The throat diameter is not meanigless, it just doesn't dicate a narrowing polar response because of its size. There are two different things going on.
The larger the throat the lower the first HOM cut-in frequencies are and so as the driver goes beyond these cut-in points the response will most likely fall unless the wavefront in the aperature if very close to being flat, which is seldom the case.
The fact that the larger diaphragm drivers tend to die is generally a power response thing, i.e. they die everywhere, on axis and off. This is completely different than the response narrowing at the HFs because of the aperature width. The power response from the driver can die and the polar response still be maintained - this is what happens.
In the 1" drivers the power response does not die until about 12-15 kHz. In the larger format drivers that I have measured it dies at about 1/2 that number. Makes perfect sense if you think about it - double the rdaius, half the frequency where the power response dies.
In horns that narrow the narrowing can compensate for the power response falling. In a CD device this can't happen. This is one of the things that make CD waveguides sound different than beaming horns.
Well, you still have to deal with some other effects- lower diaphragm breakup frequency is probably the most obvious of them, but higher inductance of the larger coil also would play a role.
I know that in my 2426h, trying to EQ above 10-12k was an excercise in shrill. The phragm breakup (titan...) made it no fun.
The bottom line is that you can ONLY EQ the power response. If the power response and the directivity don't match then you can EQ along one axis, but thats all. Generally if there is no power response then you don't have anything to EQ without a lot of gain. Hence, once the power response begins to fall to maintain the output along any line, you can only direct what's left to an ever narrower polar angle along that line.
If you have acoustic power available and its going equally in all directions of intent then you can EQ it all you want.
Acoustic Relevance
The exit diameter of a compression driver is arbitrary set typically to 1”, 1-1/2” or 2”. The acoustically important dimensions of a compression driver are that of the diaphragm, phase plug passages and the diameter where these passages are joined to a conical, or near conical bore, which leads to the driver exit. Only when a flare discontinuity is introduced at the horn/driver connection does the driver exit diameter become acoustically important. Ideally the horn flare profile should be implemented along the phase plug passages as well as beyond. Again, under these conditions, the exit diameter remains arbitrary and acoustically insignificant.
Regards,
WHG
The exit diameter of a compression driver is arbitrary set typically to 1”, 1-1/2” or 2”. The acoustically important dimensions of a compression driver are that of the diaphragm, phase plug passages and the diameter where these passages are joined to a conical, or near conical bore, which leads to the driver exit. Only when a flare discontinuity is introduced at the horn/driver connection does the driver exit diameter become acoustically important. Ideally the horn flare profile should be implemented along the phase plug passages as well as beyond. Again, under these conditions, the exit diameter remains arbitrary and acoustically insignificant.
Regards,
WHG
I would like to amplify Mr. Geiger comments, not because they are wrong, but they are incomplete.
Consider a plane wave moving down a tube. To this wave the area of the tube, and even its cross sectional shape are acoustically irrelavent because the wave is everywhere tangent to the walls. But this is not true for waves that impinge upon the walls - the so called Higher Order Modes (HOM). To those waves the area and the shape are very important because they determine the lowest frequency at which any given HOM can propagate as well as the angles that these waves must make with the walls. Shape and size are only irrelavent to the lowest mode, the planar mode.
The wavefronts in the throat of a compression driver are not truely planar because the phase plug is not designed to yield a planar wave. They are designed to yield a constant phase wavefront, but NOT a constant amplitude wavefront. A so-called "Bob Smith" phase plug (the most typical) does not yield a planar wave at its exit. So the shape and area of the waveguide throat is relavent to the non-planar portions of the wavefront emitted from a typical compression driver. But, as Mr.Geiger says, they are irrelavent to the planar portion as long as there are no area, shape or slope discontinuities at the junction.
Consider a plane wave moving down a tube. To this wave the area of the tube, and even its cross sectional shape are acoustically irrelavent because the wave is everywhere tangent to the walls. But this is not true for waves that impinge upon the walls - the so called Higher Order Modes (HOM). To those waves the area and the shape are very important because they determine the lowest frequency at which any given HOM can propagate as well as the angles that these waves must make with the walls. Shape and size are only irrelavent to the lowest mode, the planar mode.
The wavefronts in the throat of a compression driver are not truely planar because the phase plug is not designed to yield a planar wave. They are designed to yield a constant phase wavefront, but NOT a constant amplitude wavefront. A so-called "Bob Smith" phase plug (the most typical) does not yield a planar wave at its exit. So the shape and area of the waveguide throat is relavent to the non-planar portions of the wavefront emitted from a typical compression driver. But, as Mr.Geiger says, they are irrelavent to the planar portion as long as there are no area, shape or slope discontinuities at the junction.
Earl, would I be correct in saying that power response should drop in accordance with narrowing directivity? Whether long range or a small narrowing band, that one should reduce the power by the same amount as the directivity is narrowing, rather than maintaining steady power and causing a response peak...which means putting the DI responsibility solely into the acoustic domain with the cabinet. Thus maintaining a fixed nominal output power per angular unit from the source (where it is actually radiating) and flat frequency response within the beam?
