High Efficiency Speaker Asylum: Re: Horn Distortion, kinda long by tomservo

Some thoughts.
Distortion is a result of a non linearity in the signal path, its effect is to add "bonus sound" to the signal and by "bonus" I mean
sound which is not part of the input signal but added "for free" as a product of the non linear process. This extra sound is at
multiples of the input signal frequency at 2,3,4,5,6 and so on times the input F.

The familiar "honk" you refer to in PA horns is often the result of not having the response flat enough, which is often very difficult
to do using a passive crossover especially with a CD horn.
The problem here is that the horn / driver impedance as the load for the crossover makes it DARN hard sometimes to get flat
response. With a resistor as a load, all one has to do is look up the values in a filter table or program.
With a typical horn impedance, one is FAR from a resistor and getting further from one as it reaches the low cutoff. Often extra parts are needed just to kill some of the effects of the impedance curve.
In a woofer one might need to use a Zoble network because the driver inductance messes with the filter, with a compression
driver there may be twice or three times as many parts needed to neutralize the load impedance.

Any time one has a "peak" in the response of any significant magnitude, for any reason in the mid area, one can easily have the
"horn sound" (even from a direct radiators).
In addition to the crossover issue, the horn itself can have non constant directivty which alters the spectrum one hears in front of
the horn, if more than one driver is operating (like at crossover) there radiation's interact and can also produce a narrow peak
somewhere because of the phase and distances being right for that frequency.

Sort of a general rule, if you hear a "horn like" coloration, look at the frequency response for big peaks, see if those align with
structure in the impedance curve and if so, the problem is more likely the crossover than the horn /driver.
Very often what are thought to be "mouth reflections" on mid /upper horns, turns out to be the drivers impedance was not benign enough to be connected to the crossover used.

Distortion in a horn comes from two main things, the driver motor linearity and air non linearity.
Ideally, a loudspeaker motor would produce the same force per current at any position in its travel, this would be a "linear"
relationship.
In reality, a normal driver has a motor who's current / force relationship changes with respect to position.
While the motor is often the main source, adding a non-linear suspension to a linear motor equals a nonlinear system.
Also if there is a mechanical resonance attached to the VC which alters the radiation, this can alter the linearity.

Air is non-linear, since the speed of sound is temperature dependent, one finds at high SPL's that the pressure side of the
waveshape is slightly hotter than the rarefied side and so after some distance, the hot side advances, producing a saw tooth shape
from what was a sine wave.
This is the type of distortion called "throat distortion" and in horn is a function of how intense the sound is and how quickly with
distance the sound level falls. Intensity is part of it because it defines the difference in temp between the hot and cold side of the
waveshape.
The expansion rate matters because that governs how quickly the sound level falls with distance as the wave progresses down the
horn.
As a result, slow expansion and high SPL = large throat distortion, fast expansion and low SPL = low throat distortion, there is a
thumb rule around for this in one of the old books.
Measurments of the real thing as used are the reality however.

Low frequency horns often have high levels of harmonic distortion which is normally (and incorrectly) attributed to throat
distortion.
In reality, the sound levels that a VC driven cone can produce in a throat are not high enough to cause much throat distortion.
As an extreme case, examine the BT-7. Although the two 15 inch radiators are driven by a servomotor in stead of a Voice Coil, look at the Measured SPL and distortion on a BT-7 at full power.
It has a very linear rotary motor that has no X-max and is an example of T&S parameters suitable for horn loading. Note this is more output than a VC motor can produce but look how low the distortion can be while producing several hundred acoustic Watts. Throat distortion is not a real issue down low. (see link)

High frequency horns are a different story, they have a much higher compression ratio and much stronger motors (proportionally)
and are often pushed to operate over a wider BW.
Distortion figures would best be displayed (I think) as a 3 d plot of F, D, I (Frequency, Distortion level at Intensity) and since this
could easily be done but it is not, I can only conclude there is a marketing advantage to having the specifications for loudspeakers
being so sketchy compared to what is possible with electronics.
I make that conclusion speaking not as a DIY'r but as a person who has been in the business for 30+ years designing stuff for living most of that time. I am serious, loudspeakers in general perform so poorly compared to electronics that the mfr's are effectively hiding what they do and not showing any more that absolutely necessary.
Other than an occasional rant, there is not much I can do about either on the other hand.

Anyway, the problem is also perhaps that distortion numbers are close to meaningless with out putting them in the perspective of
what one can hear.
For example, you ears do not have flat frequency response (Fletcher - Munson or the more up to date Robson - Dadson equal
loudness curves).
Looking at the curves (if your not familiar with them do a Inet search and find them) one see's that at 20 HZ, the threshold of
audibility is about 80 dB as I recall. One see's that as you go below 400 Hz or so, ones ears are decreasingly sensitive to the
sound.
For the woofer, this means that if one produced 80 dB at 20 Hz (the minimum level to be audible), that because of the ears LF
response, a 7 % 3rd harmonic would have the same perceived loudness as the fundamental. This makes the possibility of truly
clean bass a distant possibility.
In the Dolby labs paper of sub woofer requirements they concluded that none of the high end HiFi subwooferes they tested came
even close to producing "inaudible" levels of distortion down low.

If one takes the hearing sensitivity into account and folds into that the ears adjacent frequency masking criteria (see link) then
what one see's is that distortion audibility is very dependent on frequency. In contrast to the 20 Hz example, consider how much
5th harmonic of say 5 KHz would be needed to be audible, even 50% isn't enough to be detectable.

Ultimately, if one looks at the shape of the sensitivity curve, one see's that between 3 and 4 KHz the ear is most sensitive, the ear
is then most sensitive harmonics that fall in that range. If one said 3300 HZ were the peak sensitivity, then the 3rd harmonic of
1100 Hz would be where the ear was most sensitive, or the 4th harmonic of 825 Hz or the 5 th harmonic of 660 and so on.
Where the harmonics fall where the ear is most sensitive, that is also the range which distortion is most audible.
Any time you are on the curve where the LF is rolled off, the ear is more sensitive, where the curve rolls off in the high end, the
ear is less sensitive to distortion.

All this means that a 1 inch compression driver may work well as a HF producer even though up high it is very distorted, you
just can't hear it because those frequency components fall out of range or in a decreased sensitivity part of your hearing.
Throat distortion is the primary source of this distortion as while the motion of the radiator is small but the horn is many
wavelengths long.

Lower down, particularly if one uses a compression driver for midrange, one also finds high levels of distortion at modest SPL's
and if the driver is used down below the ears peak sensitivity, then they are generally increasingly audible above a few hundred
milliwatts.
A larger driver can be used and down low it generally has less distortion but also has less of an extended hf response and more
distortion up high.
In Pro sound, 2 inch drivers are normally driven well past audible distortion so much so that the extra hf content causes sibilance
problems and a response curve that is different at different operating levels (similar to but different than the effect of increased Rdc
as a function of input power (once above about 1/6 rated power where this dynamic non-linearity takes place).

A solution below about 1 KHz is to horn load a cone driver, that has much larger linear motion and area than the compression driver.

Anyway, I know this wasn't a simple answer, it is not a simple subject and I am sure I left things out as well.
Cheers,

Tom Danley
.

Links to

Masking criteria
http://www.dolby.com/tech/parametr.html

Equal loudness curves
http://arts.ucsc.edu/EMS/Music/tech_background/TE-02/AcNumbers/AcNumbers.html

BT-7 SPL / THD
http://servodrive.com/BASSTEC7.PDF