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RE: Puzzled by your two examples vs desired output range

Posted by tomservo (M) on December 31, 2023 at 07:07:39

In Reply to: Puzzled by your two examples vs desired output range posted by Edp on December 30, 2023 at 10:54:51:

Hi
There are several considerations one can follow if one seeks the greatest acoustic power vs power input and lowest distortion. These are not always important unless those things are important.

A "perfect" horn/driver that is N= 50% efficient exhibits a property visible in it's impedance curve that is an indicator. In the frequency range where it is 50% efficient, it has an impedance that is resistive and about 2 times the Rdc of the driver. This means that the heating (I^Rdc) or "work" being done is 50% in the VC DC resistance and the other half is acoustic radiation.
Sound simple but what you measure is a function of efficiency AND unlike a small speaker also the system directivity AND the issue that with a large speaker (like a bass horn) the inverse square law is altered by the size of the source (the law requires a small point) and a thumb rule is measure outdoors at at least 5 times the largest cabinet dimension then calculate back to one meter..
So, so far as electrical power capacity, 50% efficiency also infers the electrical capacity has also doubled in that bandwidth.

There is also the excursion, tied to which is most of a horn and direct radiator's linearity or lack of. The horn connects the acoustic impedance of "the big end" to the driver at the small end with an acoustic shape that ideally "acts like" a transformer...with a high pass frequency set by the length and expansion rate. Like putting your bicycle in a much higher gear, each pedal rotation covers more ground and so thanks to Huygens hydraulic principal, the higher the compression ratio, the greater the air motion into the throat compared to the radiator and motor but the greater the force placed on the radiator etc (part of the idea of impedance matching the driver to the horn load).
A less often considered fact, Excess hf bandwidth is actually undesirable.
Consider a simple direct radiating woofer driver that has a frequency response that had a large rise of say +12dB at 3KHz.

Ok, it's good woofer and who cares about 3K, i will low pass this guy at 300Hz or lower. So on listening there was still something there at 3k so add a brick wall filter at 300Hz and then a passive notch filter and it never went away.

The reason was the distortion harmonics the driver always adds are all multiples of the input, the bad ones you hear most easily are 3,5,7,9,11 th and so on.
You hear these most easily because your hearing becomes much more sensitive as you climb out of the frequency basement. For example to be just detectable at 20Hz, a sound has to be around 75-80dB SPL actual and just a 7% 3rd harmonic at 60Hz sounds equally loud as the 20Hz fundamental.

The driver wasn't overly "bad" in linearity but magnifying all the distortion harmonics by that +12dB or 16X made them detectable and made the speaker "locate-able" when eyes were closed..

Free sound and localization you don't want, not part of the input signal.
With a horn, there is the front volume to consider, if sized correctly, it can actually extend the hf corner some (just like the vented box is a low pass filter driven differently that does the same at the bottom end) ...in exchange for a sharper hf and lf acoustic low pass roll off.

This acoustic "low pass" between the driver and horn rolls off the distortion components that enter the horn and radiate unlike a passive or active electrical filter and is part of all the Synergy Horns.

This front volume appears to have been considered in your model and as Bill suggested, these models usually don't consider HF directivty which increases the on axis level vs total sound power.

I have not used hornresp, does it produce an impedance curve?
Happy New Year!
Tom

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