Midrange horn design, cone-driven - 201

I’m in the process of building my first horn and would very much appreciate input from experienced users. Many have helped me learn about horns from scratch in my midrange horn 101 thread – thank you very much!! It has been an intense learning experience.

The system is 4-ways fully active, DSP with linear-phase crossovers, time alignment. The tweeter is a Beyma TPL-150H, and the horn to be designed is targeted to operate from 400 to 2500Hz. Below the midrange horn, a pair of direct radiators per side in sealed boxes, and below that subwoofers in sealed boxes. One goal is to use this horn directly connected to a 45 SET. Another 45 SET for the tweeter. Below that is class-D.

Given what I learnt at my other thread I purchased Faital Pro M5N12-80 for these horns. I was advised to use a flare cutoff frequency about an octave below the intended xo point to minimize colorations from the horn at the lower end. I’m taking 215Hz for fc.

One significant decision is shape of the mouth: circular vs. rectangular. Circular has the benefit of a more even and predictable response, while rectangular (2:1 width:height) has the benefit of reducing the center-to-center distance between the TPL and midrange horn (which is still going to be larger than twice the 2500Hz wavelength). Feedback on this will be helpful.

A Hornresp simulation is attached below. It’s a tractrix profile extended to 90°, with a circular mouth. S1=Sd, and fc=215Hz. Mouth comes out to be S2=1990cm2. Both attachments are the same, but one is lower resolution. I can't figure out how to unattach a file here...

As of today I’m leaning towards a rectangular horn. Open to be proven wrong, though. Bruce Edgar’s Tractrix midrange horn is a bit of a baseline for me.

I’m thinking either tractrix or LeCléac’h with 0.7 factor and limited to 180° opening for the width profile. For the top and bottom sides I’m not sure if I should settle for the simpler to build conical (like Edgar’s), uniform or exponential profile. What do you think?
Keeping the 2:1 mouth aspect ratio, a 631 x 315mm mouth will have the same surface as S2 above (1990cm2).

I guess before I go further into the design I should decide:
  • Rectangular vs circular mouth
  • If circular: Tractrix vs. LeCléac’h
  • If rectangular: profile for the width and profile for the height.
Any additional feedback very welcomed!
 

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The first thing to be considered when choosing any cone driver as a horn loader is to determine if it is suitable for horn loading, which not all cone loud speakers are.

The EBP ( Efficiency Bandwidth Product ) is my first indicator. The EPB for your Faital driver is 333.33.

For example; a cone loudspeaker with an EBP of 100 is not a good candidate for horn loading, and it is best used in a vented or sealed enclosure. And EBP of 150 is acceptable for horn loading. There are also many other factors to consider when choosing a cone loud speaker for horn loading.

I have found by using my horn design program that the higher the EBP, the smaller the chamber is required. Conversely, the smaller the number a larger chamber would be in order. I have also found that cone loud speakers which have a high EBP work admirably in vented enclosures of smaller volume compared to less acceptable horn drivers that require a larger volume for the same results. In my program I have written in several redundant equations for confirmation of the data, which on occasion, I discovered errors in published Thiele-Small parameters. Electro-Voice and Precision Devices come to mind.

Also, the throat area and chamber volume are inter-related. To change one changes the other. There is a convoluted set of equations I use to determine the throat area and the horn cut-off frequency. That frequency typically being within 5 cycles >> below << free air resonance. As a rule of thumb, a throat area between 1/3 and 1/4 that of the cone area is acceptable should you pursue an increase in bandwidth. A larger throat will provide increased efficiency. It's up to you to decide to what degree you chose to trade off efficiency over bandwidth. When the acoustic resistance of the throat is at unity with the acoustical reactance of the chamber is when you have a perfect match. The technical process for that term is Reactance Annulling.

