Well, from Wright's paper, it seems there is secondary order diffraction :
"p6 The second order diffraction across the diameter of the disk arrives 0.375msec after the first order diffraction.
Presumably some of this has diffracted around the back with no phase changes, and some has diffracted across the front with two phase reversals
...The latter appears corrupted by the onset of second order diffraction."
You are correct, the DED model is not capable of generating higher order diffractions. The DED diffraction source magnitude was chosen as 1/2 of the half-space primary source magnitude(independent of wedge angle) so that on-axis in the far field you would always see the -6dB transition from half-space to full-space. The angular functions for the primary and diffraction sources were then derived to match off-axis response trends (even at 90 degrees).
The reality is that higher order diffractions can/do occur, although with finite size source and non-circular baffles they are usually smeared out in time to make them difficult to see in the impulse measurement. If you look at the Vanderkooy paper you can see in the examples(figures 9 thru 12) if only 1st order diffraction is considered, his diffraction model uses magnitudes of -0.58 for on axis with wedge angle of 90 degrees which over-predicts the half-space to full-space transition. However, once second and third order diffractions are considered, the -6dB step is seen.
Attachments 1 – 3 show a simple example of impulse responses for a point source on the front face of a 34cm diameter tube. The DED model shows the expected -6dB step. The Vanderkooy model with only 1st order diffraction over-predicts the step. Adding in a 2nd order diffraction similar to what was seen in the Wright paper and you get the -6dB step. You can see that the first diffraction peak is flattened and the transition from half-space to full-space is steeper. These attributes agree with measurements and FEA results shown in later papers by Vanderkooy and Jeff Candy.
- "A Study of Low-Frequency Near- and Far-Field Loudspeaker Behavior"
- "Accurate calculation of radiation and diffraction from loudspeaker enclosures at low" frequency
So the DED gets the general trends correct and behaves well off axis, but misses the second order effects.
The Vanderkooy model requires higher order diffraction modes to be considered to get reasonable LF trends, and diverges as the shadow boundary is approached.
Attachments
As Prof. Porter and I commented on John Vanderkooy's paper at the time, this ("independent of wedge angle") is not precisely correct and can lead to errors in a many situations. (But likely not for a dipole baffle edge diffraction as there isn't a "wedge".)
U. P. Svensson, R. I. Fred, J. Vanderkooy, "An analytic secondary source model of edge diffraction impulse responses," J. Acoust. Soc. Am. 106, pp. 2331-2344 [1999].
jlo pointed me to this JASA paper which develops a diffraction model along the same lines as the earlier Vanderkooy model but without the HF assumptions. According to private correspondence with J. Vanderkooy this new “BTM” model gives correct results at all angles and frequencies, although LF results may require many higher order diffraction terms to converge.
Some details can be found on Peter Svensson’s website here:
Peter Svensson - edge diffraction
There is also a thesis paper written on optimizing computation time for this diffraction model.
http://www.cs.princeton.edu/~pcalamia/thesis/calamia-phd.pdf
Attachment # 1 & #2:
Snapshots of two different summaries for this diffraction model I located on the web, which may be of interest to those not wanting to obtain the JASA paper.
Note that magnitude of the diffraction terms are a function of source and receiver angle relative to the wedge plane, as well as source and receiver angle relative to a perpendicular from the edge. The earlier Vanderkooy model incorporated the former, but not the latter angular dependence. For loudspeakers, the source angle relative to the wedge plane will generally be zero.
Attachment # 3 & #4:
A comparison with analytical results for monopole and dipole sources on thin circular baffles. The analytical results were taken from: Tim Mellow & Leo Karkkainen, "A dipole loudspeaker with balanced directivity pattern", J. Acoust. Soc. Am. 128 (5), November 2010, pp. 2749 - 2757
S. Linkwitz has a copy of these plots and many more on his dipole model page.
Electro-acoustic models
I included second and third order diffractions in my BTM model calculations. The LF behavior was already matching well (and run time already getting inconveniently long) so I did not investigate further. The DED model results are also shown for comparison.
Attachment # 5 & #6:
Since this thread is about baffle edge diffraction for dipoles, here is a comparison with experimental(on and off-axis) results of a BG Neo-8 planar ribbon mounted in the center of a thin 12” x 12” square baffle. The dipole measurements were normalized by an on-axis measurement taken in an infinite baffle. Due to windowing of the impulse response, measured results should only be considered valid for frequencies > 300Hz. The BTM model matches both shape and roll-off slope of the lowest diffraction peak, as well as "far" off-axis response to a surprising degree.
