It seems to me that you can create a conversion curve to convert from volts to excursion. Until the ka number gets fairly high the excursion is simply a 12dB per Octave (rising at the bass end) filtering of the actual frequency response of each section. (Lets asume all the drivers are in infinite 2 pi so that we don't have to worry about 4pi to 2 pi transitions.)
Since much of the excursion is determined by the LF end of things then the actual cutoff frequency, slope, and Q must be an accurate part of the model.
The absolute scaling of the SPL vs. voltage (based on effective diameter) would take a lttle digging but the formulas are around. You will assume flat output for the system, so the excursion in each band will need to scale (based on diameter) to give that.
Figure it out for a sine wave of a given output SPL and then convert to pink noise. For that case the N sections must add to the target output. Regarding the Gausian amplitude probability distribution of noise all generators are limited to so-many standard deviations away from the central value. I believe that GenRad used to make a generator limited to +3 sigma. That gets around you having to worry about the infinite excursion peak every blue moon. Still, it would be better to think in terms of the mean value of noise or better, a sinusoidal input.
Not a full answer to your question but it might get you a little closer.
David S.
Since much of the excursion is determined by the LF end of things then the actual cutoff frequency, slope, and Q must be an accurate part of the model.
The absolute scaling of the SPL vs. voltage (based on effective diameter) would take a lttle digging but the formulas are around. You will assume flat output for the system, so the excursion in each band will need to scale (based on diameter) to give that.
Figure it out for a sine wave of a given output SPL and then convert to pink noise. For that case the N sections must add to the target output. Regarding the Gausian amplitude probability distribution of noise all generators are limited to so-many standard deviations away from the central value. I believe that GenRad used to make a generator limited to +3 sigma. That gets around you having to worry about the infinite excursion peak every blue moon. Still, it would be better to think in terms of the mean value of noise or better, a sinusoidal input.
Not a full answer to your question but it might get you a little closer.
David S.
Now that I think about it any woofer box program that gives absolute SPL values and excursion for a given input level will give you most of what you need. Model a 3 way as 3 different sized woofers, 12" to 1 " for example. Set the levels of each to give the output you want and the excursion curves (for sine wave) will be provided.
David S.
David S.
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