Should you use the effective piston diameter or less as your throat area there is a simple method of determining the chamber volume;

V = St x c x (18.1 x (2 x Pi x c)) x L

V = Volume in cubic inches
St = Throat area in square inches
c = Velocity in inches @ 13,560.92
L = Length of horn where the throat area approximately doubles ( for the standard exponential equation that number would be 2 )

Or: St = V/(2.9xL)

The length of the horn where the throat area approximately doubles may be different between a standard exponential horn and Tractrix. If you're looking to build a short horn with a large mouth area, the Tractrix is the way to go. I perfer to use Vincent Salmon's Hyperbolic equation because my focus is on low frequency horns. With that I can maintain a desired horn length but able to manipulate the mouth area within reason. A typical 'T' number using that equation would be between .6 to .8. The horn behaves more exponentially as the number increases to 1. Greater than 1 and the flare becomes more Catenoidal. Conversely, as the number approaches 0 the horn then behaves more like a resonant tube. Not a desirable condition.

One last thing. Your horn cut-off frequency should be one octave below the lowest frequency a horn is designed to produce. For example; the ALTEC 811 actually has an approximate flare rate for a 400 Hz horn. The 511 has an approximate flare rate for a 250 Hz horn.

If I can be of any other assistance, feel free to ask.

H.F.
 
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ICG

Disabled Account
Joined 2007
You want a horn that operates from 400-2500Hz, or in other words, about 2,5 octaves. That's on the edge of needing a phase plug. You can ofcourse pull down the level of the horn in the middle of it's frequency band with the crossover but that's not always desireable.

I have to mention that the opening constant also got a huge influence on the radiation pattern at the upper end of the horn, so faster opening horns usually have much better, constant radiation pattern than horns which open slowly and following 'exactly' the horn function.
 
The first thing to be considered when choosing any cone driver as a horn loader is to determine if it is suitable for horn loading, which not all cone loud speakers are.

The EBP ( Efficiency Bandwidth Product ) is my first indicator. The EPB for your Faital driver is 333.33.

For example; a cone loudspeaker with an EBP of 100 is not a good candidate for horn loading, and it is best used in a vented or sealed enclosure. And EBP of 150 is acceptable for horn loading. There are also many other factors to consider when choosing a cone loud speaker for horn loading.

I have found by using my horn design program that the higher the EBP, the smaller the chamber is required. Conversely, the smaller the number a larger chamber would be in order. I have also found that cone loud speakers which have a high EBP work admirably in vented enclosures of smaller volume compared to less acceptable horn drivers that require a larger volume for the same results. In my program I have written in several redundant equations for confirmation of the data, which on occasion, I discovered errors in published Thiele-Small parameters. Electro-Voice and Precision Devices come to mind.

Thanks for chiming in!

Yes, experienced users pointed me to an AES paper that explained EBP, and the M5N12 looked good on this account vs other options considered. The Beyma 605Nd was better, but nobody had direct experience with it.

A couple of very experienced users had very good things to say about the M5N12, it looked good on paper, and modelled well. So that was it.


Also, the throat area and chamber volume are inter-related. To change one changes the other. There is a convoluted set of equations I use to determine the throat area and the horn cut-off frequency. That frequency typically being within 5 cycles >> below << free air resonance. As a rule of thumb, a throat area between 1/3 and 1/4 that of the cone area is acceptable should you pursue an increase in bandwidth. A larger throat will provide increased efficiency. It's up to you to decide to what degree you chose to trade off efficiency over bandwidth. When the acoustic resistance of the throat is at unity with the acoustical reactance of the chamber is when you have a perfect match. The technical process for that term is Reactance Annulling.
I was also pointed to the AES paper by Keele where he discusses reactance annulling. Further discussions with an experienced user suggested shooting for an impedance spike at about 10Hz above fc, so 225Hz in my example.


Should you use the effective piston diameter or less as your throat area there is a simple method of determining the chamber volume;

V = St x c x (18.1 x (2 x Pi x c)) x L

V = Volume in cubic inches
St = Throat area in square inches
c = Velocity in inches @ 13,560.92
L = Length of horn where the throat area approximately doubles ( for the standard exponential equation that number would be 2 )

Or: St = V/(2.9xL)
In my example St=Sd=94.2cm2=14.6in2.

