Hi,

I'd like to implement some 4th order Linkwitz-Riley L-C filters for
loudspeaker crossovers, preferably without too much tedium. But it
seems all the L-C filter synthesis progs I've been able to find were
really intended for RF use (equal source/load impedances, with
Butterworth/Bessel/etc shape rather than Linkwitz-Riley). I know I
need to use driver impedance correction as well, and ensure correct
time alignment, and tweak the final system, and that it would be lots
better with active crossovers (preferably digital), but there are
still times when a simple passive crossover is the most useful (and
often more efficient - search for Art Ludwig's interesting research on
music spectra), but I'm still unwilling to compromise too much.

The "Thiele method" might even be better than an L-R shape - it seems
it just needs an extra cap in series with the final shunt inductor
(vice versa for the LPF) to make a null about an octave past the
crossover frequency, but that's as much as I have been able to find
out.

Does anyone have any useful tips for me on any of these subjects?
Tony (remove the "_" to reply by email)

Tony wrote:
Hi,

I'd like to implement some 4th order Linkwitz-Riley L-C filters for
loudspeaker crossovers, preferably without too much tedium. But it
seems all the L-C filter synthesis progs I've been able to find were
really intended for RF use (equal source/load impedances, with
Butterworth/Bessel/etc shape rather than Linkwitz-Riley). I know I
need to use driver impedance correction as well, and ensure correct
time alignment, and tweak the final system, and that it would be lots
better with active crossovers (preferably digital), but there are
still times when a simple passive crossover is the most useful (and
often more efficient - search for Art Ludwig's interesting research on
music spectra), but I'm still unwilling to compromise too much.


If you have one of those programs, you can specify the input impedance as
zero and the DC-impedance of the driver Re as load impedance. But it would
be better to have a special CAD program for LS like Audiocad, which even
optimizes these values after importing an impedance curve. There is not any
advantage using electronic xovers, apart from being cheaper and making it
adjustable. If you want a digital solution have a look at "Speaker
Management Processing".

The "Thiele method" might even be better than an L-R shape - it seems
it just needs an extra cap in series with the final shunt inductor
(vice versa for the LPF) to make a null about an octave past the
crossover frequency, but that's as much as I have been able to find
out.

Does anyone have any useful tips for me on any of these subjects?
Tony (remove the "_" to reply by email)

Driver impedance compensation for closed cabinets. Measure the TSP with the
driver mounted and the enclosure dampened. The R-C on the right side deals
with the inductive rise of the voice coil impedance, the values are only
approximately. Re and Le from datasheet the rest needs to be measured with
an impedance plot.


o---+------------------------+-----------+
| | |
| 0.1592*Qes*Re | |
C| L= ------------- | | Le
C| fs | --- C= ----
C| | --- Rc^2
| | |
--- 0.1592 | __ /| |
--- C= ---------- +-|+ | | |
| Re*Qes*fs +-|__| | .-.
.-. | \| | | R= 1.25*Re
| | | | |
| | Qes*Re | '-'
'-' R= Re+ ------ | |
| Qms | |
o---+------------------------+-----------+
created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de

I copied this from "The Loudspeaker Design Cookbook" by Vance Dickason. Get
also the book "Testing Loudspeakers" by Joe D'Appolito. Both from Audio
Amateur Press

--
ciao Ban
Bordighera, Italy

Thanks Ban.

The Lance Dickason info was welcome, as I hadn't even started to
search that one out. Also the AudioCad tip; I think you're right - I
will need to use a purpose designed tool.

I do still firmly believe that digital active crossovers have a number
of advantages, particularly much higher potential slopes, and the
ability to tweak the delay independently of the crossover curves (it's
hard to get time alignment any other way with a typical cone MF + horn
HF arrangement). But for this project a 4th order passive is the
limit.

/On Thu, 05 Aug 2004 03:41:03 GMT, "Ban" wrote:
Tony wrote:
Hi,

I'd like to implement some 4th order Linkwitz-Riley L-C filters for
loudspeaker crossovers, preferably without too much tedium. But it
seems all the L-C filter synthesis progs I've been able to find were
really intended for RF use (equal source/load impedances, with
Butterworth/Bessel/etc shape rather than Linkwitz-Riley). I know I
need to use driver impedance correction as well, and ensure correct
time alignment, and tweak the final system, and that it would be lots
better with active crossovers (preferably digital), but there are
still times when a simple passive crossover is the most useful (and
often more efficient - search for Art Ludwig's interesting research on
music spectra), but I'm still unwilling to compromise too much.


