The Three Octave Rule

[Chris A]

How can a horn that's been truncated, and has a Fc less than 100 cycles below the crossover point, be loading the driver correctly?

See https://community.klipsch.com/index.php?app=core&module=attach&section=attach&attach_id=44054

[babadono]

Hows come i can't open the above link?

[CECAA850]

Hows come i can't open the above link?

 

It's not a link, it's an attachment (adobe).

[Chris A]

Carl - you can open it?

 

Dean asked the question, and I hope that he puts his boots on for this one, because it's mostly all about the math. 

 

I know of no simpler explanations, i.e., switching to an equivalent conical representation or using conical wave-numbers, of modeling horns below cutoff frequency.

Edited October 3, 2014 by Chris A

[IB Slammin]

From the linked site...

 

 

"With 'no horn', the cone movement increases 4 times for each octave decrease.   With a horn the speaker cone movement is reduced to 2.   Efficiency increase is approx 4 times (+6dB).   In theory, power to the speaker can also be doubled (+3dB).   Total advantage is approx +10dB with increased directivity."

 

You get ~5x reduction in cone motion with horn loading for equal SPL output (not 2x), and an efficiency increase of 7x to 10x (not 4x). 

 

The total advantage between horn vs. direct-radiating (baffle) is between 15-20 dB in SPL (or alternatively, reduction in required input electrical power of 50x-100x) and a typical 20-25 dB reduction in modulation distortion--the most notable difference, IMHO. 

 

Harmonic distortion levels are lower for horn-loaded due to lower required input power/driver amplitudes required to generate the same SPL in-room. 

 

All this assumes the same driver used as a direct radiator vs. in a proper horn-loaded configuration, i.e., apples-apples.

 

Why someone would subdivide this advantage into separate smaller quantities--with the combined effect to obfuscate the perceived difference (but NOT hearing difference)--is beyond me.  

So let me get this right. 

You are saying that a 107db reflex unit has more harmonic distortion (due to the need for higher input power)  than a 107db horn unit?

107db 1w @ 1m  is 107db 1w @1m !    Horn or direct-radiating bass reflex.   

There are many wonderful things about horn loaded LF bins that best most reflex designs.  But an increase of harmonic distortion due to low efficiency is something I can't buy.  As well as excessive diaphragm excursions being a fault.   I just can't find those things in a well designed direct-radiating bass reflex bin. 

tc

[Chris A]

I believe that I said that the horn-loaded loudspeaker will have somewhat lower harmonic distortion, but dramatically lower modulation distortion than a direct radiator--vented or closed box (acoustic suspension), using/comparing apples-to-apples drivers. 

 

Modulation distortion is, by far, the most objectionable form of distortion because, by definition, it's non-harmonic, and therefore much more objectionable to hear.  The primary type of modulation distortion in bass bins is AM distortion, not FM (Doppler) distortion.

 

IMHO, the definitive article is the following...and if I said anything above that takes issue with this article, the article is right: http://www.hps4000.com/pages/special/woofer_distortion.pdf

Edited October 8, 2014 by Chris A

[wvu80]

How does modulation distortion manifest itself?  Is it as "noise," or is it as an inaccurate reproduction of a sound, such as a piano that does not sound like a piano should?

 

Edit:  Chris, I read the article.  Thanks for posting.

Edited October 8, 2014 by wvu80

[Chris A]

How does modulation distortion manifest itself?  Is it as "noise," or is it as an inaccurate reproduction of a sound, such as a piano that does not sound like a piano should?

 

Distortions can be harmonic or inharmonic--such as amplitude and frequency modulation distortion (AMD, FMD), transient intermodulation distortion, slew-induced distortion, compression distortion, aliasing, etc.  Distortion alters the sound of the reproduced music/sound but is directly correlated with the source music/sound itself. 

 

Noise is usually not correlated with the music, such as background hum, hiss, or rumble, but it can also be periodic such as wow/flutter that isn't related to the source music/sound itself but due to the recording medium, playback medium, or playback device itself.

 

Here is a link to an interesting PWK article discussing modulation distortion: https://community.klipsch.com/index.php?app=core&module=attach&section=attach&attach_id=94224

[DrWho]

 

 

How can a horn that's been truncated, and has a Fc less than 100 cycles below the crossover point, be loading the driver correctly?

See https://community.klipsch.com/index.php?app=core&module=attach&section=attach&attach_id=44054

 

 

...which shows that the loading transitions towards being more reactive at the Fc?

 

Btw Dean - you gotta talk about the Fc in terms of bandwidth. 100Hz away from a 400Hz Fc is a lot different than 100Hz away from a 4kHz Fc. For example, 500Hz is 0.3 octaves above 400Hz, but 4.1kHz is only 0.04 octaves above 4kHz. This means a 500Hz xover on a 400Hz Fc horn is 10x further away than the 4.1kHz xover on a 4kHz horn.

