New Wave Guide Study

[dwk]

Now, how about a stack of 4 NS12's on each side, a waveguide loaded BG RD50, then a stack of ribbon tweeters above 4 kHz?

Oh yeah, better be careful with that idea, that's Evil Twin's Saint-Saens...

Given the results I had with my waveguide-loaded Monsoon planars, I really think this idea has merit. I have some 60" Carvers laying around, and if I had the space I would have persued the waveguide idea. The tweeter arrangement is challenging, though. Seems to me you'd have to have them inside the mid waveguide to avoid horrible horizontal lobing, and at that point the ribbons seem to be too big. If you can get 10k out of the planars, then a short row of neo's might do it, but even there mounting might be tricky.

[Dennis H]

Of course, given that I threw in the towel on all this and just shelled out $$$ for the real Yorkville Unities, I guess I'm obligated to point out that there are some real practical challenges involved.

Cool! How do they sound?

[ThomasW]

Doug,

Are you really located in Denver? If so I'd certainly like to hear the Yorkville Unity speakers.

[dwk]

Cool! How do they sound?

For the most part, excellent IMHO. Straight out of the box they have some issues, but removing the grilles (mandatory IMHO), adding a bit of fill to the box and throwing a few parametric sections did wonders. They preserve the good points of my Unity experiments, and add great dynamics - both micro and macro. Needless to say, a speaker capable of playing all day at 120dB+ has completely effortless dynamics in a home setting.

The U15's by themselves are only good down to maybe 50Hz, so they need a sub. I'm still working on this (currently using a couple of the TB W8-740C's in a ported enclosure), and am still dialing in the EQ.

Where my current rig is not fabulous has more to do with the room/setup. My room is narrow and long (7' x 16'), and the speakers are in the corners firing down the long axis. While the speakers disappear, the image is laterally compressed and lacks a degree scale; better than the overly exaggerated size of some 'big rigs', but not as immersive as would be ideal. I'm still working on this as well.

Doug,

Are you really located in Denver? If so I'd certainly like to hear the Yorkville Unity speakers.

Yeah - I'm in town just east of the museum/zoo. It had been in the back of my mind to drop you a line when I have things a little more pinned down. Having been called out, I guess I can't avoid it now :-). I'll send you a PM in the new year, since my calendar is pretty much booked until then.

You have to promise not to make fun of me for having 15" midbass drivers and 8" 'subs', though.

[Tommythecat]

As soon as I read that my jaw dropped. 8" subs....why bother?

[dwk]

As soon as I read that my jaw dropped. 8" subs....why bother?

Well, as I said the sub is a temporary setup, and the TB's were the only drivers I had on hand that would do something interesting in the 2 cu ft cabinet I had laying around.

There was also a bit of curiosity factor - both on the TB drivers themselves which are pretty amazing 8" drivers, as well as on ported subs, since previously I'd been using sealed.

Having said that, two of them actually account themselves pretty well, all things considered. Power hungry, but if my WinISD modelling is right they'll comfortably do 105dB from 30Hz on up, and the very low tuning (20Hz) means that in the music passband group delay is quite low. So, certainly rather small-time compared to the monster rigs discussed around here, but for a music-only system in a small room it's not quite as comical as it first looks.

[Dennis H]

I wonder if Yorkville will sell parts, e.g. the unity horn, mid drivers and tweeter driver?

[ThomasW]

I wonder if Yorkville will sell parts, e.g. the unity horn, mid drivers and tweeter driver?

Interesting question. I'd be surprised if their licensing agreement with Danley (ServoDrive?) allowed that, but we never know unless we ask......:wink:


For the hardcore DIYers in the crowd, here's the real thing from William Cowan in Oz....

http://diy.cowanaudio.com/unity.html

http://web.archive.org/web/20030602202055/www.lambdacoustics.com/unity.html

http://web.archive.org/web/*/http://www.lambdacoustics.com/

[Hank]

Now, how about a stack of 4 NS12's on each side, a waveguide loaded BG RD50, then a stack of ribbon tweeters above 4 kHz?

Oh yeah, better be careful with that idea, that's Evil Twin's Saint-Saens...

IT'S ALIVE, IT'S ALIVE!!! :B

[Scott Simonian]

How would I go about building a unity, Thomas? I've read that website countless times in the past 3 years and all it has on it pretty much is the patent. It is very complicated to me, I wasn't sure if there was an easy formula.

I've been chasing the idea of a unity horn for ages but it never seemed very popular.

