Acoustic 3rd order with Linkwitz-Riley characteristics?

[fatmarley]

I was just looking at the WD25TS designed by Peter Comeau when I noticed this Quote "Acoustic 3rd order with Linkwitz-Riley characteristics?" - To me, the fact that It has a reverse null makes me think It can't be 3rd order.

Am I missing something?

(Link Below - Scroll down to frequency response graphs)

[billfitzmaurice]

L-R is by definition even order.

[Millstonemike]

Bill is right. The reference to LR could be the drivers are down ~6 dB at the XO point. A Butterworth XO slope would have the drivers down 3 dB at the XO point (sans any phase difference).

[billfitzmaurice]

Perhaps what he's trying to say is that between the acoustical roll off of the drivers and the electrical roll off of the crossover the overall result is -6dB at the knee frequency, with the summed response flat. That's not exactly a revolutionary concept.

[dlr]

I googled it and found this. It crosses at 2K -6db with 2nd electrical on a woofer acoustic lowpass that is approximately first order according to him. He correctly points out that there is no LR3, but it's just the combination of a third order filter crossed at 2k that happens to be -6db at his desired Fc, though there is no phase shown whatsoever. It's the result of the driver/filter response that probably results in the phase around Fc being close enough to in-phase at -6db, probably due to the natural low slope of the raw woofer.

It's not really any different that any number of people here might design due to the nature of the drivers. You start with an ideal target of some kind and tweak the crossover to get the summed result acceptable. How shows target curves, probably BW3, but he crosses at 2K where they are both down 6db. The resultant phase, largely due to the the woofer section I would say, is good enough to sum reasonably flat.

Looking more, the final crossover looks awfully close to an LR4. He shows the inverted connection with a good null around Fc. I would not call what he has a quasi-anything, it's pretty much an LR4 tweaked for flat response to accommodate driver irregularities around crossover. Maybe I didn't read it thoroughly enough, but it looks like he started with a BW3, crossed at the -6db points, then tweaked and ended up with close to LR4. He does show the horizontal off-axis, very good BTW, but not the vertical which is really what the focus was for Linkwitz in creating the LR filters, no peaking lobes in the vertical off-axis.

No doubt a good result, but just a lot of fancy talk for things done here all the time, we just don't take his starting target approach. Who would guess designing a 2-way with large midwoofer, a really good 1" tweeter and crossing LR4 @2K?

dlr

[billfitzmaurice]

No doubt a good result, but just a lot of fancy talk for things done here all the time

+1, the goal was flat response through the crossover region, and that was one way to get it. There's nothing superior about it. I'd still find a way to get the same result using at a minimum 3rd order electrical high passing.

[xmax]

What I find interesting on this forum, members regularly talk about LR or BW characteristics like -3 or -6 at
Fc but often the cap/coil ratios are seemingly random (to obtain flat-ish FR) With no regard to transient
performance.

[dlr]

What I find interesting on this forum, members regularly talk about LR or BW characteristics like -3 or -6 at
Fc but often the cap/coil ratios are seemingly random (to obtain flat-ish FR) With no regard to transient
performance.

Cap/coil ratios have nothing to do with transient response as a separate consideration when it's the acoustic response of the system that matters and it's not random. The electrical crossover is simply that which is required for a particular crossover combination to arrive at the desired summed acoustic response and therefore its transient response.

dlr

p.s. It's not just the summed response of course, the transient response is also based on the individual driver section acoustic responses.

[DDF]

Dickason talks about this in the LDC. Standard 3rd order acoustic Butterworths have a +3 dB hump on axis as we know. By spreading out the crossover (fc) points a bit, the result can sum flat "on axis" with just a bit of inconsequential ripple. Vance shows how far apart to stagger the -3dB down points, but any sim package can show the same thing.

I like this type of crossover for those times when 4th isn't needed, but maybe 2nd doesn't provide quite enough rejection of woofer break up, or enough tweeter power handling. You also don't need to strictly use Butterworth shape; when its possible, I like to use a more shallow initial roll off (lower Q for the 2nd order biquad than called for by Butterworth alignment) and adjust fc to suit. I find this reduces tweeter bloom and makes violins and vocals more natural without sacrificing bight on brass.