For L, on Hornresp I went to Export Data>Axisymmetrical horn>data and found the area doubles by 8.5cm, or 3.35in

So V=2.9xLxSt=141.7in3 or 2.32 liters. Are you referring to the back chamber for reactance annulling, or a throat chamber?

One last thing. Your horn cut-off frequency should be one octave below the lowest frequency a horn is designed to produce.
Yeap, exactly as I designed it: fc is 215Hz and the intended xo point is 400Hz.

What are your thoughts regarding rectangular horn to reduce center-to-center distance to the (large!) tweeter vs circular mouth?
 
You want a horn that operates from 400-2500Hz, or in other words, about 2,5 octaves. That's on the edge of needing a phase plug. You can ofcourse pull down the level of the horn in the middle of it's frequency band with the crossover but that's not always desireable.

I'm hoping to get away without a phase plug. I was pointed to a couple papers about phase plugs, and while they are less complex than I initially thought, if I can do without them, the better. FWIW, my midbass should have no problem playing higher than 400Hz, so I might end up raising the xo.

I have to mention that the opening constant also got a huge influence on the radiation pattern at the upper end of the horn, so faster opening horns usually have much better, constant radiation pattern than horns which open slowly and following 'exactly' the horn function.
Thanks for pointing this out. Do you consider the horn I modelled a fast opening horn? I have no point of reference.
 

ICG

Disabled Account
Joined 2007
That would be a medium-fast opening horn. The opening starts soon but not very progressively. If I had to guess, I would say probably about maybe 50° dispersion, at 2,5kHz probably 40°.

What kind of tweeter/horn do you want to use?
 
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Joined 2008
Paid Member
For a tweeter, a round waveguide makes for the smoothest transition to reduce diffraction within the horn. If it radiates at the ceiling that can be dealt with there, but it can be more difficult to absorb lower frequencies practically.

If your mouth size is dictating the low end, a conical top/bottom will give the greatest extension of the directivity. A secondary flare can be kicked in. A flaring profile on the other hand can more easily round back onto a tweeter but lets go of the lows.

It depends on the band of interest. Some frequencies are easy to absorb, some should be kept clean WRT diffraction and some primarily need only to be kept at the right levels.

You can also consider matching the patterns (cross sectional shape), again depending on the crossover point. You may be able to change the shape part way through the horn.

Tractrix has a quick directivity index transition. Maybe that makes them useful near the Schroeder frequency. I can imagine you'll have to make some careful choices covering your intended range.
 
Thanks for chiming in!
What are your thoughts regarding rectangular horn to reduce center-to-center distance to the (large!) tweeter vs circular mouth?

Typically, when I design for bass horns the chamber volume is either for a compression type, or rear loaded. For the rear loaded horn, the acoustical reactance of the compliance should resonate with the acoustical mass reactance at the throat, resulting in an acoustical low-pass filter. The same can be done with a compression type horn as well if one chooses a throat area less than the piston area, whether it be folded or straight axis.

The low-pass chamber for a straight axis would be much smaller in volume compared to the volume required for the back of the cone. In that configuration the throat area would have to be smaller than the piston area, resulting in a rectangular throat exit. I would estimate that if you did employ an L-P chamber on the front of the cone the depth of the chamber may be only 1/4 of an inch. Just an educated guess. In that respect, the roll-off frequency for a straight axis horn should be one octave above the crossover frequency of the high frequency horn being used. The higher the roll-off frequency, the smaller the chamber.

Personally I prefer rectangular high frequency horns. I haven't heard a round horn that I liked. Technically, a Tractrix horn should be round, but I prefer the sound of a rectangular Tractrix over a round one.

