First, thanks SL for stepping in. I believe we are now on the same page.
Second I will apologize for this rather long post up front.
Dave, it is not correct that the AC varies with baffle size. The AC of a dipole is always at the AC of the forward source. I showed that with the 3cm and 10 cm models. It gets a little confusing to discuss over the net because of terminology like "forward" source.
We are really talking about flat baffles where the delay is not due to different axial position but due to the rear wave wrapping around the baffle. So, let's consider the theoretical flat disk radiating in a circular baffle. Let's ignore directionality. Close off the back side and let's further assume that the AC of that boxed disk is in the plane of the disk. Now remove the box. What we get is the rear wave wrapping around the baffle. Ignoring the peak/null behavior above the 1st dipole peak we have what looks very much like a 1st order HP response. And like that 1st order HP filter there is a constant group delay in the gradient region. That group delay (GD) will be exactly R/(2c) where R is the radius of the baffle and c is sound speed. That doesn't mean the AC is R/2 behind the baffle. Now, like the 1st order HP filter, the inverse of the HP filter (or dipole response) can be applied as EQ to flatten the response. The GD of the inverse filter is exactly -R/(2c) and the result is that the Eqed response will be perfectly flat and have zero GD. Does that mean the AC shifted? No. All it means is that the shape of the response has changed and being minimum phase, so does the GD. The position of the AC has nothing to do with the GD associated with the response shape, or how it changes with applied Eq. The AC is simply the position relative to which the phase response reduces to minimum phase and remains in the plane of the disk.
I previously likened this to the baffle step. Dipole and baffle step are related with the primary difference being the strength of the baffle diffracted wave compared to the rear wave of a dipole. So, would follow that changing the baffle size of a box speaker would alter the position of the AC of a driver mounted on that baffle? No. That doesn't happen. The baffle step frequency changes and that can affect the GD at low frequency, but the AC remains where ever it was to start with.
Now, looking at SL's revamped web page I think I have a better understanding of what he is trying to get across. And this does relate to the NaO Note design. It appears to me that the point he is trying to make is that if you take two naked dipoles, like a 10 cm and a 3 cm and apply a text book crossover to the unEqed response you can not expect them the combine into a single, smooth gradient roll off (after accounting for differences in level) which can be Eqed with a simple shelving filter. With that I agree. This is because of the differences in GD. This difference in GD is a result of baffle size and is due to the shift in the dipole peak. It is not a shift in the AC. And let’s not forget about the real world cases where the native driver’s response introduces additional GD and phase shifts. It is also no different than trying to combine a woofer with a 2nd order band pass response of 30 to 1k Hz with a midrange with 2nd order bandpass response of 80 to 3k Hz using text book crossover slopes at 150 Hz. Even if the AC of the woofer and mid are aligned, the native bandpass responses of the drivers superimpose their phase and GD on filter response and compensation must be made. In passive systems, or in hybrid system like the Note, this is typically done using nonstandard filter slops with staggered poles, etc.
The bottom line is that any non flat response, whether dipole monopole or otherwise, introduces a frequency dependent GD (nonlinear phase) which depends on where the poles and zeros of the response are. This is in addition to possible AC offsets. All must be addressed in the design of a crossover whether the speaker is dipole or otherwise.
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Hi KSTR,
Thanks for the interesting simulations. Its good to see it as a group delay and see that it confirms a GD equal to half the second unit's offset. It is not too surprising that your low pass with notch matches the dual unit sim, both in phase response and GD, at least over the range where they are a good match in Frequency Response. I believe that is generally true, that two different filters will have matching phase over a range if you can adjust them to be very close in response.
Now the question (and to John's point) is whether the acoustic center is shifted, or that the phase (and GD) are a natural consequence of the non-flat response. I believe that is his arguement, that the phase shifts are a natural effect of the changing response (changing with baffle D) and that the acoustic center never changes.
I'm still thinking about that. It seems a bit semantic to me but it may be a valid point. Still, if the sim shows an assymptotic 1.5mSec delay for all upper frequencies, I would be tempted to call that an acoustic center shift. Certainly it is a delay that must be dealt with in crossover generation (as SL shows) and we clearly have a case where broad band delay is impacted by dipole D.
Also thanks to SL for the updated graphs and explanation.
David S.
Things could be more simple, i own a pair a W5-1685 and they doesn't sound good to my ears. The sound is clean but misses life. I prefer a lot more my peerless 830656, worse classic distortion measurements but a far better sound ( not as clean) and consequently more music.
The measurements you used cannot detect that. You should try an other brand of fullrange, before conclude.
Very interesting topic otherwise.
Dave,
All that is really being said is that sources with different response have different phase and GD and this must be accounted for. SL is using dipole sources as an example and a B1 crossover because it sums in quadrature and is sensitive to GD differences, particularly at higher frequency. An LR4 crossover would be less sensitive. But the argument applies to application of text book filter functions to any set of different sources.
Here is a simple example. The first figure shows two sources. One has a bandwidth of 40 to 1k Hz. The other 80 to 5k Hz.