[ThomasW]

The Lambda kit was available but discontinued.

To make one now one would need to take the drawing below, import it to a CAD progam and scale it to the correct size to obtain a working drawiing. The actual dimensions of the outlet are posted on several websites. Just Google 'Unity Horn' or 'DIY Unity Horn', and you can find a ton if info about the horn.

I thought at one point there was a dimensioned drawing floating around but perhaps that was wishful thinking on my part...

There was quite a bit of bandwidth dedicated to how exact the construction of the horn and the placement of the drivers needed to be.

Some additional information might be available from the LambdaDrivers Yahoo group

http://tech.groups.yahoo.com/group/LambdaDrivers/

[dwk]

The problem with a DIY Unity is that everything is related to everything else. So, unless you get the *exact* same parts, things will change. This is a large part of what all the DIYers have been struggling with - the midrange drivers used in any 'real' Unity are not available, and it seems that there is no obvious slam-dunk candidate out there. So, the diagrams from the Lambda kit or the patent are only basic guidelines if you have to use other drivers.

There is a fair bit of scattered discussion over on diyaudio, but little in the way of working results. John Sheerin, 'Patrick Bateman' and I are the only ones I know of that have indicated 'working' prototypes, and mine wasn't even really a true Unity, and Patrick's was an unusual car application. Patrick did put together a list of promising mid drivers that may be worth looking at, though.

Given that the pair of U15's I got was under $2k delivered (to a freight terminal), I suspect that Yorkville could make money selling just the horn + drivers + mid/high xover at $1k-$1.2k. I don't believe they're inclined to do so, though - they're a high-volume value-oriented brand, and it would probably undercut their market, not to mention introducing support headaches (this was a problem with Nick, if I remember correctly). Tom and Servodrive were addressing the high-end, so a few DIY variants floating around didn't matter much to them.

Realistically, I think Nick was selling the Lamdba kits at around $1.5k (anyone remember the actual price?). Getting a cabinet and two good 15" drivers (which appear to retail to the diyer at $250+ each) for another $400 isn't a bad deal. If they could hit 40Hz solidly on their own, I'd say there would be little point in a ground-up DIY effort, as parts cost would be a significant fraction of this whatever you do. The need for a sub even in a music-only system undermines the value proposition a bit, though.

This isn't to say that I'm not already thinking about a complete overhaul with new fully-active DSP xovers and possibly a new cabinet, though

[ThomasW]

Kit pricing depended on the HF compression driver chosen.

Radian or B&C were $795ea, TAD was $1495ea

Here's the original kit...



Rear shot of just the raw horn

[dwk]

I had a chance yesterday to finally spend some time primarily listening to the Unities, rather than mostly focussing on tweaking and setup. I did play around with the listening position though, with some interesting observations.

Originally I had them set up according to Geddes (among others) suggestion with the speakers toed-in so that the main axes cross well in front of the listening position. In addition, since the speakers are on the floor, my ears are 8-10" above the tweeter position. I moved the listening position forward so that it was close to the equilateral triangle geometry about 8 ft form the plane of the speakers, and sat on the floor so that my ears were basically level with the tweeter. The speaker axes still cross in front of the listening position, but only just barely. Even so, this avoids the 'head-in-a-vice' problem that many nearfield setups suffer from. I can lean far-right to far-left without a significant change in presentation. IMHO this is a big benefit of the waveguide/CD design.

Since I was now closer to on-axis, I had to tweak the eq a bit, toning down the high end just a bit. The overall improvement was noteworthy. Moving closer expands the soundstage, as well as improves the direct-to-ambient ratio, which already is improved by the controlled-directivity design. The presentation is probably a bit closer to the proverbial 'big set of headphones' than most of the dipole fans around here would prefer, but for the moment I'm digging it. The increased ability to listen into the recording compared to the previous setup is remarkable.

So, I guess the 'generic' observation out of all this is that the results seem to me to validate my belief that controlled directivity is a big benefit in small rooms. The U15 setup works far better in this room than the various attempts using my ACI Sapphire XL's (mini-monitors). Obviously this is a bit different than the tweeter-only waveguides that most folks are looking at, but some of the experience might translate.

