Home » Sponsored » Pi Speakers » Subwoofer Group Delay and such. Long post, but I hope its interesting, maybe :P
Horn phase [message #42497 is a reply to message #42490] Mon, 15 September 2003 02:22
 Wayne Parham Messages: 18006Registered: January 2001 Illuminati (33rd Degree)

I think it was good to point out the distinction between acoustic impedance and electrical impedance. There is a reflection of acoustic impedance in the electrical impedance though, through the mechanical system. The acoustic load modifies the mechanical load which then in turn causes an effect in the electrical load.

The best examples are those that that are highly loaded acoustically, i.e. horns. I've noticed that horns exhibit electrical peaks where the horn's acoustical load becomes more reactive. The acoustic phase angle of horn forms a rippled curve, which is caused by the changing acoustical reactance and resistance. It acts very much like a series of resonators and as such, generates ripples in the acoustic impedance curve. These are translated into the mechanical system and, in turn, in the electrical system. So while acoustic impedance is not the same thing as electrical impedance, there is some inter-relationship between the two.

The relationship between phase and impedance is determined by the following formula:

θ = ArcTan i / r
where,

θ is the phase angle
i is the imaginary or reactive impedance, and
r is the real or resistive impedance

Considering this, you can easily find the phase where impedance is known.

So let's look again at the response chart for a horn:

You can see that the horn is intended to be used from 40Hz to 400Hz, so that's the region of interest. You'll notice that the device is quite reactive, meaning that it has non-zero phase. And it isn't trivial - It is a significant amount. For example, phase θ = 65° at 55Hz, 45° at 110Hz, 30° at 200Hz and 20° at 400Hz, where the horn has reached upper cutoff. Phase isn't consistent either, but instead is a series of ripples representing large closely-spaced changes in phase. You'll find this reflected in the electrical impedance, where you'll see ripples in the impedance curve.

Re: Horn phase [message #42498 is a reply to message #42497] Mon, 15 September 2003 06:32
 Adrian Mack Messages: 568Registered: May 2009 Illuminati (1st Degree)

Could we liken it to a simplification as well; As the acoustical impedence gets higher (by means of compression chamber in horn, for example), then efficiency is greater and maximum output is therefore increased. And as the acoustical impedence gets higher, excursion is reduced. This seems to be what happens in a horn, and ones with higher acoustical impedance reduce excursion more and increase efficiency and therefore total output.

I guess it happens sort of in a vented system too, but to a much smaller degree. Technically speaking its +3db in efficiency over a same-sized sealed cabinet. So it has a slightly higher acoustical impedence, and also means excursion is reduced.

Generally horns have more response ripple than direct radiating cabinets. The acoustical impedence you shown in your graphs have lots of ripples, which show up in the frequency response. Maybe some horns don't do this, but it looks like most do.

 Wayne Parham Messages: 18006Registered: January 2001 Illuminati (33rd Degree)

In a sealed box, there is only one mass/spring resonant frequency, and that is fo. Fs could be said to no longer exist, because it has been shifted up to become fo. Of it could be said that fo = fs, because there is only one resonant frequency. The distinction is maintained because the speaker's free-air resonant frequency is not determined by the system, and is a stand-alone parameter.

When the speaker is removed from any system - electrical, mechanical or pneumatic - it will resonate at its natural free air resonance, fs. Energies will tend to excite the moving system at fs. If you short the voice coil, that will provide some motor braking which will add moving resistance and help control the cone.

If you put the speaker a sealed box, the air in the box will act as a shock absorber and that will help control the cone and shift the resonant frequency up a bit. If you put a weight on the cone, it will shift the resonant frequency down and if you place something on the cone that interferes with its movement without adding mass, that will damp the resonance without altering the frequency.

Fo is where the sealed system resonates, so that's where control is the least. But remember that the sealed system acts to damp the cone pneumatically, so a well-designed system will have better control of the cone at fo than the speaker alone would have at fs.

Re: Horn phase [message #42500 is a reply to message #42498] Mon, 15 September 2003 07:54
 Wayne Parham Messages: 18006Registered: January 2001 Illuminati (33rd Degree)

I agree with you, 100%

 Adrian Mack Messages: 568Registered: May 2009 Illuminati (1st Degree)

Cool, makes sense.

One last thing, the sealed box resonantes at Fo, so thats where control is the least. On a vented box, is control the least at Fb because thats where it resonants? Or is it Fo and Fb because theres a Helmholtz resonator and the shifted mechnical resonance of the cone? I wouldn't think its Fo because apparantly thats right no near Fh.

Thanks!