If you have one of those programs, you can specify the input impedance as
zero and the DC-impedance of the driver Re as load impedance. But it would
be better to have a special CAD program for LS like Audiocad, which even
optimizes these values after importing an impedance curve. There is not any
advantage using electronic xovers, apart from being cheaper and making it
adjustable. If you want a digital solution have a look at "Speaker
Management Processing".

The "Thiele method" might even be better than an L-R shape - it seems
it just needs an extra cap in series with the final shunt inductor
(vice versa for the LPF) to make a null about an octave past the
crossover frequency, but that's as much as I have been able to find
out.

Does anyone have any useful tips for me on any of these subjects?
Tony (remove the "_" to reply by email)

Driver impedance compensation for closed cabinets. Measure the TSP with the
driver mounted and the enclosure dampened. The R-C on the right side deals
with the inductive rise of the voice coil impedance, the values are only
approximately. Re and Le from datasheet the rest needs to be measured with
an impedance plot.


o---+------------------------+-----------+
| | |
| 0.1592*Qes*Re | |
C| L= ------------- | | Le
C| fs | --- C= ----
C| | --- Rc^2
| | |
--- 0.1592 | __ /| |
--- C= ---------- +-|+ | | |
| Re*Qes*fs +-|__| | .-.
.-. | \| | | R= 1.25*Re
| | | | |
| | Qes*Re | '-'
'-' R= Re+ ------ | |
| Qms | |
o---+------------------------+-----------+
created by Andy´s ASCII-Circuit v1.24.140803 Beta www.tech-chat.de

I copied this from "The Loudspeaker Design Cookbook" by Vance Dickason. Get
also the book "Testing Loudspeakers" by Joe D'Appolito. Both from Audio
Amateur Press

Tony (remove the "_" to reply by email)

Tony wrote:

I do still firmly believe that digital active crossovers have a number
of advantages, particularly much higher potential slopes, and the
ability to tweak the delay independently of the crossover curves (it's
hard to get time alignment any other way with a typical cone MF + horn
HF arrangement). But for this project a 4th order passive is the
limit.


Digital xovers have certainly a lot of advantages, but also the disadvantage
that in an analog system you need A/D and D/A conversions and the price will
be higher. What I have seen so far, most if not all professional digital
systems use filters derived from analog, Linkwitz-Riley for example, with
the same frequency and phase behaviour. This is done with IIR filters, which
are not so trivial to design, so the next disadvantage is the design
difficulty.
Certainly the biggest advantage is the possibility to induce a frequency
independent delay, which in analog can hardly be done with the tweeter,
exept moving it closer or nearer to the listener. ;-(
And that is exactly how it was done before the arrival of digital. For home
entertainment you will hardly need horns, so there will be different
conditions. Also the 3dB/oct boost in the high frequencies of a constant
directivity horn is then not an issue.
The most significant difference is that you can do the analog filters
passive after the amp with L-C and R components, and that is why the digital
multiple amp approach hasn't found more followers.
--
ciao Ban
Bordighera, Italy

On Sun, 08 Aug 2004 05:54:08 GMT, "Ban" wrote:

[snip]
The most significant difference is that you can do the analog filters
passive after the amp with L-C and R components, and that is why the digital
multiple amp approach hasn't found more followers.

You can build your own amplifiers inexpensively.

So the best crossovers are active filters in front of individual power
amplifiers.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

I read in sci.electronics.design that Jim Thompson
wrote (in s5gch0l7l408lc554k3j5js4ed2u8183c1@
4ax.com) about 'Passive (L-C) Linkwitz-Riley or "Thiele Method" filter
design resources?', on Sun, 8 Aug 2004:
On Sun, 08 Aug 2004 05:54:08 GMT, "Ban" wrote:

[snip]
The most significant difference is that you can do the analog filters
passive after the amp with L-C and R components, and that is why the digital
multiple amp approach hasn't found more followers.

You can build your own amplifiers inexpensively.

So the best crossovers are active filters in front of individual power
amplifiers.

I agree entirely. The only components that have to be at the
amplifier/loudspeaker interface are Zobel networks, if you choose to use
them to make each drive look resistive over its active frequency range.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

On Sun, 08 Aug 2004 05:54:08 GMT, "Ban" wrote:

Tony wrote:

I do still firmly believe that digital active crossovers have a number
of advantages, particularly much higher potential slopes, and the
ability to tweak the delay independently of the crossover curves (it's
hard to get time alignment any other way with a typical cone MF + horn
HF arrangement). But for this project a 4th order passive is the
limit.


