Duelund XO: the Big Concept

[Dennis H]

The big concept of the Duelund XO can be summarized as "all drivers in phase at all frequencies." To do that, he stacks LR2 filters when using 3 or more drivers. For example:

Woofer: LR2-400 lowpass, LR2-2500 lowpass
Midrange: LR2-400 highpass, LR2-2500 lowpass
Tweeter: LR2-400 highpass, LR2-2500 highpass

It seems reasonable that you could apply the same big concept to other filter types so I gave it a try with B3 filters. I modeled the MTM section of a WMTMW using B3 filters and "perfect" drivers. I only have the demo version of LspCAD so I couldn't do the whole WMTMW but this will show it well enough.

Here's the standard non-Duelund-style schematic.



B3 filters should track in phase quadrature, i.e. 90 degrees apart. Notice how the phase tracking falls apart at lower frequenies.



Because of the poor phase tracking, there is a broad 2dB hump around the crossover frequency.



Too many pics so the Duelund-style version is in the next post.

[Dennis H]

Now for the Duelund-style. We'll add another B3 highpass to the tweeter at 400 to match the midrange. That makes the ultimate rolloff of the tweeter 6th order.



Now the phase tracks in perfect quadrature.



And the XO sums flat. You wouldn't think stuff happening below -50dB where the tweeter goes 6th order would make so much difference but it does. Of course we are talking about acoustic targets here but the electrical transfer functions show the Big Concept.

[ch83575]

It sounds like an interesting idea, but can you describe the benefit over the alignment described by the Duelund formula?

[Dennis H]

Duelund's formula uses 12dB/octave slopes for everything. With some drivers or some alignments, say a dipole mid with heavy cone breakup, 12dB may not be steep enough on either the high or the low end. The Big Concept just expands on Duelund's formula and allows you to use any (acoustical) slopes at any frequencies as long as you duplicate the filters on all the drivers. The Duelund formula is symmetrical around the center frequency but that isn't really necessary. You could still fulfill "all drivers in phase at all frequencies" with something like:

Sub: LR4-60 lowpass + LR2-300 lowpass + b3-2000 lowpass
Woofer: LR4-60 highpass + LR2-300 lowpass + b3-2000 lowpass
Mid: LR4-60 highpass + LR2-300 highpass + b3-2000 lowpass
Tweeter: LR4-60 highpass + LR2-300 highpass + b3-2000 highpass

[ch83575]

Sorry if I am asking a lot of dumb questions, I am in the process of trying to wrap my brain around the theories behind these filters. I still have no idea what the "complex s-plane" is, perhapse I should find a textbook on the subject. Here is what I am wondering: in Duelund's formula there is a variable "a" that changes the width of the midrange, and when "a" is small the formula lowers the mid level to maintain a flat FR. In your big concept how would this be accounted for? Likewise, in an asymeyrical topology is it even possible?

Thanks,
-Chad

[AJINFLA]

Pretty cool Dennis. Might have to drag out the DCX and cascade some filters. I guess my only issue with all this is audibility of the different topologies vs what we know really matters, which is polar uniformity, low levels of non-linearities, diffraction, etc, etc.

cheers,

AJ

[Dennis H]

Chad,

You're not alone, S-plane math makes my head hurt too. Short version, it's a way to use a single formula to describe both the magnitude and phase behavior of a filter using imaginary numbers: j=sqrt(-1). The stacked LR2 filters match Duelund's formula for any reasonable spacing of the crossover frequencies. I checked it at a=2, with the two frequencies at approximately 950 and 1050, and it still works. As a goes below 2, it starts to not match, but you'd never build a real 3-way with the two frequencies so close.

AJ,

Yeah, this is all just bench racing on the computer. As JonMarsh likes to remind us, there's a lot more to building a speaker that sounds good.

[ThomasW]

https://www.htguide.com/forum/showpost.php?p=450285&postcount=331

[Smokinghot]

ya... I'm going to have to bookmark this and re-visit it in a couple of years...

[dlr]

B3 filters should track in phase quadrature, i.e. 90 degrees apart. Notice how the phase tracking falls apart at lower frequenies.



Because of the poor phase tracking, there is a broad 2dB hump around the crossover frequency.

This is a bit misleading. To be accurate, B3 filters DO track in phase quadrature. The problem is not the B3, the problem is the highpass only section shown. You've also left out the lowpass of the upper driver, using a perfect driver flat to infinity there. The Duelund won't actually sum properly for the w/m in a 3-way or a w/t in a 2-way due to the woofer highpass even if you somehow manage to make those highpass functions perfect Duelund responses as well. The m/t section won't, either, due to the tweeter lowpass (ignoring the midrange imperfect response). No crossover function specified for a single Fc is going to fully sum properly with these taken into account.

It's academic to large degree, except maybe low w/m Fc, but the point is that a B3 and other crossovers do sum appropriately with the correct input, i.e. ideal driver responses. Make that input a raw driver bandpass and you can't expect ideal response. Since woofer highpass box response cannot be tailored to be flat nor the tweeter lowpass, non-ideal response of all crossovers will be the norm, even the Duelund. They all require some compromise.