This next figure shows what the individual and summed responses look like when crossed over with a 300 Hz B1 crossover,
The response doesn't sum flat because of the differences in phase and GD between the two sources.
Now, apply the same crossover between two identical sources:
The response is now flat because the additional GD and phase rotation of the two sources is identical.
All that is really being said is that sources with different response have different phase and GD and this must be accounted for. SL is using dipole sources as an example and a B1 crossover because it sums in quadrature and is sensitive to GD differences, particularly at higher frequency. An LR4 crossover would be less sensitive. But the argument applies to application of text book filter functions to any set of different sources.
Here is a simple example. The first figure shows two sources. One has a bandwidth of 40 to 1k Hz. The other 80 to 5k Hz.
An externally hosted image should be here but it was not working when we last tested it.
This next figure shows what the individual and summed responses look like when crossed over with a 300 Hz B1 crossover,
An externally hosted image should be here but it was not working when we last tested it.
The response doesn't sum flat because of the differences in phase and GD between the two sources.
Now, apply the same crossover between two identical sources:
An externally hosted image should be here but it was not working when we last tested it.
The response is now flat because the additional GD and phase rotation of the two sources is identical.
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Most interesting John, it seems the issue is not dipole specific then. Thanks.
Linkwitzlab's new explanation is very much clearer too
linkwitzlab.com/frontiers_7.htm#D2
Linkwitzlab's new explanation is very much clearer too
linkwitzlab.com/frontiers_7.htm#D2
No, more interestingly he points out that GD in the crossover region is set by baffle diameter. This is different than our experience with most drivers that GD is set by approximated driver depth and, yes, frequency response. Because of the strong impact of baffle diameter on frequency response the diameter directly impacts GD in a manner that tracks the mid point between the front driver and the virtual delayed rear driver.
In that way the best time allignment between two units varies as baffle diameter is varied. (This assuming a crossover scheme is fixed.)
I am still not understanding your comment on woofer AC being forward of the mid AC for the typical case of a common baffle plane? Or that the mid would need to be moved forward for allignment? AC aside, certainly both your's, SL's and KSTR's curves show a downward phase trend and greater group delay for any unit with a larger baffle diameter. For a first order network, that might give good response if the drivers are time alligned, the mid will have to be moved back to have phase matching to the woofer.
David S.
Yes, it is certainly not anything unique to dipoles. Actually the bigger issue with the dipole example is that if you start with sources that have the same sensitivity then the 10 cm response in the gradient region will be about 10 dB more efficient than the 3 cm one. So before you can even consider the effect of GD on the crossover the efficiency difference would need to be considered. Assuming that can be dealt with then there are a number of ways to deal with the GD differences. We do it all the time with box speakers without a second thought. That is why I was kind of surprised to see this brough up as an issue for dipoles.
I would say that in the effort to extend the dipole response to higher frequencies by introducing an upper midrange on a smaller baffle, as I have done in the Note, and as a number of people have now attempted, this is the least of the problems.
Dave, part of this was due to my misunderstanding what SL was trying to convey in his initial web page. Yes, there is a difference in GD due to different baffle size. This has nothing to do with AC location. In SL's case the AC would be considered aligned. The difference in GD is because of the different is the response, i.e. the different position of the dipole peak. Where SL went from there was to show that if you tried to crossover the unequalized dipoles you would have to account for the different GD. Then you could EQ the summed response flat with a single shelving filter.
What I was showing on the web page I put up was that if you eq each dipole flat first (requiring different eq functions for each source) then the GD goes to zero for both sources and there would be no need for delay compensation. That is, the different GDs are the result of the nature of the unequalized dipole response.
The source on my misunderstanding with SL's initial presentation was where the eq came in.
In SL's case, correct to have similar GD, crossover, eq to flat with single function.
In my case, eq each source (flat) separately to reduce the GD of each to zero, then crossover.
My comment regarding a woofer AC in front of the mids was not for a flat baffle system I was thinking of a symmetrical dipole speaker. Suppose the midrange was two back to back dome separated by 5 cm. The woofer a box 40 cm long with two woofer back to back mounted on opposite ends. Now, place the mids so that the center of the mid pair at the center of the woofer pair. From the front the mid AC would be nominally in the plane of the front dome and the woofer AC would be in the plane of the front woofer. So the woofer AC would nominally be 17.5 cm forward of the mid.
I hope this clears things up.
Okay, that isn't what I was picturing but now I understand.
Thanks for the simulations.
David S.
JohnK,
I know I'm a little late to this thread but my thoughts may be relevant to this discussion.
Your explanation makes perfect sense to me but I have one further question I hope you might ponder: There has been little discussion of the possible negative effects (on Frequency Response, Group delay etc) introduced by the delayed step response of a typical 10" subwoofer.
Assuming that one has already aligned the acoustic centers of all the drivers, consider the step response of a typical 10" subwoofer is approximately 5ms slower than the typical midrange/tweeter.
Have you ever considered introducing a corresponding time delay on the remainder of your drivers to more closely align the step response of the smaller drivers with the larger subwoofer?
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