The Keele article is the basis of my horn program I began writing 25 years ago, although slightly modified here and there. I have integrated Keele's equations with a plethora of equations gleaned from Olson, Klipsch, Beranek, Morse, and many others.

H.F.
 
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That would be a medium-fast opening horn. The opening starts soon but not very progressively. If I had to guess, I would say probably about maybe 50° dispersion, at 2,5kHz probably 40°.

What kind of tweeter/horn do you want to use?

The tweeter is a Beyma TPL-150H. It's on a 23x23cm waveguide with 80°x30° (HxV) dispersion pattern.

Indeed, dispersion mismatch is one of the things that worries me. On Hornresp, the horn I posted above displays a beamwidth of 80° at 1000Hz, 55° at 2000Hz, 48° at 2500Hz.


Reasons for 400 - 2500Hz:
  • While several folks use the TPL down to 1500Hz xo, and some even lower, several other folks report improvements in sound by using higher xo. There is a noted resonance at 2-2.2kHz, so starting at 2.5kHz and using steep slopes (like 8th order) seems a good place to shoot for.
  • Starting lower than 400Hz: several folks suggest it is best to keep xo out of the (if I recall correctly 300-3500Hz band). Others say it doesn't matter. But going lower than 400Hz means a horn with fc lower than 200Hz...which starts to get large in diameter.
  • Starting higher than 400Hz: certainly an option. As I go higher, though, I worry about how my midbass drivers might sound in that range vs a midrange horn. Bottom line, I would be ok going higher, but would rather do so after listening to the alternatives instead of designing it like that from scratch - unless there is a compelling reason for that.
 
The low-pass chamber for a straight axis would be much smaller in volume compared to the volume required for the back of the cone. In that configuration the throat area would have to be smaller than the piston area, resulting in a rectangular throat exit. I would estimate that if you did employ an L-P chamber on the front of the cone the depth of the chamber may be only 1/4 of an inch. Just an educated guess. In that respect, the roll-off frequency for a straight axis horn should be one octave above the crossover frequency of the high frequency horn being used. The higher the roll-off frequency, the smaller the chamber.

Personally I prefer rectangular high frequency horns. I haven't heard a round horn that I liked. Technically, a Tractrix horn should be round, but I prefer the sound of a rectangular Tractrix over a round one.

The Keele article is the basis of my horn program I began writing 25 years ago, although slightly modified here and there. I have integrated Keele's equations with a plethora of equations gleaned from Olson, Klipsch, Beranek, Morse, and many others.

H.F.

What is the name of your horn program?

I think you are the first one I recall saying you like rectangular horns over round. All along I was assuming rectangular was a compromise some were willing to make.

How is the high roll-off frequency of a horn defined? Is it -3dB on axis for acoustical pressure? If so, that point is at about 2500Hz for the horn I posted above. That means that horn should be crossed over no higher than 1250Hz?

In terms of the effect of the throat chamber size, I tried 110cm3 (base case), 200 and 300cm3, but the simulations showed little change. Am I missing something?
 
Horn Fanatic said:
In that respect, the roll-off frequency for a straight axis horn should be one octave above the crossover frequency of the high frequency horn being used.


How is the high roll-off frequency of a horn defined? Is it -3dB on axis for acoustical pressure? If so, that point is at about 2500Hz for the horn I posted above. That means that horn should be crossed over no higher than 1250Hz?

I've been thinking more about this, and maybe I misunderstood. Maybe you meant the xo point should be at 5kHz if the horn is -3dB at 2.5kHz, and assuming a passive crossover with shallow slopes?
 
What is the name of your horn program?

I think you are the first one I recall saying you like rectangular horns over round. All along I was assuming rectangular was a compromise some were willing to make.

How is the high roll-off frequency of a horn defined? Is it -3dB on axis for acoustical pressure? If so, that point is at about 2500Hz for the horn I posted above. That means that horn should be crossed over no higher than 1250Hz?