Here's an ideal BW1 3-way example, but in this case, ideal drivers are shown. This is for acoustically aligned drivers at the test point, an issue with any crossover, of course.



So again, the Duelund isn't going to hold if woofer highpass or tweeter lowpass is included. This, of course, also only if the acoustic centers are perfectly aligned for the design point. Then you'll have to be at the precise design point for listening.

None of this touches on the unrelated problem of how to integrate a Duelund with the unavoidable and most prominent reflection, the floor bounce. Though I may try a Duelund myself one day, the requirements for woofer and mid vertically positioning coupled with a very careful w/m Fc selection to minimize the floor bounce of each of these two drivers makes much of the issue of imperfect response a much smaller issue for the w/m section.

Dave

Edit: One last thought. When constructing a Duelund, is anyone going to go to the lengths that Dunlavy did in controlling diffraction? If not, all of that perfect Duelund response on-axis is going to degrade quickly within a 5 degree horizontal window by far more than the error involved with non-ideal driver issues.

[dlr]

https://www.htguide.com/forum/showpo...&postcount=331

Interestingly, all of those examples leave out woofer highpass and tweeter lowpass.

The other point I would make is that the comment about "perturbations" in BW power response due to its lobing is also incorrect. The BW power response of all orders, shown at john k's site, is superior to any LR (or Duelund by extension, I think) of equivalent order. Lobing is not an issue for power response, as it is not an axial issue, the integrated over the full surface of an enclosing sphere is the concern.

Dave

[Dennis H]

So again, the Duelund isn't going to hold if woofer highpass or tweeter lowpass is included.

Right, Dave! Those transfer functions should be included on all the drivers as well when you're building target curves. I thought the big concept was complicated enough already without mentioning that. Most drivers are rolling off anyway outside the passband so some of that extra rolloff is built in and doesn't necessarily require extra components.

As you say, the whole thing is mostly theoretical and perhaps not very practical but I enjoy figuring out how things work in terms my simple brain can grasp -- I have a hard time visualizing sqrt(-1).

[Dennis H]

The other point I would make is that the comment about "perturbations" in BW power response due to its lobing is also incorrect. The BW power response of all orders, shown at john k's site, is superior to any LR (or Duelund by extension, I think) of equivalent order. Lobing is not an issue for power response, as it is not an axial issue, the integrated over the full surface of an enclosing sphere is the concern.

Dave

I agree with the power response comments but lobing can still be a problem with odd order crossovers. A 3rd order MT with the preferred inverted polarity will have a big null not all that far above the tweeter axis. In some rooms, you could find yourself in the null when you stand up. That's why I picked a WMTMW for my 3rd order example rather than a TMW.

[dlr]

I agree with the power response comments but lobing can still be a problem with odd order crossovers. A 3rd order MT with the preferred inverted polarity will have a big null not all that far above the tweeter axis. In some rooms, you could find yourself in the null when you stand up. That's why I picked a WMTMW for my 3rd order example rather than a TMW.

True, in fact there's a peak at the lobe as well as a trough in the other direction as opposed to the peak being on the design axis for a L-R or Duelund. Probably one reason Dunlavy preferred the WTMTW, to improve the vertical off-axis response. The power response changes, of course, but it's just another tradeoff among many.

The thing is, ALL non-coincident crossovers will suffer from some form of off-axis irregularity unless it is within the range where both drivers are somewhat constant directivity and with long enough wavelength at Fc , one good reason for 3-way or more systems. If you're listening a bit farther back, the BW1 lobing is much less of an issue as well. Much depends on the overall design considerations. I think that too many are prepared to dismiss a BW crossover out-of-hand, not necessarily justifiably. BW3 has good protection for a tweeter, it is better than that provided by an LR2, but the latter is seldom questioned if the Fc is selected appropriately. The same thing works for the BW3, though I would probably limit use of that to a 3-way system to be used at farther listening distances. Plus, when I listen seriously, I'm not standing up.

Dave

[augerpro]

Awesome work Dennis! I've been wondering about using this method with BW3 filters. So where is the handy Excel file like the Duelund one you did? SE doesn't seem to able to generate target slopes using cascaded filters.

[mkc]

Hi Brandon,

I'm a fellow SE user. You can do something similar in SE and export the transfer curve. This can then be used as a target slope. I have a mail somewhere from JohnK, where he describes how to do a Duelund filter in SE. But, I can't seem to locate it at the moment ops: .

Another possibility is to use the web based calculator here:

http://pro.speakerbuilder.dk/synkron/

Unfortunately it only generates target files with 500 points and SE use 750 points. You could either import these and do the usual stuff and export them again or I could contact the owner web site and make him change the resolution of the generated files. I think I will do that.

Best regards,
Mogens

[Dennis H]

I've been wondering about using this method with BW3 filters. So where is the handy Excel file like the Duelund one you did? SE doesn't seem to able to generate target slopes using cascaded filters.

