Yes, for a two way or three way crossover design you have to model each speaker individually, all with a common time base. Otherwise you cannot do a crossover simulation that is accurate for the entire polar map. This was the original intent of my modeling the sources the way I do. It facilitates this kind of simulation, which I have found critical in my design process.
It is interesting to note that the use of real numbers in room modal calculations also leads to large errors in the predictions because real modes are complex not real. I believe that my modal simulation on my web site is the only publicly available software for this kind of analysis. Doing complex modes is not trivial!
If I could explain, Charlie has a point, but it is one that I have just gotten used to. Not each angle represents the same projected area. The area goes up as the angle increases to 90°, and then falls again. But this is still a problem in his plots because they are still 2D cross-sections.
To visually represent correct weights to angles, it should be sufficient to use nonlinear scale on Y-axis in the common rectangular plot - the same nonlinear scale as the projected area changes with angle. I wanted to do this in my own software many times but have never found the time. It's quite easy to do.
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If anyone could explain why the angles should be weighted, I do not understand. 
Aren't we just trying to look at the frequency response at every point along a 1.5 m (or whatever) circle (or half of one)?
Aren't we just trying to look at the frequency response at every point along a 1.5 m (or whatever) circle (or half of one)?I think we might be using the term "speaker" differently. I usually refer to each source of sound as a "driver" and the assemblage of drivers and crossover as the "speaker".
With that in mind, I model each driver as a complex source with a "timebase" referenced tothe plane of one of the driver's acoustic center. I can then use interference measurements to accurately establish the relative difference in "timing" (I use the term delay in my work) between each driver at a particular point in space, usually where some measurements of the driver's response were made.
Is this the kind of thing you were referring to in the quoted text?
Charlie - your terminology is correct - my was poor.
I am not sure what you mean below:
What are "interference measurements"?
How do you lock the time base? Based on a first measurement and then synch everything to that measurement?
You can get the data that you need with standard rotated angles, but you will need more of them than I do.
I am not sure what you mean below:
What are "interference measurements"?
How do you lock the time base? Based on a first measurement and then synch everything to that measurement?
You can get the data that you need with standard rotated angles, but you will need more of them than I do.
If anyone could explain why the angles should be weighted, I do not understand.
Think of a sphere. Now move out angularly from some radial line. Each point represents the SPL on an annulus about the reference line/point. Each annulus grows in area.
The thing about "correcting" this visually depends on how you think of the measurements. If each angular line is just the SPL along that direction in space then no correction is required. But if you are thinking about Sound Power then each line needs to be weighted by the area. I think in terms of SPL at a point, not integrated Power. I do plot the power because it is important but the power from each point is not really what I think of.
Setup: two sources of sound that are fed the same input signal and are located at different distances from the measurement position.
Q: How do you determine the relative distance to the listening position of the two sources?
A: Use an interference measurement, plus a measurement of each source alone. Model the sum of the sources with a frequency-independent delay added to one source. When the model of the sum is the same as the measurement of the two sources together, the delay in seconds time the speed of sound in air is the relative separation distance.
This approach is now widely used in the DIY community to obtain accurate info on driver spatial positioning (e.g. the x,y,z coordinates). I only care about relative delay between sources, since this is all that is needed to accurately determine the phase angle between them at a given position in space (e.g. where all three measurements were done). I do the "modeling" using my active crossover design tools.
For me, the nonlinear scale on angle axis would give a lot better "sound power feel" of the whole 2D plot. In this regard what happens right on axis is kind of irrelevant, so only a small horizontal strip is representative there. As you move out from axis, the distance between angle marks would become larger. So in the plot the area between say 20 - 30 deg would be larger than between 0 and 10. This all assumes that the data are symetrical around the axis, which is allmost never the case, however.
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Oh, I see. I definitely prefer to have these kind of graphs be only intended to represent SPL at single points, as you put it. The relationship to power seems clear enough without a visual representation on the same graph.
P.S. I do what Charlie is talking about with the "interference measurement". Easy, very fast, and accurate.
IMO polar maps should be about power. I see no point to make polar maps just to show the SPL as a function of frequency and angle. The color scale just doesn't work very well. To show just the SPL as a function of frequency (for some angles), I like the traditional Bode plot much better. YMMV, for sure.
Do you know of any software tool that makes such plots. I would like to see the data in both the "normal" way and the "power" way to make up my opinion. Is does sound interesting however...
Well on that I agree with you and I said the same thing in another thread once, but I thought I was the only one. Oh well, the actual data is the important thing. Everyone can always keep adding graphing options to their software.
It is a lot of work up front, but in my opinion it's the work that is necessary to create an accurate model of the loudspeaker. You need one measurement for each driver, on each axis you want to model, plus at least one "multiple driver" measurement. This can be pairs of drivers, or three of more drivers as long as there is enough frequency overlap. The interference measurement is very sensitive, and you can just automatically fit the N-1 relative delays using a fitting algorithm.
Once you create this model for the acoustic side, then you just are changing the source side of things as you construct the crossover transfer functions. You get multi-axis modeling with the result changing on the fly as you tweak the crossover functions.
I think that is a bit harsh because it is a matter of preference and I prefer it the way that it is.
I have thought about doing this many times, but as I say, I have gotten used to the linear scale. Maybe if there is interest in using the PolarMap database I'll make it an option, like color, but thus far I am still the only one using it so my interest level in changing it is pretty low.
I didn't mean to urge you to change anything, Earl 🙂
I think the reason why so few have participated so far is that those who already build and measure speakers on regular basis, allready have some software tools which they are used to a have no need to see their data in other plotting software. And those who have never measured anything, have to learn it first...
I think the reason why so few have participated so far is that those who already build and measure speakers on regular basis, allready have some software tools which they are used to a have no need to see their data in other plotting software. And those who have never measured anything, have to learn it first...
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REW does complex modal calcs for its room sim. Not sure how it could be done any other way with a frequency domain approach, otherwise where would the damping feature?
Marcel
I have often thought about just what you are saying. But what does one do if the listening axis is not the normal axis? Then that makes the situation much more complicated. I use polarmaps to find angles for which the DI is near flat and smooth and the direct sound is likewise. This then is a good listening axis. If you change the angle scale as Sin^-1 the you loose this ability, unless you rescale the entire display for the new axis. Not impossible just not trivial.
If people aren't interested in sharing the data for what they have made then there is no point to all of this and we can all just hide behind the fact that there is no data to support or refute anything, thus allowing anyone to say anything. Makes for more sparkling conversation I suppose.
It reminds me of when we showed that THD was a meaningless measure some years back. People just said "Yea, we know it is meaningless, but we've always done it."
Dumptruck
No I do not have that speaker.
I have often thought about just what you are saying. But what does one do if the listening axis is not the normal axis? Then that makes the situation much more complicated. I use polarmaps to find angles for which the DI is near flat and smooth and the direct sound is likewise. This then is a good listening axis. If you change the angle scale as Sin^-1 the you loose this ability, unless you rescale the entire display for the new axis. Not impossible just not trivial.
If people aren't interested in sharing the data for what they have made then there is no point to all of this and we can all just hide behind the fact that there is no data to support or refute anything, thus allowing anyone to say anything. Makes for more sparkling conversation I suppose.
It reminds me of when we showed that THD was a meaningless measure some years back. People just said "Yea, we know it is meaningless, but we've always done it."
Dumptruck
No I do not have that speaker.
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