In terms of the effect of the throat chamber size, I tried 110cm3 (base case), 200 and 300cm3, but the simulations showed little change. Am I missing something?

I must apologize for not being clear. The roll-off of the horn is a result of the acoustical low-pass filter on either side of the driver cone. That type of filter is at a fixed 6dB / octave roll-off at the frequency which is a result of the parameters of the throat area and chamber volume. There are also acoustical filters constructed as to pass only high frequencies, and band-pass frequencies.

Take the JBL 4530 enclosure for example. The chamber is very small, and the throat is a restriction. When the acoustical mass reactance of the throat is at unity with the reactance of the chamber acoustical compliance, the two resonate very much in the same manner an inductor and capacitor behave in a dividing network network. The calculations are the same for electrical and acoustical, and mechanical should some use that analogy.

In the JBL catalog it mentions that the drivers in the 4530 and 4520 enclosures become direct radiators starting at 150 Hz, meaning all the frequencies below 150 Hz radiate from the horn mouth. If you put a sine wave generator on a rear loaded enclosure starting at say, 30 Hz, then slowly sweep to higher frequencies, you can literally 'watch' the sound move from the horn to the driver. The literature also claims both horns are usable to 30Hz. I find that claim a bit odd, since the mouth of the 4530 in free air can barely support 100Hz. The 4520 can barely support much lower than that in free air. It's more likely a single cabinet is producing a harmonic of 30Hz.

A simple calculation reveals that for a horn to support 30Hz in free air, the minimum mouth dimensions would have to be 12 feet by 12 feet. The JBL rear loaded horns would be capable of supporting 30Hz only in a large array in a 2Pi deployment.

Personally, I wouldn't mess with using an acoustical low-pass filter on the front of a driver in a straight axis horn for domestic use. Typically, they would be too small in volume to make much of a difference, hence why I mentioned in my previous post it would be no more than 1/4" in depth. The only enclosure I know of that has enjoyed any success that employed that type of filter is the RCA 'Ubangi' theater bass horn.

The horn 'program' I use is one that I wrote. It is not a software program, but a spread sheet which includes tables that indicate the impedance of certain aspects of the horn and driver at pre-selected frequencies, and phase angle calculations. It took me several years to refine it.

BTW - One thing about simulations, is that they are >simulations<. I actually tested the effect of acoustical low-pass filters by getting my hands dirty. Making test fixtures and measuring the results acoustically.

http://users.cms.caltech.edu/~ps/All.pdf

H.F.
 
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You may also find interesting to know, that in Medieval churches, numerous Helmholtz type resonators that were tuned with various amounts of sand to inhibit room resonance, were embedded in the walls.

The Greeks also knew of resonance, as in some of their theaters were placed urns of different sizes that served as Helmholtz resonators.
 
Hi,

Sorry to ask : when talking about cone horn does the compression chamber is the aera between the cone and the reduced throat ? Is it about this and how to choose the trade off between some beaming patern and high end extension ?

(Just trying to follow)

PS : so the compression chamber should be an Helmholtz camber with an active back ?
 
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What is the name of your horn program?

I think you are the first one I recall saying you like rectangular horns over round. All along I was assuming rectangular was a compromise some were willing to make.

Here's someone who emphatically prefers rectangular.

http://www.diyaudio.com/forums/multi-way/100392-beyond-ariel-952.html#post3687058

Also, in some applications, a round horn will give an on-axis dip.

http://www.diyaudio.com/forums/multi-way/273053-3d-printing-2.html#post4296678

I did a lot of trials with 4" wideband drivers in 2015, and got a similar (huge) on-axis dip with a round horn, better results with a rectangular one - but my horns were also different sizes, so not a perfect comparison.

If you have deep pockets, the large Iwata horns (as made by Auto-Tech of Poland) look like the best of both worlds. For a couple thousand $ less, you can just start with standard biradial horns and extend them to have whatever mouth shape you fancy.

