I'm hoping that someone has a copy of this they could kindly upload somewhere so i can download it.
W. James Trott - effective acoustic center redefined
I've managed to track it down to here
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Sounds like it could be very interesting
Thanks in advance
W. James Trott - effective acoustic center redefined
I've managed to track it down to here
Cookies Required
Sounds like it could be very interesting
Thanks in advance
If there is a fee to download the paper, then putting it a free share site would not be approved by this forum.
I agree. In practice interdriver delay ('acoustic centre' offset and displacement on the baffle), driver and crossover phase response become inseperable. They should all be designed together to meet the flat group delay requirement.
I understand what you are trying to say here but it is said poorly. Excess GD (GD associated with excess phase) will always be flat since it is associated with an physical offset or constant propagation distance.
Better stated as the point along the driver axis relative to which the phase reduces to minimum phase.
But in truth it is pretty academic and there is no need to try to find the AC of a driver.
Some time ago I helped a friend design an electrodynamic dipole loudspeaker with very good front-back-symmetry (a good engineering exercise - however, I doubt the merit in terms of sound quailty). We invested quite some time (and his money ) to find the best drivers for the job. We wanted to get the response at the rear to be an as close as possible copy of the response at the front. In order to be able to do this, the acoustic centres of the drivers had to be aligned. In practice it turned out to be quite difficult to achieve this, because the delay changes with frequency. After trying many different ways to measure the delay difference between the drivers, we settled on trial-and-error.
Now I have some more ideas of how you could measure where the acoustic centre is, but in general it is not necessary to know this.
) to find the best drivers for the job. We wanted to get the response at the rear to be an as close as possible copy of the response at the front. In order to be able to do this, the acoustic centres of the drivers had to be aligned. In practice it turned out to be quite difficult to achieve this, because the delay changes with frequency. After trying many different ways to measure the delay difference between the drivers, we settled on trial-and-error.Now I have some more ideas of how you could measure where the acoustic centre is, but in general it is not necessary to know this.
Some time ago I helped a friend design an electrodynamic dipole loudspeaker with very good front-back-symmetry (a good engineering exercise - however, I doubt the merit in terms of sound quailty). We invested quite some time (and his money
Now I have some more ideas of how you could measure where the acoustic centre is, but in general it is not necessary to know this.
The problem is not that the delay changes with frequency so much as the AC is not a single physical position. As was stated above, on axis it is the point where the phase response reduces to minimum phase (which is what the HBT yields) but off axis, a) the response changes so the minimum phase changes as well, and b) just where would you define the AC to be? Along what axis? It is very unlikely that it would reduce to the same position as when using the in axis response. Then when you measure from the rear it is another can of worms.
As I said, the AC is not a real physical position. It is more of a mathematical construction than anything else.
An externally hosted image should be here but it was not working when we last tested it.
What about a driver whose response isn't minimum phase to begin with ?
No amount of time delay will eliminate all excess phase, making trying to define it this way ambiguous.What about a driver whose response isn't minimum phase to begin with ?
True, but first, show me a driver for which the phase a the measurement point can not be reduced to minimum phase.
Hi Fi News (British audiophile mag.) once displayed a 3d modeled "map" of a driver's acoustic center vs. freq.. (..wish I remembered the issue number, or better yet had a link to the image.)
Anyway, it looked like a twisting vortex. (..and of course it wouldn't be static either, but rather would change with intensity due to excursion and bending wave properties.)
The problem I have with this is that the difficulty may lie with the method used to determine the AC for any given measurement point. The response that we measure is essentially the integrated response of all points that radiate. Move off-axis and the integrated response should change. But the output of the points does not change. So things like relative distances come into play and any possible occlusion. On the latter, some frequencies will see more influence than others, generally increasing with frequency.
But given all of that, I'm not convinced that the AC truly changes. Part of the problem is that when you measure off-axis, then remove some amount of excess-phase to reduce to minimum-phase, that distance is being assumed as being a change in a straight line from the measurement point, when in reality the change is an integrated change that includes a total distance to occluded points that are essentially "around the corner", so-to-speak. That the output from those points is not line-of-site should be a factor in the "integrated" total distance called excess-phase.
I see it as a lack of our ability to differentiate the measurement components in a meaningful way.
In the end, we still cannot adequately measure the absolute AC, even on-axis. Just the fact that it's not a point source probably precludes that from being possible. I would suggest that what we use is closer to the best approximation that we can get.
Even for a relative offset. Dave
Dave,
You argument actually supports mine point. The idea of a single, well defined AC is based on the assumption that a source reduces to a point source and that the source is also causal and stable (required for minimum phase). In essence, the start of the source's impulse also defines the point of minimum delay to the source. We generally don't use the start of the impulse to define the AC because for system with LP response it can be very difficult to define where the impulse actually starts to rise. In any event, if we could discern the start of the impulse then, due to the nature of a finite source as you point out, where the response is the integral over the surface of the source, we would see that start of the impulse change with changes in the observation point.
