0 Hz to "L" Hz, the Mid band covers "L" Hz to "H" Hz, and the >> Hi band covers "H" Hz upward. Name the filters "lpL" (lowpass-L), >> "hpL" (highpass-L), "lpH" (lowpass-H), and "hpH" (highpass-H). > > [...] > >> Think that's complicated? You should see the 4-way configuration. > > I am surprised to see the interest in that kind of sophistication. Being > involved with the design of the audio electronic for many years, I was > always told by the acoustic engineers that for crossover filter you > never actually need anything more complex then the Butterworth of the > 4th order; and I tend to agree with them. In the most of cases, you can > get by just the 2nd order filters. I've seen the bizarre arrangements > like Bessel lowpass + FIR highpass; the sound was neither better or > worse compared to the trivial Butterworth filters. IMO that pre-ringing, > linear phase, LinkwitzRiley and such is the audiofoolery of the second > kind (The first kind is about the tubes and the silver wires).
Linkwitz-Riley filters are about avoiding destructive interference in auditoriums (auditoria?) where the seats are on a sloping floor. The floors in my house are reasonably level. 'Nuff said? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Jerry Avins May 19, 20092009-05-19
Vladimir Vassilevsky wrote:
> > > Greg Berchin wrote: > >> Let's create a generic Linkwitz-Riley 3-way crossover. The Lo band >> covers 0 Hz to "L" Hz, the Mid band covers "L" Hz to "H" Hz, and the >> Hi band covers "H" Hz upward. Name the filters "lpL" (lowpass-L), >> "hpL" (highpass-L), "lpH" (lowpass-H), and "hpH" (highpass-H). > > [...] > >> Think that's complicated? You should see the 4-way configuration. > > I am surprised to see the interest in that kind of sophistication. Being > involved with the design of the audio electronic for many years, I was > always told by the acoustic engineers that for crossover filter you > never actually need anything more complex then the Butterworth of the > 4th order; and I tend to agree with them. In the most of cases, you can > get by just the 2nd order filters. I've seen the bizarre arrangements > like Bessel lowpass + FIR highpass; the sound was neither better or > worse compared to the trivial Butterworth filters. IMO that pre-ringing, > linear phase, LinkwitzRiley and such is the audiofoolery of the second > kind (The first kind is about the tubes and the silver wires).
Linkwitz-Riley filters are about avoiding destructive interference in auditoriums (auditoria?) where the seats are on a sloping floor. The floors in my house are reasonably level. 'Nuff said? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Vladimir Vassilevsky May 19, 20092009-05-19

Greg Berchin wrote:

> Let's create a generic Linkwitz-Riley 3-way crossover. The Lo band > covers 0 Hz to "L" Hz, the Mid band covers "L" Hz to "H" Hz, and the > Hi band covers "H" Hz upward. Name the filters "lpL" (lowpass-L), > "hpL" (highpass-L), "lpH" (lowpass-H), and "hpH" (highpass-H).
[...]
> Think that's complicated? You should see the 4-way configuration.
I am surprised to see the interest in that kind of sophistication. Being involved with the design of the audio electronic for many years, I was always told by the acoustic engineers that for crossover filter you never actually need anything more complex then the Butterworth of the 4th order; and I tend to agree with them. In the most of cases, you can get by just the 2nd order filters. I've seen the bizarre arrangements like Bessel lowpass + FIR highpass; the sound was neither better or worse compared to the trivial Butterworth filters. IMO that pre-ringing, linear phase, LinkwitzRiley and such is the audiofoolery of the second kind (The first kind is about the tubes and the silver wires). Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by Martin Eisenberg May 18, 20092009-05-18
Greg Berchin wrote:

> . +---+ +---+ > . +--|apL|--|hpH|-- Hi > . | +---+ +---+ > . | > . | +---+ +---+ > . --+--|hpL|--|lpH|-- Mid > . | +---+ +---+ > . | > . | +---+ +---+ > . +--|lpL|--|lpH|-- Lo > . +---+ +---+ > > The difference between this and your configuration is the > substitution of the lpH filter for the apH filter in the Lo > band. > > Think that's complicated? You should see the 4-way > configuration.
Please don't scare the demon unnecessarily. It's good that you've sketched the algebraic justification but the construction is principled and simple if you proceed purely by splitting, rather than adding, branches. Starting with the 2-way crossover network <2> below, split the lower branch (say) by inserting another crossover, and keep the phase shift through any branch the same by inserting the appropriate allpass in the unsplit branch. The result <3> is a factored and commuted form of Greg's last flowgraph: ,--> ,--[A2]---> -->[C1] -->[C1] ,--> `--> `--[C2] `--> <2> <3> To make a 4-way, put another crossover on one outlet and an instance of the appropriate allpass on every other outlet, then push the allpasses as far as possible up the tree to minimize the number of computational blocks. Let's pick the uppermost branch for prettiness, resulting in <4.1>; and let's do it again picking another branch of the 3-way to make the point, in <4.2>. ,--> ,->[A2]-->[A1]---> ,->[A2]->[C3]---> / ,--> ->[C1] ->[C3] ,->[C1] `->[A3]->[C2]---> `-->[C2] `--> `--> `->[A1]---> <4a> <4b> Take note of the relabeling -- equal-numbered blocks have equal critical frequencies (w2 < w1 < w3) between <4a> and <4b> so that both networks realize the same decomposition. Also observe that the network <4b> makes you calculate more because we can't commute the instances of A1 up the tree until they fuse as we did with A3 in <4a>. So which form to choose? For minimal calculation, arrange crossovers in a balanced binary tree, splitting first on the middle (by count) bandedge and recursing on the high and low ranges. However, for noise performance it may be preferable to split high channels more often because of two factors. First, a filter block's SNR worsens with decreasing critical frequency (at fixed Q, as we have here) and we can combat this by choosing a low-noise topology for blocks in the lowest branches. Now, those topologies are more expensive than the direct forms but -- second -- this is counterbalanced if we apply them to allpasses, which are simpler than magnitude filters to begin with. And coming around, splitting high branches first concentrates the allpass blocks in the low branches and therefore may help to alleviate noise gain while checking cost growth. The reason I've used the weasel word "may" is that, as mentioned below fig. <4>, unbalanced splitting also increases the sheer number of filter blocks and I don't know how to make the noise/cost tradeoff except by simulating and comparing different crossover trees. Martin -- Quidquid latine scriptum est, altum videtur.