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RE: Basic question on the coax horn match

Posted by tomservo (M) on May 7, 2023 at 10:01:06

In Reply to: Basic question on the coax horn match posted by Edp on May 7, 2023 at 08:45:29:

Umm good question. The BMS coax driver has the hf section too far away in time to make a non-dsp crossover that acts like a single source. The B&C is different and doesn't have that issue, it acts like a synergy horn inside.

On the other hand the horn does two main things so far as this conversation, the horn increases the driver efficiency and increases the system's directivity and BOTH increase the SPL on axis for a given power..

The impedance transformation part has a "high pass" effect set by the rate the cross sectional area expands. For example, if one wanted a 30Hz bass horn, the exponential expansion dictates the area double no faster that about every 2 feet. A 60Hz horn would double every one foot and so on all the way up in frequency. For this part of a horns performance, the impedance transformation doesn't go on for ever, it stops when the horn is 1 WL in circumference. For a 30Hz horn in free space, that comes out to be about a 10 foot diameter. No need to make it bigger, no acoustic gain anyway...but.


The directivity but first consider the 1 inch exit hf driver and the rule above. At 20KHz, the wl is 5/8 inch and so ALL of the impedance transformation is done well before the sound reaches the driver exit and that inside the horn is a passage that continues the horn shape getting smaller as it gets to the radiator.
So this doesn't mean the horns job is done, no, the part of the horn past the end of the impedance transformation continues to direct the sound.

If you imagine a conical horn with the driver at the apex, what radiates away from the driver is a part of a spherical wavefront who's pressure front is perpendicular to the horn walls. As one goes down in frequency, the point where the horn no longer controls the radiation angle can be found / measured. Don Keele's thumb rule is quite good.
If one had a conical horn who's mouth was 10 inches and was a 60 degree angle, then pattern loss F is 10^6 / 60 degrees /10 inches = 1666Hz
Because the pattern control is the horn wall above that F, above that the radiation angle continues to be 60 degrees.

Well all the up to the where the throat dimension takes over pattern control. A 1 inch exit hf driver sitting face up with no horn, has an exit large enough to control the pattern up high.
That formula rearranged is pattern angle given the diameter and frequency
10^6 / diameter 1 inch / 20Khz = ~ 50 degrees so 10KHz = 100 degrees.

So, this was the long way to get to the point that your driver exit size also controls how wide a CD horn it can drive how high without diffraction inside the horn.

The older type horns (curved walled horns like exponential) are very useful where one has a smaller seating area.

The same pattern loss rules apply but now starting down low, as you go up in frequency, the part of the horn that controls pattern moved up the horn and because the horn walls angle is decreasing, the radiation angle also gets narrower and narrower. This changing directivity used to used to off set the naturally falling acoustic power from the hf driver, making if flat or near flat on axis where if mounted on a CD horn with a constant angle vs frequency it would show a typical 6dB/oct roll off of the real acoustic power.

Well a longer answer than i intended, hope it makes sense
Tom

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