Hey Brandon,

I like BW3 because the phase rotation is the same as LR2 if the drivers are inverted. You could do a WMTMW with BW3 filters and the summed phase behavior would be very similar to the original Duelund but with better driver protection.

Sorry, no Excel file. There are just too many possibilities for filter slopes, etc. I don't know anything about SE. Can it add two curves and get the phase right? Could you do something like export each filter separately and then add them together?

[augerpro]

Mogens> if you can find that email from JohnK let me know, I've been poking around and don't see a way to cascade filters and produce a slope I can export. I haven't tried importing each filter response into the SPL/Zin portion of Easylab and see how they add though...maybe that's the ticket. Thanks for the link, but I already use Dennis H's excel file he made for the Duelund filter some time ago. Very straightforward and easy to use.

Dennis> How would this differ from the Duelund excel file? Wouldn't you just be substituting BW3 for the LR2 formula? Not trying to badger you about though, I just really liked the excel file you did :T So is the assumption that the mid would be inverse phase to the tweeter and woofer?

[mkc]

Hi Brandon,

I have located the mail. But, I will check with "john k..." if it is ok the forward the SE Duelund specifics here.

John k... has also made an interesting article about the Duelund crossover on his website.

https://web.archive.org/web/20090715144236/http://www.musicanddesign.com/Duelund_and_Beyond.html

Best regards,
Mogens

[john k...]

Hi Brandon,

I have located the mail. But, I will check with "john k..." if it is ok the forward the SE Duelund specifics here.

John k... has also made an interesting article about the Duelund crossover on his website.

https://web.archive.org/web/20090715144236/http://www.musicanddesign.com/Duelund_and_Beyond.html

Best regards,
Mogens

Sure, forward the email. In fact, also send a copy back to me. My apologies for the typos on my web page, but all the details are there to do this with B3 and LR4 HP and LP sections.

[Dennis H]

How would this differ from the Duelund excel file?

I used Duelund's native S-plane equations in the old file. I'd have to start from scratch to build an Excel file to cascade filters and then I'd never use it because LspCAD is easier. Sounds like you'll get what you need from Mogens and John to do it in SE.

Don't forget to do like Dave said and include the woofer's low-end roll off and the tweeter's high-end roll off, whatever they are, when building the target files.

[mkc]

Hi Brandon

Sorry for not getting back to you before know ops:

Below you can find the information I got from John K... The first quote is from the e-mail and the second quote is the content of the attached doc.

I tried it out when I recieved the mail from John K, but I can't seem to locate the SE project, which might mean that I didn't saved it. Please let me know if you have any trouble. I will try to respond a little faster

I have looked at the Duelund 3-way and found, in fact, that while the approach to the derivation is unique the resulting crossover is quiet simple actually fairly well known. I have attached a doc which explains. You can generate the target function in SE using T components (two per branch) and selecting Butterworth Qo/Fo type along with 2nd order LP or HP as required. For the bandpass, set one T component gain to 1.0 and the other as given in the attached doc. Plot each response and export as a target. Remember the bandpass target is connected with inverted phase, so if you export it that way you will not be able to generate the minimum phase response in agreement with the target.

An easy way to think of the Duelund 3-way crossover it that it basically a deviation of and LR4 2-way. That is, in the limit it reduces to an LR4 2-way. The phase response is always a derivative of the LR4 2-way with 180 degree rotation at the center frequency of the band pass filters. Note that the denominator of the 3-way transfer function in factored form is

(S2 + aS + 1) x (S2 + aS + 1)

which is just the detonator of a 2nd order filter squared with a = 1/Q. So what Duelund has, in simpler terms, is HP and LP sections which are formed by cascading two similar 2nd order HP or LP sections. and a BP formed by cascading an LP and HP section. All sections have the same center frequency. For example the HP section is

HP = s2 / (s2 + s/Q + 1) x s2 / (s2 + s/Q + 1)

the LP = 1 / (s2 + s/Q + 1) x 1 / (s2 + s/Q + 1)

and the BP transfer function is

BP = -1 / (s2 + s/Q + 1) x s2 / (s2 + s/Q + 1) x G

where G is the BP,

G = (1/Q)2 – 2 (linear, not dB)

and s = jω/ωc

ωc = 2π f

When Q = 0.707 the HP and LP sections are LR4 and the BP section has G = 0.0.

In any event, the on axis phase and transient characteristics are similar to the LR4 2-way but off axis, for real system with noncoincident drivers, the response degrades differently than the LR4 2-way.

Best regards.
Mogens

[Dennis H]

Thanks Mogens. I don't know anything about SE but I hope that helped Brandon. Is the 'T component' an element with a specified transfer function that you can use to build a circuit? If so, it sounds like it should work okay -- series T components with LR2 curves for the standard Duelund or series T components with B3 (or whatever) curves for the modified version.

[augerpro]

Mogens thanks for the info. Don't have much time now, but I'll have to dig into it later.