So for example, could I plot something similar to the -6dB beamwidth vs frequency, change the Y-axis to Watts and have a target power response? (with acoustic mods where it is not flat)
So for example, could I plot something similar to the -6dB beamwidth vs frequency, change the Y-axis to Watts and have a target power response? (with acoustic mods where it is not flat)
I am not completly sure that I follow the question.
With Constant Directivity the power response and the response along the central axis will be parallel. If the directivity is dropping but there is a flat power response then the main lobe has to be rising.
I just do not understand your last question.
If the polar response maintains a constant shape, which is not necessarily and rarely the case, then maybe you could swap the axis for pressure and power response. But with a changing shape, even though the -6dB points may be constant, this would not be true.
First and formost the response needs to be flat (well a small falling with frequency is desired) along the listening direction (the direct field) - which need not be the direction of the main lobe and in fact I do recommend that this be the case. Hence the DI along this axis should be flat so that the reverberation field is neutral with respect to the listening axis. This will tend to make the power response fall parallel to the listening axis. When these things are not true then if the DI is not flat one can EQ this, but if the power response and the listening axis are not parallel then EQ will not correct them both at the same time and only acoustical actions can correct this situation.
Again, I don't know if this answered your question of not.
With Constant Directivity the power response and the response along the central axis will be parallel. If the directivity is dropping but there is a flat power response then the main lobe has to be rising.
I just do not understand your last question.
If the polar response maintains a constant shape, which is not necessarily and rarely the case, then maybe you could swap the axis for pressure and power response. But with a changing shape, even though the -6dB points may be constant, this would not be true.
First and formost the response needs to be flat (well a small falling with frequency is desired) along the listening direction (the direct field) - which need not be the direction of the main lobe and in fact I do recommend that this be the case. Hence the DI along this axis should be flat so that the reverberation field is neutral with respect to the listening axis. This will tend to make the power response fall parallel to the listening axis. When these things are not true then if the DI is not flat one can EQ this, but if the power response and the listening axis are not parallel then EQ will not correct them both at the same time and only acoustical actions can correct this situation.
Again, I don't know if this answered your question of not.
Not quite. If you don't mind I think I've stumbled across a fundamental (objective) connection, and hope you could tell me what it is. My directivity does vary, eg it narrows above 500Hz, the woofer is a little wider than the waveguide at the crossover, the waveguide narrows just a little like a tractrix horn, plus the usual issues, but nothing huge.
When I have previously set the crossover to the power target, I have felt the need while listening to EQ away from it...and always to the same place within 2dB of the calculated curve. Most noticeably dropping a couple of dB above the crossover.
So yesterday I was looking at your older Summa response and was thinking about the power dip near 2k which is accompanied by a narrowing of the pattern. And then I saw it...
If I look at the included angle between the -6dB points and compare this angle to a different frequency, there's an apparent connection to the power response. The relative coverage angles at two frequencies seems to relate to the relative power response that you've chosen and plotted for them. Wider gets more power and narrow gets less. Even taking the log*20 of the ratios seemed to give me the number difference in power that is shown on your plot.
So I went and plotted my directivity as a function of the widths of the -6dB points per frequency. Then pretending it was a power target, I crossed the drivers to meet that (using my usual sim and working with my peviously calculated power responses of each driver). The measured result from my listening chair was the same result I always achieve by ear, except for a straight response from around 2kHz up. I tilted that toward a few dB down at 10kHz like always prefer, and all is well.
When I have previously set the crossover to the power target, I have felt the need while listening to EQ away from it...and always to the same place within 2dB of the calculated curve. Most noticeably dropping a couple of dB above the crossover.
So yesterday I was looking at your older Summa response and was thinking about the power dip near 2k which is accompanied by a narrowing of the pattern. And then I saw it...
If I look at the included angle between the -6dB points and compare this angle to a different frequency, there's an apparent connection to the power response. The relative coverage angles at two frequencies seems to relate to the relative power response that you've chosen and plotted for them. Wider gets more power and narrow gets less. Even taking the log*20 of the ratios seemed to give me the number difference in power that is shown on your plot.
So I went and plotted my directivity as a function of the widths of the -6dB points per frequency. Then pretending it was a power target, I crossed the drivers to meet that (using my usual sim and working with my peviously calculated power responses of each driver). The measured result from my listening chair was the same result I always achieve by ear, except for a straight response from around 2kHz up. I tilted that toward a few dB down at 10kHz like always prefer, and all is well.
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Ok, thats good, still not sure that I understand. For the most part the -6 dB points will track the power response, especially in a CD waveguide. I don;t think that will be true of other types of sources as well however.