[Mark Seaton]

Knowing a bit about the U215 design, I have often given thought to gutting the crossover or at least the section on the LF and modifying these for some very high performance HT LCRs. The molded horn and the mid & compression drivers are very good performers. There is some room to improve the crossover, but it's certainly not a task for the faint of heart or the ability to measure the speaker accurately with phase data. If using these for home use, I probably would start by taking off the grill and covering the face to a smooth surface and place something like felt or foam around the front edge of the horn. Again, ability to measure is key. I'd also consider covering the ports internally or externally and just use a little EQ or other means to use them as a sealed box and cross them to a sub. Of course that's just my thoughts on how I'd love to use them...

[Dennis H]

Yeah, looking at the manual for the Yorkville active processors, the U215 looks like a better box. The processor for the U215 doesn't have the big notch filter at ~180 Hz so I'd assume the box doesn't have the resonance there. Of course, some people say you can fix the resonance of the U15 with some stuffing so one has to wonder why the factory doesn't do that. The powered U15P is attractively priced (only something like $250 street price more than the passive version) but it probably includes that notch filter for the box resonance and that doesn't appeal if stuffing is a better fix.

[AJINFLA]

Mark,

what might the advantage be of using the unity above 300hz as opposed to a high performance, larger (maybe 8-12")format coaxial mid/tweeter (with optimized mid surround)? Perhaps even dipole or cardioid for further directivity control (and possible boxless sound benefits) as frequencies decrease.

cheers,

AJ

[dwk]

.
The molded horn and the mid & compression drivers are very good performers

Understatement. They are *excellent* performers from 300 on up. I'm really very very impressed.

If using these for home use, I probably would start by taking off the grill

Yup, already done, and it made a big difference all by itself.

and covering the face to a smooth surface and place something like felt or foam around the front edge of the horn.

Yup, on the agenda. I do have to say that it's not anywhere near as bad as I was expecting even without any absorption.

I'd also consider covering the ports internally or externally and just use a little EQ or other means to use them as a sealed box and cross them to a sub.

Yup, already talked to Todd about this, although I haven't acted on it yet. I'm using a ~10W amp on them right now, so I can't eq/boost as it is. I need to go active and drive the woofer separately to achieve this, but I'm pretty sure this is where I'll end up going. I need to swap amps around and get the sub situation sorted out first.

Cool that your list is basically exactly what I came up with for my approach. I've decided that I'm not going to touch the xover at all until/unless it is to completely replace it with a custom DSP/FIR phase coherent version. They sound so good as it is that I don't think that tweaking the passive is going to be worth the effort.

[dwk]

Of course, some people say you can fix the resonance of the U15 with some stuffing so one has to wonder why the factory doesn't do that.

It helps, but in my case it doesn't eliminate it completely. I didn't really spend a heck of a lot of time tuning/measuring/re-stuffing, though. Part of the problem may be that it hits very close to a resonance from my ~7' ceiling, so my specific case may be worse than average.

[ohenry]

I'm certainly the least experienced diy'er here. So forgive the simple question.

Some of the most respected speaker building amateurs on the web have tried their hands at waveguide mounted tweeters - with almost universally positive results. Very few professionally designed products (for the home) sport this design.

How is it that amateurs would seem to be at the technological leading edge of something so fundamental as waveguide integration? Why wouldn't the manufacturers themselves (Vifa, Peerless, Eton, ScanSpeak, SEAS, et al) of components to the diy community be leading the way by offering a few models with dedicated large waveguides? It seems counterintuitive to me somehow.

Sorry for the intrusion if this seems a little boneheaded. But I've been dying to ask this question. It may already have been adequately answered in this thread, but simply gone right over my head. Thanks.

[JonMarsh]

Well, a few manufacturers do use this technology, more on the pro sound side, and guys like SP Technology on the consumer side.



Mfrs of the drivers aren't integrating it because it's more system dependent, and it's still a bit "new" or perhaps controversial? Plus, systems tend to be bigger, and if your wife thinks those little Bose satellites are so cute, a lot of focus has been on making the smallest satellite speakers possible for HT.

Unfortunately.

[Chris7]

The very latest version (v4) of the Paradigm Atom (a perennial best-selling commercial speaker) uses a waveguide:



All of Paradigm's lineup seems to be moving in this direction.

[JonMarsh]

Well of course, especially that they're now part of Klipsch!

~Jon

[AJINFLA]

Why wouldn't the manufacturers themselves (Vifa, Peerless, Eton, ScanSpeak, SEAS, et al) of components to the diy community be leading the way by offering a few models with dedicated large waveguides?

