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Re: Horn stuff and a post back for Tom

Posted by tomservo (M) on July 10, 2002 at 19:32:50

In Reply to: Re: Horn stuff and a post back for Tom posted by Wayne Parham on July 10, 2002 at 15:13:49:

You wrote:

>> What your saying is correct then that the speaker, especially a
>> point source direct radiator "moves around in time", it in effect
>> moves front to back depending on frequency.

and then I replied:

And, it is non-linear around system resonance too.

to which you said:

>> Not non linear but its acoustic phase is at its maximum rate of
>> change at resonance.

my next reply was:

It's Non-linear. This is where it's shifting the most. Not a slow movement, but a rapid transition. Only after this point does it
become relatively linear.

And then you said:

>> It is not "non linear", even at resonance, it is acting as its
>> R,L,C components dictate. Non linear is when the Xmax is reached
>> or if the BL^2 / Rdc changes with respect to radiator position.

Now you're using semantics. The phase is non-linear, meaning that it isn't like a line. It isn't flat, nor is it diagonal. The phase
response with respect to frequency is curved. It's moving. It isn't linear.

Semantics or the engineering use of the word?? non linear normally means a departure from linear operation and is evidenced by
generation of harmonics or non proportional change in loudness with a change in power, neither of which are related to being "At resonance".
Non-linear phase?? do you mean non minimum phase? Group delay is related to the rate of change of the phase.

>> Horn loading is a way to make the radiation resistance dominate
>> the moving system and in this case the resonance is damped to
>> invisibility.

The horn itself is a resonant system. The systems are modified, but resonance is not removed, not by a long shot. The
impedance curve of your device shows several impedance peaks, each showing resonant conditions.

If one looked at a unity impedance curve, one would see the impedance of the crossover network, it has several peaks.
If one looked at the drivers, one has a different impedance curve which reflects the resistive horn loading.

>> You speak of the conical horn as if it were a "band pass" device
>> which is simply wrong, ALL horns have a "high pass" corner
>> frequency. The higher "low pass" corner which forms the other
>> half of the peak IS set by the driver and has NOTHING to do with
>> the horn loading.

It is a part of the system.

[about the simulation program]

>> I have 2 that work well, one is the NASA funded program written to
>> model any driver on any acoustic passage way.

So what is the mathematical model that this loading is based upon? Or are you saying that this is a general purpose case?

It is an assign able wave progression transmission line model which can be configured into nearly any shape passageway.
Generally I slice up horns into 200-400 slices, the acoustic properties of each are calculated and folded
in with the driver and drive signal info.
The frequency range is also in segments, 500 slices is enough to make a good curve but not take too long to compute.
In the version I use the air is a constant temperature @ 70 deg F.
I can tell you the math is hairy, Green's functions and stuff but if anything it predicts more structure than one measures as it has more resolution
than one usually measures with. A typical simulation runs in 15 seconds on a 700 MHz p2.

>> Loading at the apex is un necessary, one needs to be acoustically
>> close yes, but that is a function of frequency.

That brings us back to the question, so I ask again - How far are the midrange orifices from the compression tweeter
diaphragm, at the apex?

Do you mean physically, acoustically (with respect to the respective drive signals) or in time?

You wrote:

>> Flat amplitude AND zero degrees phase are the conditions needed to
>> preserve the waveshape of the input signal, no wonder so many like
>> horns.

and I replied:

This is true, and it is simultaneously impossible for any filter to accomplish.

then your response was:

>> That is right, only a constant power into resistive radiation load
>> without any significant reactance will do this.

So we are in agreement on this.

but then you said:

>> Yes and an efficient horn is one of the very few ways to achieve this situation.

We have already determined that the Unity device doesn't qualify through most of its bandwidth.

You keep saying that but it is not clear which one you refer to or why.
Most people consider a compression driver to be "efficient" yet the mid section on the one your familiar with is 2 dB more efficient so what is not
efficient about that?
There is no doubt at all that one could build a large mouth version and have an lf section that was 40%+ from say 50 to 200 Hz, a second
segment that was 40%+ from 200 to 800 Hz and that dividing that range into 3 sections one could exceed 50% efficiency over that range.
High efficiency is more difficult as the frequency rises, the "velocity response" is hard to get out of ANY cone driver above 1 kHz and to actually
drive a horn one needs the velocity profile.
Our mid drivers are at the edge of what can be made without much more expensive parts and have a 1200 Hz break point, even with exotic
parts 1500 - 1600 Hz is about the practical limit for high efficiency loading of any cone.
In all of this though it is worth mentioning again that the radiation resistance felt by the radiator is essentially constant above the low cutoff.