I did say things wrong in my previous post and wanted to correct that. The DI is what cannot be changed by EQ. Hence if along the listening axis the DI is not flat then there is nothing that you can do electronically to correct it. If, however, you can find some axis for which the DI is flat, but the listening axis is not flat, then that can be corrected with EQ. This is why I plot those in my plots and how I design the crossover. They show what is acoustic and uncorrectable and what is correctable with EQ. Looking at a single axis curve or a stack of curves will not show you this.
I did say things wrong in my previous post and wanted to correct that. The DI is what cannot be changed by EQ. Hence if along the listening axis the DI is not flat then there is nothing that you can do electronically to correct it. If, however, you can find some axis for which the DI is flat, but the listening axis is not flat, then that can be corrected with EQ. This is why I plot those in my plots and how I design the crossover. They show what is acoustic and uncorrectable and what is correctable with EQ. Looking at a single axis curve or a stack of curves will not show you this.
If there is a point I'm aiming at learning it is how to create a power target for a given speaker (without listening). It has been said that it shoud be mostly flat but I'm finding this limiting. Anyway, here is the change since using a planned power target.
A) Subjective result (old, typical)
Listening position response of all sources. Includes DI plot for 20 degree axis chosen solely for its smoothness of DI.
The need of shelving above the crossover was correctly predicted.
On the other hand the initial driver targets were fabricated and then tweaked, sometimes blindly, sometimes badly.
B) Objective result
This sounds better. These have been asking for a greater dip at 2k although that would seem counter-intuitive.
Includes DI plot for 10 degree axis, chosen because it corrected the direct response (by using the same directivity narrowing issue against itself). I can see this was poor logic and is wrong, and I will be looking into splitting the difference at 15 degrees to find a more smooth DI.
Significant improvements below the crossover although it isn't easy to tell this from the two plots.
I can't take this much further as it is.
A) Subjective result (old, typical)
Listening position response of all sources. Includes DI plot for 20 degree axis chosen solely for its smoothness of DI.
The need of shelving above the crossover was correctly predicted.
On the other hand the initial driver targets were fabricated and then tweaked, sometimes blindly, sometimes badly.
B) Objective result
This sounds better. These have been asking for a greater dip at 2k although that would seem counter-intuitive.
Includes DI plot for 10 degree axis, chosen because it corrected the direct response (by using the same directivity narrowing issue against itself). I can see this was poor logic and is wrong, and I will be looking into splitting the difference at 15 degrees to find a more smooth DI.
Significant improvements below the crossover although it isn't easy to tell this from the two plots.
I can't take this much further as it is.
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How are you calculating DI? You cannot measure DI in a room, its deffinition requires anechoic data.
Calculating DI and power response is not trivial and it took me years to be able to do this with reasonable accuracy. Thats why I question how you are doing it.
So the DI axis can be chosen w/respect to any arbitrary axis?
Obviously the polars are then asymmetric, but just go ahead and integrate/average them to get the power response and DI?
Looks like you arrived at the Audyssey target curve
It doesn't look that way to me; for both curves >1 kHz is several dB lower than <1 kHz, whereas I believe all Audyssey standard target curves are flat to at least 7 kHz.
I have a set of discrete anechoic polars. I have processed them to create one extra plot that I use where I need a power response. Plus, I have one phase set from 20 degrees (one for each driver).
The 'power' calculations ignore phase. I have insert the chosen phase plot into a few of the polars and also the 'power' plot so that I can make use of it experimentally in a sim.
On this occasion I built a crossover (for a single main speaker) using the 'power' plots, and saved the total response. I then substituted the 10 and 20 degree plots in turn with the previous phase and impedance data intact, recalculated the crossover and divided the result by the saved total to give me the DI.
I use my computer for the power calculations to save time. I essentially take the ploars and weight them based on the region at each angle, and average them.
I'm assuming so. I have some reasons for not wanting to choose too low or too high an angle, and would prefer something less than 45 degrees.
This is what I'm presently doing. The polars are not symmetric, and I don't think this is a significant problem, within reason, although it does seem to put up some constraints.
DI is defined with respect to the axis being considered. It is the frequency response along any axis normalized by the power response (in dB). The power response is independent of any axis so it stays constant as the axis of consideration is changed.
In other words the DI plots were created from anechoic data, then I simmed in the crossover rather than to 'build and measure'.
And I just realise that's another mistake I've made. The directivity index should be 3dB higher around the crossover than I've accounted for due to power losses from lobing.
OK, so I guess I'd need to calculate the power response of the drivers after crossing them, convert the powers to a linear magnitude and then sum them?
I can't imagine this will be totally accurate due to the fact that I'm hardly dealing with coaxial point sources, but I assume the errors would average out somewhat in reality.
And I just realise that's another mistake I've made. The directivity index should be 3dB higher around the crossover than I've accounted for due to power losses from lobing.
OK, so I guess I'd need to calculate the power response of the drivers after crossing them, convert the powers to a linear magnitude and then sum them?
I can't imagine this will be totally accurate due to the fact that I'm hardly dealing with coaxial point sources, but I assume the errors would average out somewhat in reality.