I had asked this of Ken Kantor a while back https://www.htguide.com/forum/showpo...80&postcount=8
He finally did get back to me. Cost. His bean counters would not allow it.
The demand simply would not be there to justify the added $$.

cheers,

AJ

[Bent]

The very latest version (v4) of the Paradigm Atom (a perennial best-selling commercial speaker) uses a waveguide:



All of Paradigm's lineup seems to be moving in this direction.

Geeze, that mid on the Atom looks like something a therapist would prescribe to a patient to prevent/alleviate inverted nipples. :lol:

[JonMarsh]

Other folks recognize the waveguide usefulness also, such as this design from Duelund Audio in Denmark.

Image not available

There are a lot of other unusual concepts in this speaker, as it's based on a lot of Steen Duelund's concepts, many of which are well often the beaten path. They and Gryphon Audio, who uses many of Duelunds concepts, like the ringradiator tweeters loaded into a waveguide. Then there's my old friend Chas Hansen who wondered why folks would build a tweeter in which the radiating area all behaved like the surround in a standard tweeter...

[JonP]

Interesting pics.... Had seen the SP speakers, hadn't seen the Paradigm's or the Duelund's...

It looks that one of the other barriers to DIY'ing it with these is that it would seem that a fairly shallow angle produces the best working reinforcement and dispersion. The ones shown seem to be about 30deg or so for the main angle of the WG.

This makes it a bit tough for the average DIY'er to machine such a flat horn... I was looking into making horns in MDF, using common router bits, such as a 45deg chamfer, and a 3/4" roundover. 45deg is pretty steep, you seem to end up with an overly deep waveguide/horn...

Buying a off the shelf item, with some modification, a la Zaph's experiments, is the easiest way to go, but I still would like to come up with a fairly easy and repeatable way to machine/cast/manufacture horns on demand.

Hopefully after the Xmas season settles down, I'll get some measurments done on my experiments so far...

[TacoD]

Other folks recognize the waveguide usefulness also, such as this design from Duelund Audio in Denmark.

Image not available

There are a lot of other unusual concepts in this speaker, as it's based on a lot of Steen Duelund's concepts, many of which are well often the beaten path. They and Gryphon Audio, who uses many of Duelunds concepts, like the ringradiator tweeters loaded into a waveguide. Then there's my old friend Chas Hansen who wondered why folks would build a tweeter in which the radiating area all behaved like the surround in a standard tweeter...

Steen Duelund's concepts are indeed very special, next to his crossover components he also promotes a special crossover concept (comparable to the filler concept of B&O), these filters are difficult to get right, especially on driver selection.

[Evil Twin]

Steen Duelund's concepts are indeed very special, next to his crossover components he also promotes a special crossover concept (comparable to the filler concept of B&O), these filters are difficult to get right, especially on driver selection.

One filter to rule them all...

The entire three way filter is derived at one, and adjusted for each section with a common coefficient, to produce an all pass network summing to unity, with a 360 degree continuous phase rotation. If the drivers are selected correctly and the acoustic transfer function implemented correctly, all three drivers in a three way will be in relative phase at every frequency. This eliminates destructive interference and the should produce a very coherent sounding multi-way speaker.

If the filter coefficient is at the baseline level (square root of 2, i.e. 1.414...), the midrange element reduces to zero, and what is left for the high and low pass is a LR4 network.

As the filter coefficient is raised, the midrange level comes up, and the corner frequency of the LP and HP move apart.

At a coefficient of the square root of 3, a Bessel filter results for LP and HP, with a narrow range mid filler having a peak level of -9 dB. Very high stress on woofer and tweeter, unless SPL requirements are limited, as for a 1 kHz center frequency the woofer and tweeter are only down 9 dB. Ultimate LP and HP slopes are 24 dB/octave, midrange slope is 12 dB/octave.

Optimum/feasible ranges for the filter coefficients with "real" drivers seem to be in the range of 2 to 2 X the square root of 2 (2.828). The latter is demanding on the midrange driver, the former on the woofer and tweeter.

Only the determined, with large driver budgets or modest SPL requirements, are likely to get this to work...

[Paul W]

After replacing my sound card, finding an intermittent 1/8" phone plug, plus 2 open alligator test leads, it is time to go back to work...whew!

Here is a direct comparison of three drivers and two waveguides. In all cases, the microphone is flush with the baffle plane, maximum time, maximum window, no high-pass, to try to learn about driver interaction with the waveguides while leaving out as much of the room and baffle as practical. (Note that an unusually large 11.5" diameter WG is used with the Hi Fi drivers. Though it stretches CTC distance, I'm trying for a high-output/low distortion 1.1k crossover to compliment a region of reduced hearing sensitivity.)

