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Re: Horn phase

Posted by tomservo (M) on September 16, 2003 at 18:12:07

In Reply to: Horn phase posted by Wayne Parham on September 14, 2003 at 22:29:09:

Hi Wayne

I don’t know the dimension of the horn you have modeled but there are a few things one can tell about it from the curves.
It would appear to be a horn that is 1 / 2 wl or longer vs the minimum 1 / 4 wl length (a guess based on the spacing of the ripples).
Based on the frequency response ripples, I would guess the driver is not a good match and / or the mouth is not large enough. This would not be a high efficiency horn.
Response ripples in the output can be caused by a mis-match at either end of the horn IE: mouth too small or driver not suitable. The latter is where the M.L. math is useful.
Fwiw, simpler models (like spice models or the transmission line model I use) also tend to over state the “Q” of such ripples compared to measured results (suggesting there are un-accounted acoustic losses).

While this model show ripples in the output up to the high cutoff, it is not necessary to have them when everything is right.
The thing is, whatever the horns impedance is, it is not the definition of what comes out the mouth of the horn.
The horn has an acoustic “impedance” curve, which changes most rapidly in the range near the lf cutoff. Driving that horn is a driver that also has an acoustic impedance and reactance.
When the source and load (driver and horn) are matched, there can be a considerable change in either with a minimum effect on the output.
For example with a nominally matched source and load, one can change the load to 2X or 1 / 2 the original and see less than a 2 dB change in output power. Contrast that to the 6 dB spread when a voltage source is used on a changing load.
Since the driver’s impedance is in series, the effects of phase shift are also reduced (like any reactance in series with an R compared to just the reactance).
The driver also has reactance, however it is customary to make this a conjugating quantity, either by proper sizing of the driver properties and rear volume and / or adjusting the horn flare hyperbolic constant which shapes the rate of change of resistance and reactance (reactance annulling)

Anyway, I have to help with some homework so I have to keep this short.
Since you have a way to model horns, how about if I see if I can find parameters which result in little or no ripple in the response. I will post the specifics (since I can’t post images) and you take your program or Mc Beans and see how it looks. Conversely, if this is a real horn you have, let me know the specifics and I will see if I can find a driver which is a better fit.

40 to 400 Hz is wider bandwidth than most of the single horns I do but I think flat response in that range would be possible.
Without ripples in the output, there will be no ripples in the output phase as well.
With a horn that is more resistively dominated, the phase will be around zero at the output (after all the fixed delays are removed ala Heyser) and the result is also a more efficient horn
Remember it is only the efficient horn which is resistively dominated and having an acoustic phase around zero degrees.

Shortly at the new web site there will be measurements for the Bdeap, while narrower BW than your example, acoustic phase is around zero from somewhat above low cutoff through its operating band.
Also if I recall, the BT-7 response curve also has the acoustic phase plotted.
Got to run

Tom

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