We assume that for an on axis measurement the AC will be on the measurement axis at some distance behind or in front of the radiating surface. That seems reasonable for an axially symmetric driver. But what about a nonsymmetric driver like an old KEF B139 (well not really a good example since there is still some symmetry there)?
The point is that the AC is not a real physical location. It is the apparent location of the source of the sound, nothing more. I would say that it is inherent in the definition that straight line propagation form the source is assumed.
If you were to consider some curved path back to the position of the on axis AC you my just fine that removing such a delay would place the start of the impulse before the T = 0 point which, of course, would violate the requirement of causality.
You argument actually supports mine point. The idea of a single, well defined AC is based on the assumption that a source reduces to a point source and that the source is also causal and stable (required for minimum phase). In essence, the start of the source's impulse also defines the point of minimum delay to the source. We generally don't use the start of the impulse to define the AC because for system with LP response it can be very difficult to define where the impulse actually starts to rise. In any event, if we could discern the start of the impulse then, due to the nature of a finite source as you point out, where the response is the integral over the surface of the source, we would see that start of the impulse change with changes in the observation point.
We assume that for an on axis measurement the AC will be on the measurement axis at some distance behind or in front of the radiating surface. That seems reasonable for an axially symmetric driver. But what about a nonsymmetric driver like an old KEF B139 (well not really a good example since there is still some symmetry there)?
The point is that the AC is not a real physical location. It is the apparent location of the source of the sound, nothing more. I would say that it is inherent in the definition that straight line propagation form the source is assumed.
If you were to consider some curved path back to the position of the on axis AC you my just fine that removing such a delay would place the start of the impulse before the T = 0 point which, of course, would violate the requirement of causality.
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That thought occurred to me as I was writing it.
Yes. The unusual thing is that on some given axis, say on-axis for simplicity, this appears to be the case. Every test I made indicates that this point is somewhere slightly in front of the point of attachment of the former to the diaphragm for dynamic drivers. Unusual in that it is not a physical point on the driver. What I cannot deduce is how this can occur, yet the match of measurement to model seems to satisfy the requirements in this specific case. Conjecture might be that it has to do with how the wave coalesces as it moves outward from the individual points on the diaphragm surface.
That is logical on initial consideration, but then there's the puzzling consideration that one would initially think that it must be at the earliest launch point of the wave, that is, at the attachment point of former to diaphragm. Until one considers that the impulse moves faster in the diaphragm than in air, so then there's the consideration of time delays through air vs. shorter time delay through the diaphragm. Coupled with geometry, it seems quite possible that the first portion of the output to reach a mic might actually be from the rim of the diaphragm if the speed of sound in the diaphragm is significantly faster than it is in air. Then add in that the wave is progressively launched all along the diaphragm in concentric rings (for axial measurement), complicated by wave coalescence (if this is a factor, I can only make conjecture here).
The curious part is that at least for an on-axis measurement, all of this evidently results in a minimum-phase response, at least to the best of our ability to measure and model the FR, the latter of course required if one cannot directly use the impulse response.
On this I would agree, unless, of course, it goes back to how the wave may coalesce. Does the wave at any given single frequency show some time distributed output or does it reduce to a single point in practice? The fact that drivers show non-linearity due to geometry as the geometry becomes a significant percentage of the wavelength indicates that although the response is an integration over the surface, it's vectoral in nature, hence the interference patterns we see that are sometimes considered to be breakup (not wanting to divert the topic here, however). Change the axis and that "breakup" often goes away in some cases. Similar issue, I think. Last comment on that for me in this thread!
OK. Move the observation point as you say. The start of the impulse will change? Maybe that's more a limitation of our measurement capabilities at higher frequencies vs. sampling rates. Odd thing is, the measurements at single points still seem to be minimum-phase, right? At least up to some upper limit. Another oddity is that even with large drivers with rather deep geometries, FR models can be made to match measurements with equally matching Hilbert-Bode generated phase. A new question arises, how can this occur if the wave output is an integration of vectors from the diaphragm surface? Some form of averaging? A wave coalescence issue?
Call that the $64,000 question.
Absolutely. But for our purposes, if it's a specific point in space relative to the driver's surface, that aspect is somewhat immaterial. It's reasonably fixed over most of the operating range, at least on a design/listening axis. How it may vary off-axis is similar to the issue of power response.
This is probably where we may still disagree. I do not assume it be a straight line issue. Just as when modelling a dipole that is not a straight line issue, it's an integrated response issue relative to the diaphragm surfaces.
The way I'm thinking is that you remove the amount of excess-delay required in the same way, but that the effective point may still be accurately considered to be some point on the primary axis at a point whose distance along the curve equals the amount of excess-delay removed. That point may or may not be the same point as determined directly on-axis.
Dave
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