Digital xovers have certainly a lot of advantages, but also the disadvantage
that in an analog system you need A/D and D/A conversions and the price will
be higher. What I have seen so far, most if not all professional digital
systems use filters derived from analog, Linkwitz-Riley for example, with
the same frequency and phase behaviour. This is done with IIR filters, which
are not so trivial to design, so the next disadvantage is the design
difficulty.
Certainly the biggest advantage is the possibility to induce a frequency
independent delay, which in analog can hardly be done with the tweeter,
exept moving it closer or nearer to the listener. ;-(
And that is exactly how it was done before the arrival of digital. For home
entertainment you will hardly need horns, so there will be different
conditions. Also the 3dB/oct boost in the high frequencies of a constant
directivity horn is then not an issue.
The most significant difference is that you can do the analog filters
passive after the amp with L-C and R components, and that is why the digital
multiple amp approach hasn't found more followers.

All agreed, except the price of the crossover itself. I can buy two
stereo codecs + DSP + MCU + support bits (eg using Wavefront aka
Alesis bits) for MUCH less money than the inductors and polypropylene
caps for two quality L-R passive crossover. Maybe a little more work
to build the DSP design, but the result is potentially far more
flexible than a passive crossover, and easier to tweak. In the next
project I'm integrating a digital crossover into an existing
lightly-loaded DSP, all for the cost of just one more codec. I concede
the extra amps will often push the total system cost in favor of
passive.

Commercial digital crossover systems DO seem to just model the analog
filters, but that seemed to me to be for controllability (it's much
harder to adjust the frequencies on an FIR filter). But that doesn't
mean there aren't (perhaps subtle) gains to be made using with
linear-phase methods (at least for the higher crossover frequencies).

But, as I said, I'm still doing passive this time around.

Tony (remove the "_" to reply by email)

Tony wrote:

Commercial digital crossover systems DO seem to just model the analog
filters, but that seemed to me to be for controllability (it's much
harder to adjust the frequencies on an FIR filter). But that doesn't
mean there aren't (perhaps subtle) gains to be made using with
linear-phase methods (at least for the higher crossover frequencies).


Even if it seems desireable for a digital guy to make "linear phase" filters
(in the digital sense), it is not so from the analog point of view. Each
driver has a lower (and higher) frequency limit. This is a mass-spring
system and has a minimum phase characteristic. Now these interfere with your
nice clean digital zero-phase approach and make it go havoc. :-(
With minimum phase filters you can incorporate the drivers' characteristics
into your design. For example a 4th order Linkwitz-Riley filter consists of
2 cascaded sections of Butterworth 2nd order filters.
You can scale the drivers lower -3dB frequency to the desired value by
correcting the Q with a bell-filter at resonance and applying then a
12dB/oct. low shelf filter to get to the xover frequency. Then another 2nd
order BW HP is cascaded.
The second reason is very important in live music. you do not want long
delays from the singer to the PA and the *minimum phase* approach guarantees
the shortest possible delay.
This is of course not an issue for your home stereo.
So the best would be a "mixed" filter, but so far I have never seen that.
Maybe that is what you should go for? Well those FIR for a 50Hz LP for the
subwoofer will have to be loooong, so better get another DSP just for those.
:-(
IMHO FIR are not appropriate for this kind of work. The real challenge lies
in IIR !
--
ciao Ban
Bordighera, Italy

On Mon, 09 Aug 2004 05:36:28 GMT, "Ban" wrote:

Tony wrote:

Commercial digital crossover systems DO seem to just model the analog
filters, but that seemed to me to be for controllability (it's much
harder to adjust the frequencies on an FIR filter). But that doesn't
mean there aren't (perhaps subtle) gains to be made using with
linear-phase methods (at least for the higher crossover frequencies).

Even if it seems desireable for a digital guy to make "linear phase" filters
Actually my background is all analog - the digital is relatively new.

(in the digital sense), it is not so from the analog point of view. Each
driver has a lower (and higher) frequency limit. This is a mass-spring
system and has a minimum phase characteristic. Now these interfere with your
nice clean digital zero-phase approach and make it go havoc. :-(
Things get worse with real drivers no matter which crossover one uses,
but if there's no real penalty, why not try to get as close as
possible? Certainly the MF driver's time/phase response will mess
things up a bit, but it will always be worse when the 360 degree
rotation of an L-R crossover is added on, and fairly easily "tweaked
out" with a small adjustment to the MF's time delay setting, even with
an FIR. My 2.7kHz crossover is well inside the horn's bandwidth, so
the horn at least should be quite clean down to well below the
crossover.

