Linkwitz-Riley or Butterworth

[leon]

I've noticed that many people are using the Linkwitz-Riley over the Butterworth, what would be the reason for this?

[dthomas]

> I've noticed that many people are using the
> Linkwitz-Riley over the Butterworth, what
> would be the reason for this?

Seems that this question is getting posted a lot. Personally I don't favor either and am surprised that there is much interest one way or the other any more.

I think with modern software tools most people are more interested in targeting specific acoustic slopes. Of course while accounting for phase and power response etc...

Just curious if others actually pay attention to whether their filters are butterworth or L-R? I personally think that a mix of both are commonly used to acheive proper phase alignment.

Dave

[Pete Schumacher ®]

> Seems that this question is getting posted a
> lot. Personally I don't favor either and am
> surprised that there is much interest one
> way or the other any more.

> I think with modern software tools most
> people are more interested in targeting
> specific acoustic slopes. Of course while
> accounting for phase and power response
> etc...

> Just curious if others actually pay
> attention to whether their filters are
> butterworth or L-R? I personally think that
> a mix of both are commonly used to acheive
> proper phase alignment.

> Dave

The final alignment is the convolution of both the natural response and the filter transfer function.

With most two-ways using 7" woofers, the XO point will be around 2KHz plus or minus. Most of those woofers will have a natural response that falls off above 4KHz. When you combine that slope with a 2nd order electrical filter, you wind up with a 4th order acoustic slope. It takes a woofer with a controlled upper octave to pull off a 3rd order slope by using only a 1st order filter. Any resonances or distortion peaks in the stop band will be more apparent with the first order filter vs. the second order filter.

Another reason for LR alignments is the lobing pattern produced. It projects straight ahead and is fairly symmetrical vertically due to the driver's relative phases being aligned throughout the crossover region. Phase alignment with BW filters just doesn't work the same. Whether that's audible or not? The lobing on a BW3 vs LR4 shows that the LR4 has a wider vertical lobe, but the power response on the BW3 is flatter. I'd imagine the room would have a lot to do with differences in sound .

[dthomas]

> The final alignment is the convolution of
> both the natural response and the filter
> transfer function.

> With most two-ways using 7" woofers,
> the XO point will be around 2KHz plus or
> minus. Most of those woofers will have a
> natural response that falls off above 4KHz.
> When you combine that slope with a 2nd order
> electrical filter, you wind up with a 4th
> order acoustic slope. It takes a woofer with
> a controlled upper octave to pull off a 3rd
> order slope by using only a 1st order
> filter. Any resonances or distortion peaks
> in the stop band will be more apparent with
> the first order filter vs. the second order
> filter.

> Another reason for LR alignments is the
> lobing pattern produced. It projects
> straight ahead and is fairly symmetrical
> vertically due to the driver's relative
> phases being aligned throughout the
> crossover region. Phase alignment with BW
> filters just doesn't work the same. Whether
> that's audible or not? The lobing on a BW3
> vs LR4 shows that the LR4 has a wider
> vertical lobe, but the power response on the
> BW3 is flatter. I'd imagine the room would
> have a lot to do with differences in sound .

I agree but I think since I tend to resort to over/under damping the filter to accomodate a drivers specific acoustic response that the lines that define the difference between butterworth and L-R sort of become less important.

Obviously both designs result in a power response that is less than the summed on-axis response so do you design for a reasonably flat power response in the crossove region or do you allow a dip? It would seem that a true L-R filter would have a larger dip in the power response vs. a butterworth.

I personally think this debate is of little importance as long as you are designing to flattest on-axis response with good phase alignment and a reasonable power response. I think this covers most of the bases for average listening environments. And should result in a very listenable design. Of course as you stated you need to address the acoustic anomalies in the drivers response also.

I think the real issue here is that many assume that the textbook values associated with BW or L-R correlate to the values derived in modern crossover design. I think it is a moot point anymore. With tools like PCD flat on-axis respsonse and good phase alignment between the drivers being crossed are the first priority with power response being close behind. I guess you could argue that since I am aiming for flat on-axis response that I lean towards L-R but when I do so with a 3rd order filter that argument falls apart.

Dave

[dlr]

> I agree but I think since I tend to resort
> to over/under damping the filter to
> accomodate a drivers specific acoustic
> response that the lines that define the
> difference between butterworth and L-R sort
> of become less important.

If the drivers do not have aligned acoustic centers, then some alteration of one or both drivers is definitely beneficial. But a target slope is still essential, be it L-R, BW or some other, the choice of which shouldn't be somewhat haphazard, what I infer from your take on it. There really are differences in the perceived response of these, especially if there is more room influence or the listening position can't be ideal.

> Obviously both designs result in a power
> response that is less than the summed
> on-axis response so do you design for a
> reasonably flat power response in the
> crossove region or do you allow a dip?