Note that the Unity/Synergy horns (and clones) are not round, and that's about directivity, it's not a compromise to get a tweeter in closer. The one made by Red Spade Audio is a good example: a round horn would have been less effort to design and build, so there must have been a good reason for them to transition to an elliptical mouth.

As a final thought: since you are using DSP and can use digital delay, have you considered mounting the TPL coaxially, in the midhorn's mouth?

Like the picture, but not as big :)

An externally hosted image should be here but it was not working when we last tested it.


I realise the TPL is huge (by tweeter standards), and would "shade" the mid horn considerably, so you'd have to streamline it / design around it.
 
Hi,

Sorry to ask : when talking about cone horn does the compression chamber is the aera between the cone and the reduced throat ? Is it about this and how to choose the trade off between some beaming patern and high end extension ?

(Just trying to follow)

PS : so the compression chamber should be an Helmholtz camber with an active back ?

The link ICG gave (post 3) covers this pretty well, and has pretty pictures.

"there is a considerable air space between the speaker cone and the horn throat (dotted line). This air volume acts as a low pass filter, attenuating high frequencies."
 
The link ICG gave (post 3) covers this pretty well, and has pretty pictures.

"there is a considerable air space between the speaker cone and the horn throat (dotted line). This air volume acts as a low pass filter, attenuating high frequencies."

Actually, it is the interaction between the chamber volume and throat area that creates the Low-Pass condition. Not the the air in the chamber.

"there is a considerable air space between the speaker cone and the horn throat"

Not necessarily correct. It would only hold true with a loud speaker with a low EBP. Loudspeakers with a high EBP are typically loaded into small chambers. The chamber volume required for the EVM 12L for example is approximately .6 cubic before allowing for the additional of volume of the driver, which would increase the volume to approximately .72 cubic feet. The chamber volume of the JBL 4530 is approximately 1.2 cubic feet, which means the speaker is very close to the horn throat.

If I were to load an ALTEC 515 into a rear loaded horn, the volume required would be between 3 to 5 cubic feet. It is the primary reason why I would not use a 515 in a rear loaded format. Front loaded? No question about it that I would use it.
 
Hi,

Sorry to ask : when talking about cone horn does the compression chamber is the aera between the cone and the reduced throat ? Is it about this and how to choose the trade off between some beaming patern and high end extension ?

(Just trying to follow)

PS : so the compression chamber should be an Helmholtz camber with an active back ?

I only brought up the Helmholtz resonator as a type of acoustical filter. Not quite sure what you mean by "active back".

As I stated in my previous comment on the subject, I would not use an acoustical filter on the front of the cone in a straight axis horn for domestic use. Make your horn throat the effective piston area of the cone, AKA, Sd.

For the Faital, I would be happy to provide the dimensions of a horn throat similar to the typical throat used on for example, the ALTEC A7, JBL 4560, etc... Round on top and bottom with parallel sides. In my horn program I have Trig equations that give me the dimensions of that type of throat. That type of throat would only apply if the throat area is less than the effective piston area.

There are three ways to go with a straight axis horn. 1 ) Make the back chamber sealed. 2 ) Employ an acoustical low-pass filter section on the back of the cone if you plan on building a compound horn, meaning a straight axis horn on the front of the cone, and a rear loaded horn driven by the back of the cone. If that would be the case, there are rules that must be followed regarding the length of both horns, as the phase between the two is critical. Or 3) Build a combination enclosure by constructing the rear chamber as a vented enclosure, AKA, a bass reflex design. An ALTEC A7 is considered a combination enclosure.

As the topic of the thread is about constructing a mid-range horn I assume there would be some sort of bass cabinet used in addition to the system. It is my opinion in this case, that the speaker chamber for the mid horn should be sealed. An educated guess tells me the speaker chamber for the Faital driver is going to be quite small, so venting is not only unnecessary, but out of the question unless the vent is just a hole.

H.F.

BTW - Never apologize for asking a valid question. We're all here to learn something.
 
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