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.
�����������������������������������������������������������������������

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

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

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.
�����������������������������������������������������������������������

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

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

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.
�����������������������������������������������������������������������

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.
�����������������������������������������������������������������������

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

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.