First is a standard Seas 27TDFC...no special comments.

Second is the TDFC with a diamond shaped cutout in a 1/8" felt gasket over the surround. This was done in attempt to damp the 12k notch in the standard...as you see, that didn't work.

Third is a Vifa D27TG-35. The interesting thing about this tweeter is that the dome is recessed in a small chamber so that the top of the dome is flush with the flange...the dome does not enter the throat of the WG like the TDFC dome.

Fourth is a BMS Pro 4552ND compression driver on a DDS Eng 90-1 Waveguide. This is apples-oranges vs the Hi-Fi drivers...much higher sensitivity, higher output, etc etc. Though it is nearly the same diameter, the DDS WG is not as deep as the other WG and has a more "Obulate Spheroid" shape.

To mount the Hi Fi drivers on the DDS I'd have to mill the throat way to shallow, destroying the WG for 4552 use. Maybe a 19mm driver will fit...have to try that. Anyhow, after I modify another "cheapie" WG to mount the 4552, I'll do an A-B of the two waveguides with the BMS driver. After that, pattern response, but gotta get a turntable first.

[Paul W]

Here is the next round (with a new mic preamp).

After a listening, I suspected that the DDS wasn't holding pattern control low enough to match up with the 10" mid at the 1.1k XO. In-room RTA seemed to confirm the suspicion and a 1.5k XO did sound less forward...so long overdue for a peek at WG off-axis response.

I also wanted to try the cheapie 12" WG with the BMS 4552 so a 7/8 adaptor was bored out to 1", glued into the WG, the gap filled with microballons, then carefully filed for a smooth curve between the 1" throat and the WG. (the plastic screw/bolt-on adaptors are undersize, the WG is a little over 1")

No turntable yet, so the 45 degree off-axis is strictly "eyeball".

-First is the 4552 measured at the mouth of the DDS WG.



-Second is the 4552 at the mouth of the 12"WG.



-Third is the 4552/DDS at 0.5M on-axis and about 45 degrees off axis.



-Fourth is the 4552/12" at 0.5M on-axis and about 45 degrees off axis.



Overall, the cheapie 12" WG does quite well.

[JonMarsh]

What is the cheapie 12" WG you're referring to?

[Paul W]

The cheapie is the $7 WG from MSC. It appears to be exactly like the PE 12" except that it doesn't have the threaded metal insert...easier to modify.

[JonMarsh]

Thanks Paul. More food for thought.

Gahh.... I'm getting pretty full lately!

~jon

[Paul W]

Jon,
Glad to add to your plate! I don't know how you keep up with it all.
Paul

[Paul W]

Your interpretation of screenshots?

With the idea "if we can see them, we can combat them" I spent some time this weekend trying to identify High Order Modes. While trying several different signals, I found one unusual glitch (probably not HOMs but I dunno what).

The first screen shot is a very loud pulse with the microphone in line with the sidewall of a DDS 90 waveguide. Notice not only the tail, but the whole pulse is offset to the low side.

The second shot is an identical pulse, identical mic location, but with a foam filter inserted into the WG.

The tails and offset shown in the first shot are strong only in a few narrow frequency bands, elsewhere they are weak to virtually non-existent. What interference can cause a signal to deform in this way?

[Paul W]

For now, my activity with the DDS and MSC waveguides is complete. Below are the last tests intended to see what, if any, improvement in the MSC resulted from adding a heavy resin/sand mix to the back of the WG. (As you would expect for a $7 part, the MSC plastic is much thinner than the fairly substantial DDS.)

The MSC WGs were all modified to accept a bolt-on driver by gluing a screw-in adaptor. The (undersized) adaptors were bored out to 1" and careful smoothed to the WG profile using glass microballoons. So the plots are easy to read, microphone preamp gain was reduced to show only the first 25-30 db of decay (bottom of the scale is 45db). For reference, the DDS was measured under identical conditions. The same BMS 4552ND compression driver was used for all tests.

First the DDS...

Image not available

Next the MSC with no resin...

Image not available

MSC with resin and sand damping...

Image not available

MSC with resin and sand damping, plus a sand texture added to the inside surface...

Image not available

If anything, the sand texture on the inside of the WG seems to add HF hash, so not recommended. The resin and sand on the back of the WG seems to make a minor improvement, though it certainly isn't a dramatic change.