I think that the droop in the power response is one thing that is a benefit it it's in the right place. I like 2nd order L-R that seems to help between mid and tweeter. Placed anywhere around 2-3K it results in a slight power response drop somewhat in the "BBC Dip" region that may account for my preference.

I also have liked a well-done BW1 that surprised me.

> It would seem that a true L-R filter would have
> a larger dip in the power response vs. a
> butterworth.

It depends on the order as well. The power response for the odd-order BW is the smoother of that type. It's also smoother than the L-R's, but since order also is different, I don't think that there's any absolute judgement to make. The even-order BW really need not apply IMO due to the on-axis peak.

> I personally think this debate is of little
> importance as long as you are designing to
> flattest on-axis response with good phase
> alignment and a reasonable power response.

Seems to me that this is part of what influences the choice of target and is a deliberate choice or should be, at least. "Reasonable power response" is the result of the crossover type, order and adjustments made during implementation. However, the adjustments for FR linearity likely have the least affect.

>I think this covers most of the bases for
> average listening environments. And should
> result in a very listenable design. Of
> course as you stated you need to address the
> acoustic anomalies in the drivers response
> also.

> I think the real issue here is that many
> assume that the textbook values associated
> with BW or L-R correlate to the values
> derived in modern crossover design. I think
> it is a moot point anymore.

That's been the case for more than a few years. It's just easier to do it correctly now, but the decisions as to what direction to take are not changed. I totally disagree that it's a moot point. Only those just beginning might to the route of textbook values.

> With tools like
> PCD flat on-axis respsonse and good phase
> alignment between the drivers being crossed
> are the first priority with power response
> being close behind.

I'd say that I agree with this in general.

> I guess you could argue
> that since I am aiming for flat on-axis
> response that I lean towards L-R but when I
> do so with a 3rd order filter that argument
> falls apart.

Why? There's not reason for this to "fall apart", it's just as easy as any L-R filter. Flat on-axis response with any odd-order BW should be the target and has no reason to fall apart.

dlr

[dthomas]

> If the drivers do not have aligned acoustic
> centers, then some alteration of one or both
> drivers is definitely beneficial. But a
> target slope is still essential, be it L-R,
> BW or some other, the choice of which
> shouldn't be somewhat haphazard, what I
> infer from your take on it. There really are
> differences in the perceived response of
> these, especially if there is more room
> influence or the listening position can't be
> ideal.

> I think that the droop in the power response
> is one thing that is a benefit it it's in
> the right place. I like 2nd order L-R that
> seems to help between mid and tweeter.
> Placed anywhere around 2-3K it results in a
> slight power response drop somewhat in the
> "BBC Dip" region that may account
> for my preference.

> I also have liked a well-done BW1 that
> surprised me.

> It depends on the order as well. The power
> response for the odd-order BW is the
> smoother of that type. It's also smoother
> than the L-R's, but since order also is
> different, I don't think that there's any
> absolute judgement to make. The even-order
> BW really need not apply IMO due to the
> on-axis peak.

> Seems to me that this is part of what
> influences the choice of target and is a
> deliberate choice or should be, at least.
> "Reasonable power response" is the
> result of the crossover type, order and
> adjustments made during implementation.
> However, the adjustments for FR linearity
> likely have the least affect.

> That's been the case for more than a few
> years. It's just easier to do it correctly
> now, but the decisions as to what direction
> to take are not changed. I totally disagree
> that it's a moot point. Only those just
> beginning might to the route of textbook
> values.

> I'd say that I agree with this in general.

> Why? There's not reason for this to
> "fall apart", it's just as easy as
> any L-R filter. Flat on-axis response with
> any odd-order BW should be the target and
> has no reason to fall apart.

> dlr

I think you misunderstood my point in the last paragraph. Maybe I was unclear but I lean toward L-R target slope but often I mix 2nd order and 3 order networks so what I was trying to infer is that fact alone makes the arguemnet that I prefer L-R fall apart. Personally I think that 2nd order electrical lowpass mixed with a 3rd order electrical highpass sounds good some might argue with this. Of course it is very dependant on the drivers.

I agree that target slopes makes sense, but in the traditional correlation of relating these back to textbook values is of little importance with the tools readily available today. In the end it is an acoustic slope that we are shooting for. Acheiving a flat summed response may require over or underdamping the filter which basically breaks away from the whole BW/L-R arguement. Is it an overdamped BW or an underdamped L-R? Or is it somewhere in between?

I too prefer a bit of a sag in the power response around the crossover point especially in the 1800Hz to 2500Hz range. I am not sure I would call this BBC dip if the summed response is flat though. I always thought that BBC dip inferred the summed response droops in the range around 3KHz. Assuming L-R this would mean the power response should sag in this region.

My point was that I don't think textbook L-R or BW examples are really all that important anymore and I would agree at least for the past 10 years there has been easy access to simulation software. I was not trying to say that target slopes don't make sense I just think the line between filter types gets blurred quite easily when accounting for all that is necessary in a good design.

Dave

[dlr]

nt

[dthomas]