For those interested, the EDGE diffraction simulator gives results nearly identical to the DED model for dipole.
For monopole, the EDGE differs at all angles except on-axis.
As best I can tell, a Cos(angle) term is used on the piston sources even for monopole calculations.
One final note...calculations for the BTM model are time based, so it was/is easy to re-create the impulse responses from the Wright paper shown back in post #61. The BTM results for measurement "C" at 90degrees off-axis show that the second order diffraction terms neatly cancel out essentially all of the trailing output from the primary diffraction, leaving the clean impulse shown in the figure. If anybody is interested, I can regenerate and post it.
Attachments
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Sorry, should have included that information
I treated the BG Ne0-8 as a rectangular piston with dimensions 1.35" x 6" (3.43cm x 15.24cm).
Attachment #1 A pic showing the matrix of source and baffle points I used for the BTM and DED calculations.
Attachment #2 Before running BTM analysis for the rectangular piston, I used a point source in the middle of the baffle.
Attachment #3 It is interesting to see the differences between the point source and rectangular source.
Curiously the 20 deg point source data matches measurements better than the rectangular piston in the (1.5kHz - 4kHz) range.
Attachments
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The diffraction ripple would likely be reduced somewhat if the "baffle" (including the edge) was felt instead of wood.
Perhaps it would be easier to test by replacing the out 1" border of a rigid baffle with felt?
To remove all of the ripple you would have to replace the entire baffle with thinner felt are perhaps acoustic resistive mesh mounted to high percent open area perforated metal. This is something I have been meaning to investigate for some time, but have not yet.
Peter Baxandall published a paper on this technique to gain the LF extension benefit of a baffle without the HF diffraction penalties by using a baffle of appropriate acoustic resistance.
BAXANDALL, P J, ‘A bi-directional line-source loudspeaker with Von Braunmuhl and Weber
Baffle’, preprint at AES 50th Convention, London (1975).
Harry Olson received a patent for using a similar technique with ribbon microphones. (attached)
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This idea of a 'soft absorbent baffle' may be worth pursuing if I can find a source of suitable wool felt at the necessary density.
I use a detachable sub-baffle for both the midrange and tweeter drivers for a physical time alignment with the woofer and its baffle, so experimentation could be quite easily by refabricating new sub-baffles from MDF and wool felt.
I've integrated the front baffle, the drivers and the crossovers of Jeff Bagby's ' The Tributes' into an open baffle design with a Peerless 12 inch 830669 woofer. This is all mounted on a 375 mm wide x 690 high baffle with the sub-baffle mounted above and behind this baffle. This design is still in prototype mode, thus the thought of experimentation with a new sub-baffle of the same dimensions and with wool felt.
Even at this stage it is sounding particularly good, with a very clear and coherent sound presentation and excellent definition. Jeff's designs speak for themselves.
This open baffle design is to work in with an amplified subwoofer and a Denon AVR.
C.M
I use a detachable sub-baffle for both the midrange and tweeter drivers for a physical time alignment with the woofer and its baffle, so experimentation could be quite easily by refabricating new sub-baffles from MDF and wool felt.
I've integrated the front baffle, the drivers and the crossovers of Jeff Bagby's ' The Tributes' into an open baffle design with a Peerless 12 inch 830669 woofer. This is all mounted on a 375 mm wide x 690 high baffle with the sub-baffle mounted above and behind this baffle. This design is still in prototype mode, thus the thought of experimentation with a new sub-baffle of the same dimensions and with wool felt.
Even at this stage it is sounding particularly good, with a very clear and coherent sound presentation and excellent definition. Jeff's designs speak for themselves.
This open baffle design is to work in with an amplified subwoofer and a Denon AVR.
C.M
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U-baffles tend to only be a smart idea for the bass driver because the U forms a cavity that generally resonates above the dipole roll-off point. This is fine for the bass driver since you can remove the response peak as part of the LP crossover. I previously posted some comparative measurements of H-baffle and N-baffles that show the cavity resonances; U-baffle resonance peaks are similar.
http://www.diyaudio.com/forums/plan...le-cavity-resonance-question.html#post3582579
For mids and highs, I think the best practice is to minimize baffle width and depth for each driver. Transition to a small drivers and baffles as you work up in frequency. See JohnK's website for examples of this, and much more good information on understanding and designing dipole speakers.
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