All things considered, I believe the modified 12" MSC is an excellent alternative to the 10x more expensive DDS. With slightly greater diameter and a little more depth, the MSC can be used a little lower in frequency...plus it delivers more consistent pattern control. Since the DDS is out of production for at least the next few months it may be an easy choice for any near-term projects.

The "bogie" is a big DIY ribbon tweeter.

Image not available

Though the BMS 4552ND with WG beats the ribbon in ultimate dynamic range and, at most frequencies wins HD and IM, the ribbon sounds more natural. Dunno if it is the very quick initial decay of the ribbon, radiation pattern or what, but now I am gonna have to try a one in a WG.

[JoshK]

What's MSC?

[Paul W]

MSC = Music Supply Center

[ThomasW]

Hey Paul,

Could/would you open a photo-bucket or similar account for your pictures? That way you won't keep running into Geocities bandwidth limitations.

[Paul W]

Yup, next time will not be Geocities. :T

[dlr]

Have you read through SL's page?

Unless I'm misreading, it looks like SL has expanded some on a Dueland crossover and shows how it can be implemented to a fairly close approximation using LR crossovers. The improved group delay is very intriguing. I was thinking of creating a Dueland target for optimizing then running in DF mode in SoundEasy to audition it. It doesn't look to be overly demanding on the midrange unit at all from what I see. I think it's more demanding on the tweeter, at least in the form as presented by SL.

Dueland XO at Linkwitz Lab

[AJINFLA]

Hmmm, methinks the LR4 on the tweeter centered @ 2.05k should be less of an issue than the LR2 on the mid, especially in the upper passband behavior. Still an intriguing design. The DCX comes in handy to force some nicer behavior at both ends. A 5-6" mid should fit the bill nicely. I still have my 850488s laying around in the stockpile.
BTW, hate to do this to you Dave, but is Duelund



cheers,

AJ

[dlr]

It depends on what one wants

Hmmm, methinks the LR4 on the tweeter centered @ 2.05k should be less of an issue than the LR2 on the mid, especially in the upper passband behavior.

The upper passband of the mid isn't hard to do well. I'm using the 12m in an LR2 passband easily. There are a number of drivers that can do both ends well. Hard cones need not apply, but SS or Seas 5" non-metal drivers can easily handle LR2 at 120/2050. Baffle step will always be an issue, but that's true even of any standard crossover as well. The Duelund is only a slightly altered 2nd order behavior from any standard LR2, what I think really caught SL's interest.

The tweeter is more limited as I see it. There are certainly many drivers that can do LR2 at 2.05K, but that precludes all 3/4" tweeters, my preference. This forces one to choose a tweeter with limited dispersion. The only exception may be the new 6600 and 7100 from SS.

Still an intriguing design.

What's more intriguing to me is that it can be done passively. SL suggests that using an LT on the mid and tweeter could be useful as well, though I'd hesitate to do that on the tweeter even if going active.

The DCX comes in handy to force some nicer behavior at both ends. A 5-6" mid should fit the bill nicely. I still have my 850488s laying around in the stockpile.

They look like good candidates.

BTW, hate to do this to you Dave, but is Duelund

No problem. I keep wanting to start with "Deu".

[Dennis H]

The tweeter is more limited as I see it. There are certainly many drivers that can do LR2 at 2.05K,

The woofer and tweeter use two LR2 filters each, giving a 4th order rolloff. Unfortunately the DCX can't do that so you'd have to fudge it with an LR4 and some parametric EQ to try to match the transfer function. SE should be able to do it okay.

a) Crossover frequencies at 0.24 and 4.1 (e.g. at 120 Hz and 2050 Hz)
Crossover points are at -6 dB.
Filter outputs are in phase when the midrange bandpass has reversed polarity.
Bandpass is centered at normalized frequency 1 (e.g. at 500 Hz).

b) Woofer lowpass LPD3 = 0.384 / ( s + 0.38 )4
Four real axis poles at -0.38 which can be realized with two LR2 lowpass filters in cascade (e.g. at 190 Hz).

c) Midrange bandpass BPD3 = -15s2 / [(s + 0.28 )2 (s + 3.6)2]
Two zeros at the origin and two poles at -0.28 can be realized with a single LR2 highpass filter (e.g. at 140 Hz).
The two poles at -3.6 can be realized with one LR2 lowpass (e.g. at 1800 Hz). It is in cascade with the LR2 highpass.

d) Tweeter highpass HPD3 = s4 / (s + 2.62)4
Four zeros at the origin and four poles at -2.62 can be realized with two LR2 highpass filters in cascade (e.g. at 1310 Hz).