 

Also related to this is the Q of the horn loading (back to my reactive comment):

(https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf)

 

Some horn profiles maintain the real portion of the impedance closer to the cutoff frequency. This is why exponential horns are typically preferred for low frequency horns (where length is an issue). For higher frequency horns, its easier to get the horn length, so you can go to faster expanding profiles and improve HF polar response (which isn't represented on these plots). All that to say, the actual impedance presented by the horn is important in determining how close to the Fc you can use that horn.

 

I think what's more interesting is how much throat reactance is acceptable? Is this purely something coupled to the driver, or does the horn start to "sing" and that frequency? Generally you see ringing in waterfall plots, but that gets augmented by the crossover and the interaction with the other overlapping drive unit.

 

I think it's interesting to note that the conical horns have a lower peak reactance, but that reactance happens at a higher frequency and is lower Q. Because the LF loading is dropping off so quick, you'll want to use a higher slope xover to limit LF excursion (lower distortion), but then you get lass overlap in the xover to augment the reactance - now you gotta deal with more ringing in the passband. I think there is going to be an ideal relationship between the horn profile and the xover slopes - and it might even extend a bit further to also minimize polar lobing as well. Anyone wanna crunch through the math on that? I'm also curious where the HF polars end up with such an approach. I think slightly increasing beaming of the HF is beneficial in a small room acoustics scenario because our rooms are acoustically large at high frequency, but acoustically small at low frequency. To augment the consistency of spatial cues, we need less HF information....but that relative ratio is going to depend heavily on the room acoustics...anyways, that's getting a bit off track. The point is that slightly narrowing the HF polars results in pushing the real portion of the horn loading to a lower frequency due to the slower area expansion at the throat.

 

My bigger point here is that the horn does not load well below the Fc, and really you don't want to inject energy into a reactive system - and that necessitates a xover above the Fc. However, the magnitude above the Fc is dependant on the horn profile and the xover slopes in play. This means a generic "100 Hz above Fc" is missing some of the finer points to what is happening. For a horn like the K402, I think we see the low frequency loading starting to give out at around 

Edited October 9, 2014 by DrWho

[DrWho]

On a similar subject, compare the Plane Wave response of the TAD 4002 to the frequency response of the 4002 on the K402 horn:

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CDYQFjAD&url=http%3A%2F%2Fradianaudio.com%2F%3Fwpdmact%3Dprocess%26did%3DMzcuaG90bGluaw&ei=g-Y2VMv6J7TGsQTKuYDgCA&usg=AFQjCNH_C0KF6BRgIJGsvXz8ln7pM8NBrA&sig2=oqVeIvLWw_trdbVqmPJ8mQ&bvm=bv.77161500,d.cWc&cad=rja

(PDF of Radian's replacement diaphragm, which includes the original TAD diaphragm)

 

 

Here is the raw frequency response (which is fricken awesome btw):

 

The TAD 4002 is basically flat to 400Hz on a plane wave tube, so ideally we should see that rise in LF energy continue from 7kHz all the way down to the Fc. This is the desired behavior of a constant directivity horn. However, the K402 impedance starts to roll off before the Fc because it is not a plane wave, nor anywhere close to an exponential/hyperbolic profile. What we see is that the acoustic impedance starts to drop at ~1.5kHz, and continues the slow rolloff characteristic of something between a conical and exponential horn (the photo from my last post). As a side point, I would expect the tractrix loading to also be somewhere between an exponential and conical horn in terms of LF loading behavior, so maybe this is why Roy likes to call it a modified Tractrix? He has mentioned a few times that he's more concerned about the actual loading presented to the driver.

[jacksonbart]

I agree with Zippy The Pin Head.  Classic comic.

 

Cheers

[CECAA850]

Carl - you can open it?

 

Yes

[ClaudeJ1]

So let me get this right.  You are saying that a 107db reflex unit has more harmonic distortion (due to the need for higher input power)  than a 107db horn unit? 107db 1w @ 1m  is 107db 1w @1m !    Horn or direct-radiating bass reflex.    There are many wonderful things about horn loaded LF bins that best most reflex designs.  But an increase of harmonic distortion due to low efficiency is something I can't buy.  As well as excessive diaphragm excursions being a fault.   I just can't find those things in a well designed direct-radiating bass reflex bin.  tc

 

You are forgetting that when measured on axis at 1 meter for both, the direct radiator has a different dispersion angle. So if different woofers are used as driver for each different cabinet, that would account for the difference in distortion as well.