With minimum phase filters you can incorporate the drivers' characteristics
into your design. For example a 4th order Linkwitz-Riley filter consists of
2 cascaded sections of Butterworth 2nd order filters.
You can scale the drivers lower -3dB frequency to the desired value by
correcting the Q with a bell-filter at resonance and applying then a
12dB/oct. low shelf filter to get to the xover frequency. Then another 2nd
order BW HP is cascaded.
If I understand you correctly...
"bell filter = 2 poles & 2 zeros at same frequency, different Q?
"low shelf filer" = 2 poles, 2 zeros, to shift the effective cutoff?
I think this is approximately what I'm doing between the MF's and the
sub (at 120Hz - certainly not the domain for an FIR), except I
generally select the drivers and alignments so as not to need the
shelf filter, and the overall response is a 6th order sub-Butterworth
(?)

And of course I wouldn't hesitate to use minimum-phase biquads as you
suggest to correct any other anomalies in a minimum phase system,
whatever form the crossover took, because it seems to be the correct
way to do it.

The second reason is very important in live music. you do not want long
delays from the singer to the PA and the *minimum phase* approach guarantees
the shortest possible delay.
For a 200 tap FIR at Fs=48kHz, the effective delay is 100 taps,
equivalent to setting the FOH mains about 2 feet further back. The
singers wouldn't notice 2 feet, but in any case they don't hear the
FOH mains (which are mostly too far away anyway) - they get foldback
through wide-range monitors or IEMs (once you're used to IEMs, losing
that last 8 feet or so of delay from traditional floor wedges IS
noticeable, and CAN help to make a tighter sound).

This is of course not an issue for your home stereo.
So the best would be a "mixed" filter, but so far I have never seen that.
Maybe that is what you should go for? Well those FIR for a 50Hz LP for the
subwoofer will have to be loooong, so better get another DSP just for those.
:-(
Yes, I wouldn't even consider FIR for the lower crossover, only the
upper, where it is practicable, in the critical midrange region where
its reduced lobing can clean up off-axis performance, and the steeper
rolloff can ease that ever-present compromise where the crossover
frequency needs to be higher to ease HF driver power handling, but
lower so the MF driver's ragged midrange doesn't detract too much.

So while I have mostly used analog active crossovers throughout in the
past (L-R top, various to suit the drivers at the bottom), I guess my
systems are now "mixed" - analog active at the bottom (later digital
IIR), and either traditional passive or (next) digital FIR at the top.

IMHO FIR are not appropriate for this kind of work. The real challenge lies
in IIR!
There are challenges all around us. Certainly very low frequency IIR
filters need double-precision arithmetic, but that's not a really big
issue. Because of the variety of possible sub-vs-main speaker
positions there also needs to be some easy "self-calibrating" method
to automatically set crossover parameters; that's easy in theory, but
I can see lots of bad acoustical conditions stuffing it up.

I will still follow the IIR HF path in the next project to see where
it leads. The great thing is that if I can't achieve better
performance than IIR, I can always drop back to IIR with little
effort.

But for now, a friend who has a few Speaker CAD programs is
investigating whether any of them can synthesize a passive L-R for the
current project (which is still my most pressing need). Information on
the "Thiele Method" seems to be sparse, so I'm thinking of
approximating it for my application by just adding a pair of zeros
(null) to the HPF at the HF driver's resonance (maybe just a cap in
series with the final shunt inductor).

Tony (remove the "_" to reply by email)

"John Woodgate" wrote in message
...
I agree entirely. The only components that have to be at the
amplifier/loudspeaker interface are Zobel networks, if you choose to use
them to make each drive look resistive over its active frequency range.

Why not compensate for that in the digital domain as well?

TonyP.

I read in sci.electronics.design that TonyP
wrote (in ) about
'Passive (L-C) Linkwitz-Riley or "Thiele Method" filter design
resources?', on Mon, 9 Aug 2004:

"John Woodgate" wrote in message
...
I agree entirely. The only components that have to be at the
amplifier/loudspeaker interface are Zobel networks, if you choose to use
them to make each drive look resistive over its active frequency range.

Why not compensate for that in the digital domain as well?