You said:

>> Below crossover it does what all woofers do, at crossover it IS
>> aligned with the mid section of the horn. It is the drivers delay
>> and phase at crossover that one matches.

and I replied:

So what you are saying is that the woofer's time response is
skewed, but up near the crossover point, you bring it into alignment
with the mids. Then you further match the mids to the tweeter as it
nears the crossover point.

to which you responded:

>> The woofers acoustic phase is what it is, at its low cutoff it is
>> behind in time compared to its high cutoff, ALL direct radiator
>> woofers act this way.
>>
>> When one chooses to use a direct radiator, one is stuck with how
>> they work, when one uses a horn to cover that frequency range, one
>> has a much better acoustic phase but a larger system.
>>
>> If one could accept a 36 inch square mouth, one could have horn
>> loading down to about 120 Hz.

Yes, my most popular version of the ten π has an 800 sq. inch mouth, and is loaded down to below 50Hz.

That sounds cool, where can I see a picture of it?

I wrote:

Putting aside, for a moment, the alignment problems in the overlap
region, and putting aside the rapidly changing phase at diaphragm
resonance of the woofers, midranges and tweeters, are you proposing a
system that has a slowly changing apparent location? Or does it
rapidly change in the crossover regions? And in either case, how do
you propose to keep from having problems arraying speakers having
this kind of "doppler effect?"

and you replied:

>> Again, there is no problem in the overlap region IF one has the
>> two systems at the correct time and phase. While horn loaded, the
>> effective position of ALL the drivers changes much less than if
>> direct radiators and to the extent that the acoustic phase
>> can be made to be at zero degrees, there is NO change in position
>> with frequency.

Maybe you misunderstood my question. I wanted to set aside the issue of diffraction in the overlap region for this question. I
am asking about how the difference in each of the three systems is dealt with. Do you attempt to move phase - apparent
position - slowly, though the audio range, within the device? Or do you move it abrubtly during the crossover regions? I am
asking where you have attempted to put the acoustic phase as a function of frequency.

Ideally the acoustic phase would be at zero degrees over the entire spectrum, this in real life is only possible below about 2500 Hz to what ever
the low cutoff is. As the mids are not 50% efficient and the compression driver is even less (around 20-25%), there is mass reactance showing in
the acoustic phase.
In the curve I am sending you, it shows the acoustic phase and amplitude response from 400 Hz to 5 kHz.
It is an 8192 point TDS measurement, taken at 1 meter, 1 Vrms drive, in my living room with hardwood floors.
It is not as smooth as one taken outside but it was dark out, it only has %5 smoothing (1/20 oct).
Obviously this is through crossover (1150 Hz) so you can see how well we are doing on a production model.

One see's that the acoustic phase is essentially that of the drivers. While not a straight line at zero, it is a lot closer to it than a direct radiators -90
degrees.
In the range below about 800 Hz it becomes easy to make the "right" drivers for the ranges below and there one can get 50% and acoustic phase
around zero.

>> The rapidly changing phase of the woofer IS AT the BOTTOM end of
>> its response and has nothing to do with the mid range.

Yes. And then the changing phase of the crossover filter moves it near the woofer/midrange transistion region.

Remember we are dealing with phase, one can intercept the woofers response where the phase is a straight line (starting above the low cutoff), at
Rmin where the acoustic phase has risen to zero degrees (and at zero has NO change in time or phase with frequency).

I wrote:

Your horn cannot do anything of scale smaller than one inch if
you're using a 1" exit driver device. It looks like free space at
that frequency - Its walls are merely a reflector.

No, the pressure wave is perpendicular to the walls, the walls simply confine the radiated angle until
the wave is large enough to maintain its structure.

and you replied:

>> ALL horns of ALL types cannot "load" a radiator once past the
>> point where the critical size is reached, for 20 kHz with the
>> wavelength being about 5/8 inch, this equals a diameter of about
>> 1/5 inch at 30 HZ, this is about 12 feet in diameter.

That's right, exactly.

>> Even at 5 kHz, the passage way in the compression driver is large
>> enough to fully load the driver. From that view point, one could
>> say that ALL compression drivers do not load any horn above 5K
>> (1 exit.inch driver)

That's right.