[Wolf]

Jon Marsh over at HTguide uses what he calls an LR3, for another interpretation.
Wolf

[billfitzmaurice]

Dickason talks about this in the LDC. Standard 3rd order acoustic Butterworths have a +3 dB hump on axis as we know. By spreading out the crossover (fc) points a bit, the result can sum flat "on axis" with just a bit of inconsequential ripple.

+1, there are many ways to realize flat response in the crossover region, with any filter topology if you do it the right way. Besides, L-R isn't about being -6dB electrical at the corner frequency, it's about phase coherence and driver protection.

[dlr]

Dickason talks about this in the LDC. Standard 3rd order acoustic Butterworths have a +3 dB hump on axis as we know. By spreading out the crossover (fc) points a bit, the result can sum flat "on axis" with just a bit of inconsequential ripple. Vance shows how far apart to stagger the -3dB down points, but any sim package can show the same thing.

You still have the issue of vertical off-axis lobing response if you do this, but it probably tends to reduce the lobe magnitude.

I like this type of crossover for those times when 4th isn't needed, but maybe 2nd doesn't provide quite enough rejection of woofer break up, or enough tweeter power handling. You also don't need to strictly use Butterworth shape; when its possible, I like to use a more shallow initial roll off (lower Q for the 2nd order biquad than called for by Butterworth alignment) and adjust fc to suit. I find this reduces tweeter bloom and makes violins and vocals more natural without sacrificing bight on brass.

I like to let optimizers do their thing that probably provides similar results. Design the tweeter highpass for an ideal LR (LR4 usually), lock the circuit elements for it, rough in the woofer lowpass then let the optimizer go. You end up with who-knows-what for the lowpass, but the summed and (one hopes) the polar responses are good. The polar is really where the problems come in.

I found it interesting to play with various crossover mixes in my WinFilters program. This was just a tool for me to confirm the target software in WinPCD a while back, but I made it a free-standing program since I had so much of the code to share between projects. The one thing it doesn't show is polar response, but since it can export any target created, I may do that and import those files into WinPCD to run polar calculations on them.

I've uploaded a few examples of mixed filters with an LR4 standard for comparison. These have no delay added between drivers, so on a tweeter axis it would be a bit more difficult. The ripple would almost certainly be worse, but the "relaxing" of slopes helps to compensate for this. The program uses the classic

One thing to note, as shown in the graphs, when one uses a mixed filter, what we use as the crossover Fc is likely not the Fc of the "classic" curve. Below note that the system Fc is close to that of the LR, but not at all that of the "classic" Butterworth in these examples.

Hover over a graph to see the file name for simple description. Essentially these are BW3/LR4 with reasonably flat summed response and then a bigger spread ripple. Note that the bigger spread inverted looks a lot like the inverted LR4 for phase match.

dlr

[dlr]

Dickason talks about this in the LDC. Standard 3rd order acoustic Butterworths have a +3 dB hump on axis as we know. By spreading out the crossover (fc) points a bit, the result can sum flat "on axis" with just a bit of inconsequential ripple. Vance shows how far apart to stagger the -3dB down points, but any sim package can show the same thing.

One I found particularly interesting is not a mixed filter, but it's a "spread Fc" type like this. I first read about it at the Rane web site. I got some of the polynomials for some filter responses there. The paper is

"A Bessel Filter Crossover and Its Relation to Others"

The one most interesting is the Bessel filter combination for flattest response. As noted, it comes at the expense of off-axis response, but then so does any Butterworth filter vs. Linkwitz-Riley.

Note that the target Fc for both is 2000Hz, but in reality the true Fc required of each leg is 800Hz lowpass and 5000Hz highpass. What provides the nearly flat sum is the specific spread between sections.

dlr

[fatmarley]

Standard 3rd order acoustic Butterworths have a +3 dB hump on axis as we know.

Vance shows the +3db hump off-axis (+ or -15 degrees depending on polarity IIRC). According to Jeff bagby you should get a flat response on-axis.

[dlr]

Vance shows the +3db hump off-axis (+ or -15 degrees depending on polarity IIRC). According to Jeff bagby you should get a flat response on-axis.

That's correct. Odd-order is flat on-axis, even-order is up 3db on-axis.

dlr