Because the Zobel networks are there to make the load lines on the
output devices linear instead of elliptical, which MAY offer advantages
('it depends ....'). I don't think you can do that by any practicable
sort of pre-processing of the signal.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

"John Woodgate" wrote in message
...
Because the Zobel networks are there to make the load lines on the
output devices linear instead of elliptical, which MAY offer advantages
('it depends ....'). I don't think you can do that by any practicable
sort of pre-processing of the signal.

Yes, I suppose there might be some amps where this could make a difference,
for better or worse.

TonyP.

"TonyP" wrote in message
u
"John Woodgate" wrote in message
...
I agree entirely. The only components that have to be at the
amplifier/loudspeaker interface are Zobel networks, if you choose to
use them to make each drive look resistive over its active frequency
range.

Why not compensate for that in the digital domain as well?

That's really not that easy to do, and kinda counter-productive. IOW if you
build a power amp whose complex output impedance could be controlled
digitally, you would have no doubt already solved the reactive load-handing
issues that a Zobel would deal with.

Zobels are kinda like crutches for weak amplifiers and weak passive
crossover designers. ;-)

I read in sci.electronics.design that TonyP
wrote (in ) about
'Passive (L-C) Linkwitz-Riley or "Thiele Method" filter design
resources?', on Tue, 10 Aug 2004:

"John Woodgate" wrote in message
...
Because the Zobel networks are there to make the load lines on the
output devices linear instead of elliptical, which MAY offer advantages
('it depends ....'). I don't think you can do that by any practicable
sort of pre-processing of the signal.

Yes, I suppose there might be some amps where this could make a difference,
for better or worse.

It's extremely unlikely to be worse, unless the heat sinks and power
supply are only marginally adequate.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

I read in sci.electronics.design that Tony wrote
(in ) about 'Passive (L-C)
Linkwitz-Riley or "Thiele Method" filter design resources?', on Mon, 9
Aug 2004:
Information on
the "Thiele Method" seems to be sparse,

You can get his paper from the AES. For that matter, YOU can go to
Epping and talk to the man himself. Even if you are in Perth or Darwin.
(;-)
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

"Arny Krueger" wrote in message
...
That's really not that easy to do, and kinda counter-productive. IOW if
you
build a power amp whose complex output impedance could be controlled
digitally, you would have no doubt already solved the reactive
load-handing
issues that a Zobel would deal with.

Zobels are kinda like crutches for weak amplifiers and weak passive
crossover designers. ;-)

Since we were talking about speaker Xovers, not amplifiers, I assumed he
really meant driver impedance compensation for Xover, not amplifier
stability.
The amplifier zobels are already in the amplifier!
Maybe I misread.

TonyP.

"TonyP" wrote in message
u

"Arny Krueger" wrote in message
...

That's really not that easy to do, and kinda counter-productive. IOW
if you build a power amp whose complex output impedance could be
controlled digitally, you would have no doubt already solved the
reactive load-handing issues that a Zobel would deal with.

Zobels are kinda like crutches for weak amplifiers and weak passive
crossover designers. ;-)

Since we were talking about speaker Xovers, not amplifiers, I assumed
he really meant driver impedance compensation for Xover, not amplifier
stability.

I see a relationship, in that

(a) Not all amps have zobels nor presumably do they need them.

(b) If an amp was going to be unstable with an inductive load, then the
speaker's zobel could help it.

The amplifier zobels are already in the amplifier!

Maybe.

"Arny Krueger" wrote in message
...
I see a relationship, in that
(a) Not all amps have zobels nor presumably do they need them.

Right..

The amplifier zobels are already in the amplifier!

Maybe.

See your (a) part 2!

Frankly if the amp is broken, fix the amp, not the speakers.

TonyP.

"John Woodgate" a écrit dans le message de
...
I read in sci.electronics.design that TonyP
wrote (in ) about
'Passive (L-C) Linkwitz-Riley or "Thiele Method" filter design
resources?', on Mon, 9 Aug 2004:

"John Woodgate" wrote in message
...
I agree entirely. The only components that have to be at the
amplifier/loudspeaker interface are Zobel networks, if you choose to
use
them to make each drive look resistive over its active frequency range.

Why not compensate for that in the digital domain as well?

Because the Zobel networks are there to make the load lines on the
output devices linear instead of elliptical, which MAY offer advantages
('it depends ....'). I don't think you can do that by any practicable
sort of pre-processing of the signal.


You can do that with another amp and a power resistor :-)



--
Thanks,
Fred.