You wrote:

>> On the other hand, what the air see's is in the compression driver
>> is a continuation of a conical horn down to a rather small throat
>> area. From that stand point, if you think of the horn as the
>> total air path, it does indeed fully load the driver and does so
>> all the way down to the low cutoff of the horn.

and I replied:

Again, you're at the mercy of the compression driver maker here.
What happens in the top octave is not up to you. So you cannot claim
to horn load the device from 200Hz to 20Khz. But that's a dead horse -
You've already admitted to using compensation equalization to address
this.

to which you responded:

>> No, this is wrong, the "compensation" has nothing to do with
>> acoustic load and everything to do with the moving mass of the
>> compression driver. This is why a driver with less moving mass
>> (like a TAD 2001) when mounted to the SAME horn, shows a response
>> easily an octave higher. That HF roll off HAS NOTHING to do with
>> horn loading, above the low cutoff, the load presented by the horn
>> is essentially constant with frequency.

The diaphragm, motor and flare form a horn system. The system unloads at both its upper and low frequency bounds. At the
upper limits, you are at the mercy of the motor builder, both because of its dimensions and its mass.

By unload, that would imply the acoustic load has changed which it has not, the acoustic load IS essentially constant above the high pass freq.
Your a JBL fan right?, grab a copy of JBL's "Characteristics of high frequency compression drivers" Tech note vol 1, number 8.
Item 4 and 5 deal with hf response
The hf roll off has nothing to do with horn loading, the load is the same, it does not go away only the diaphragm becomes too massive and motor
too weak and then it behaves just like a direct radiator with an acceleration response. In a horn, that produces about a 6 dB per octave roll off.

>> That also includes the part of the horn which comes with the
>> compression driver as the real throat is at the diaphragm.

That's right, yes.

I wrote:

Conical horns become peaky at their low end, this is true. They act
like a series of resonators combined with a high pass filter.

and you replied:

>> No, not peaky, it is the relationship of the low cutoff of the
>> horn and power roll off of the driver which produce that response
>> shape.

and then I said:

The low cutoff of a conical horn system of this scale is relatively
peaky, as is shown by the plane wavefront model. It can be smoothed
with a larger mouth or by constrained space, such as using multiple
horns in close proximity or installing against a rigid surface or
corner. But the lower cutoff point has a peak, and response after
that has a negative slope.

and then you replied:

>> No, this is wrong, peakyness (in a simple straight horn) is an
>> indicator if mis termination at either end exactly the same as
>> with curved wall horns.

That's right. This is shown by the mathematical models.

>> Conical horns have a differently shaped radiation curve but all
>> types reach the asymptotic load impedance eventually, conical
>> horns do it more slowly than curved wall horns and so have to be
>> larger to get to the same low cutoff.

That's right, exactly.

>> Look at the horn loading curves which show radiation impedance vs
>> size, you will not see anything different at the high end of the
>> response, only at the low end.

As we've already discussed, there is an upper bound that is set by throat size too. And motor strength and diaphragm mass
also set a limit on the system.

You keep saying there is an upper limit based on throat size, why do you say that and give me some examples.
The only place I can think of where the size effects the hf cutoff would be if the throat was already at or larger than the critical diameter for
loading but even then it does not roll off.
Remember the horn it self is not a low pass filter, it is a high pass.

>> Efficiency is determined by having the right acoustic and electrical
>> impedance's, no one (except you) is saying that one has to drive
>> the horn from its end, one can driver it from the half way point
>> (midway between throat and mouth) IF one uses a suitable driver
>> and get the same efficiency one could get driving it closer to the
>> end.

One of the conditions of the Webster equation is to have equal cross sectional pressure, which is not the case unless one
drives the horn at the apex. This is a condition of the model more than anything else, and is why I've asked what mathematical
models were used.

Take care!

So for the math, what would you say happens if the is a pressure gradient in the throat, how large would it have to be to be measurable or effect
the performance?
How large of a pressure gradient can one produce with 8 sources (the holes) all located less than 1/4 wl from each other at most?
Ans, not enough to adversely effect the operation of the horn as an acoustic transformer, not enough to measure significantly different than the
single piston computer model.
I would say though that if the dimensions were acoustically larger than they are, a "non ideal" situation exists.
When the spacing is 1/2 wl, a forward lobe is produced as used in several EAW speakers and patented by Rocha (sp?)
While useful for producing directivity, it is too large a spacing to have horn acoustic transformation, somewhere between 1/4 and 1/2 wl spacing
wall to wall is the max size limit for horn loading because if it is already "that large" the acoustic loading has already reached the final impedance
of air.
I do have to say you are tenacious and many of the things your concerned about are valid issues.
On the other hand, part of the process of design is to find those "things" and figure out how far can one push things in one way or another and still
function.
On the mids interfering for example, your concerns are all dead on.
What I did was made a good number of prototypes and taking lots ofmeasurements figuring out "how high" one could make a given size thing go
and what rules apply etc.
Cheers

Tom

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