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Transcript: Smaart Impulse & Phase Measurement
A thoughtful forum exchange sheds light on the issues of Smaart Impulse & Phase Measurement.
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Reply posted by Tom Danley on September 18, 2001
“An equal phase shift across that entire bandwidth would have to be differing delay times for differing frequencies. If I got my money’s worth from Jamie, Sam, Don, and Mr. McCarthy, that would be an all pass filter.” This is the behavior of a point source (one who’s diameter is small compared to the wavelength it is producing) with “flat” response. As defined by its electrical equivalent circuit and as measured ala Heyser, a typical woofer, to have flat frequency response, must (mid band) have an acceleration response to the VC force. This is accomplished by the motor force acting on the drivers moving mass which ends up reflecting an RC filter (C being mass). This 1 pole roll off of the radiator velocity counter acts the improving radiation efficiency (an acoustic/dimension related slope with no phase shift associated with because it is a changing resistance), producing flat response but at about a -90 degree acoustic phase shift (input Voltage with respect to output pressure after all fixed time delays are accounted for). At the low end, even in a sealed box or infinite baffle, cabinet tuning will cause a large amount of acoustic phase change, going through zero degrees at resonance (Z max where mass and spring are equal but opposite) to a positive value as the system is dominated by compliance stiffness.

Going up, the phase is also zero at the R min point in the impedance, this is where the series L in the VC is equal but opposite the mass reactance (C) and these two terms cancel out leaving the Rdc in series with the acoustic load and losses (a small R). So you see, you all ready have a “thing” which has a different delay for each frequency, a woofer and most speakers. At low frequencies, unwrapping the acoustic phase back to nominally zero degrees can be done without dsp and when done makes a wonderful sounding subwoofer. Unlike conventional woofers, the zero phase and flat response yields a system which CAN reproduce a complex waveshape.

The normal, non zero acoustic phase is the main thing which has stopped many attempts at active sound cancellation in its simplest form. I have spent a great deal of time working on speakers which had as little acoustic phase change over the widest frequency range possible as well and would also say that makes a significant audible difference.

On the other hand, I do everything with drivers, crossovers and horns and physical placement, partly because I want to actually attack the real problem but also because I am not to hip actually working with dsp. I know it is possible to correct all the phase stuff this way too and there is at least one hifi dsp correction product which claims to do this, at least at the microphone location.This is one area where an efficient horn can have an edge, to the extent they are dominated by the acoustic load, a resistance, there acoustic phase is resistive about zero degrees (output pressure and input voltage coincide over a wide range of frequencies).

Reply posted by Chip on September 19, 2001
Tom, Two questions:
1) would you consider preparing a “idiots guide to LF phase”? I’m very interested in the phase artifacts caused by different types of boxes and venting / porting methods. I never realy considered this as such a huge factor in the differing performance of different types of boxes.
2) How would you best describe an all-pass filter, and it’s effects?
David, et all, please respond as well. This type of shared information is why we are here.

Reply posted by Nathan Butler on September 18, 2001
Whenever I think of this, I like to reference some simple mathematics. Bear with me… A pure tone can be described by:
1) cos(wt) where w = frequency, t = time

With a phase shift (1) becomes:
2) cos(wt + p) where p = phase in degrees

With a time delay, (1) becomes:
3) cos(w(t + td)) where td = time delay

As an example, let’s say w = 100, p = 90, and td = 0.9
(2) becomes cos(100t + 90)
(3) also becomes cos(100t + 90)

Now let’s make the frequency, w = 200
(2) becomes cos(200t + 90)
(3) becomes cos(200t + 180)

Essentially, a time delay yields similar results to a phase shift, except that a time delay increases the phase shift with frequency. Hope this helps.

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