# Back Loaded Horn Omni Speaker

#### Dwightay

I have a design for a compact full range speaker cabinet that is based on a cone. The up firing driver reflects sound 360* horizontally off of a supended object, and the back pressure of the driver increases low frequency gain through a folded tractrix horn firing down onto the floor, radiating horizontally. Although sounding complex it is quite simple in concept: as the cone is circular in plan, as are the baffles for the folded tubes of the horn, circles within circles.

Reading of transmission line and quarter wave length tunnels, it seems that for benefits gained, problems of frequency diminishing and booming are rampant causing much effort to stuff the tunnels to assist control of unwanted frequency interference, and thereby diminishing the benefits in turn. As well the architecture of these cabinets can cause much domestic disharmony, the dreaded WAF problem.

Essays by Klipsch and Dinsdale demonstrate the science of horns, where the pressure chamber of the driver (also called coupling and air chamber) has a throat at the beginning end of the horn, and as the sound travels through the length of the horn it increase in volume. This is the goal of the rear loaded horn. As well there is an equilibrium equation linking Volume of the chamber, Area of the throat, and the Cut Off Frequency. The volume and the area can increase or decrease the frequency above which it does not enter the horn for magnification.

I am asking the forum if they have had any experience with rear loaded horns and thr equilibrium equation that would set the cut off frequency. Additionally, the literature on the folding of a horn is not well explained but suggest problems at the bending points, understandably, and I would appreciate advise on what remedies can be applied to make the transitions more fluid and enhancing to,the horn.

Dwightay,
Toronto - Anguilla

#### hollowboy

"a folded tractrix horn firing down onto the floor"

"problems at the bending points"

"I am asking the forum if they have had any experience with rear loaded horns and thr equilibrium equation that would set the cut off frequency"

Nope, but with most speaker stuff a great start is to get hornresp (free software) and experiment. You get a feel for what's possible.

#### tp147

Hi,

the lower cut off depends on the horns mouth area. The deeper the cut of the much more wider the horns mouth. Around 1m^2 (1600 square inch) by 80 Hz in a real Horn!
The top en depends on the horns throat.

HTH

#### Scottmoose

Depends what you call the lower cutoff. The QW cutoff F0 is defined by axial length & taper. The -3dB impedance-matched frequency Fc is a function of terminus area. These frequencies are not necessarily synonymous.

#### freddi

Stu Hegeman - EICO

Omnidirectional speakers

#### GM

The -3dB impedance-matched frequency Fc is a function of terminus area.

Greets!

Can you point me to where this is defined as I don't remember it being remotely like this.

TIA,

GM

#### Scottmoose

That's because it's complete twaddle and a good (well, not 'good' at all) example of why it's not a good idea to write posts when down with a dose of septicaemia & haven't slept. Make like the gibbering doesn't exist. Heavy belt of antibiotics; I think I'll live. Possibly. I can't recommend it though.

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#### GM

Ooh, bad, bad! This is how all my grief/surgery the other year got started! Hope your medical plan stays on top of it; Medi-not kept me too long on two powerful antibiotics known to do long term damage/death before granting surgery, with the long term loss in quality of life that too often occurs.

GM

#### Dwightay

Being a Canadian, we pride ourselves on speaking the Queen's English, spelling with -our's instead of or's, double consonants and other archaic North American pronunciation.

However, ScotMoose, I don't understand what you say. Rest, heal and be well for now, but later can you repeat your post in terms that a Canuck can understand!

#### Dwightay

ScotMoose,

Hope you are feeling better. I fondly remember my late August trip to your northern capital, it had turned cold for a Canadian and we had to wear just about all the c.othes we brought, yet as we froze, everyone else wore little in the cold, cold drizzle. We assumed that the Scots were immune to cold and colds.

Bundle up, take lots of lime and spirits.

#### Impunity

I hope you blokes don't mind me butting in, but I've been hot to do a project using a full range driver (say 4 or 5 inch) with a rear horn as opposed to a T.R. cabinet, so I'll watch with interest. FYI, there is an interesting post on the Parts Express gallery that has this design although there are no construction details.

#### Horn Fanatic

I have a design for a compact full range speaker cabinet that is based on a cone.

Greetings,

The length of a rear loaded horn is base on three factors.

1 ) The parameters of the driver.

2) The volume of the chamber it resides in.

3) The throat area.

The combination of the chamber volume and throat area result in an acoustical low-pass filter.

First, the acoustical parameters of the driver and chamber need to be considered, as they become half of the circuit. The driver Cas, and the chamber Cab are both an acoustical compliance. Think of the acoustical compliance analogy as an electrical capacitance analogy.

The throat area constitutes an acoustical mass, or Mat. Think of that analogy as an electrical inductance analogy.

The values of an acoustical analogy and electrical analogy are treated the same when calculating filter math. The acoustical Compliance is in Farrad, and the acoustical Mass is in Henry.

What do you get when you resonate the reactive element of a capacitor, and the reactive element of an inductor? A low-pass filter circuit. The slope will be that of a 1st Order filter network. 6dB / Octave.

Once that frequency has been determined, the length of a rear loaded horn is calculated by multiples of half wavelengths in order for the horn mouth and speaker cone to be in acoustic phase. The phasing will only occur at the low-pass frequency. As the frequency increases the horn ceases to radiate. Below that frequency the horn is the primary radiator. The cut-off frequency of a rear loaded horn does not determine it's length.

For example. If the low-pass frequency is 300 Hz, the length of your horn will be 22.6 inches, 67.8 inches, 113 inches, etc...

Another parameter to consider is the Efficiency Bandwidth Product. fs / Qes.

Cone drivers with EBP values lower that 150 IMO, make for questionable horn drivers. Those with values of 100 and lower are best suited for bass reflex and sealed enclosures. Speakers with low EBP values typically require large enclosures.

Drivers with EBP values of 175 and greater are better suited for horn loading, and also bass reflex enclosures. The higher the EBP value, the smaller chamber volume is required.

Other factors for horn loading will be high motor strength, and light cone weight.

The best equation I have found to use is Vincent Salmon's equation for a hyperbolic horn. It allows you a degree of latitude when choosing a mouth area while maintaining the proper length. That latitude being the 'T' in the equation. A 'T' of .6 is typical. As the number decreases the flare becomes Catenoidal. At that point the horn behaves more like slightly flared a tube, which will cause distortion. When the number approaches 1, the flare becomes more Exponential. A number greater than 1 is not desirable, as the horn would flare too rapidly.

A word of advise. Just because a speaker has a cone doesn't mean it is suitable for horn loading. Stuffing a speaker with a low EBP into a small chamber will produce mushy, ill-defined bass, flawlessly.

The EICO enclosure is certainly a unique enclosure. I own a pair. Not audiophile grade, but pleasant to listen to for background music.

Now, a word about compound horns. The length of both horns, not including the chamber between them must be multiples of a half wavelength. For example, if your bass horn is 67.8 inches, and you wish to make your mid horn 6 inches, then the combined length of both horns will be 67.8 inches. What ever you add in the front horn length must be subtracted from the bass horn length. That way the acoustic phasing between the two horns will be at unity at the low-pass frequency.

Also. Choosing drivers with an fs lower than 35 Hz becomes problematic. A proper cut-off frequency for a cone driven horn is within 5 Hz below fs in order to achieve proper reactance annulling. Designing a horn based on very low fs frequencies will result in a very long horn with an unwieldly mouth area. Shortening a horn with a very low cut-off in order to make it suitable for domestic use will result in what is called a discontinuity. Your horn is no longer a horn, but a tapered tube.

H.F.

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#### Impunity

Wow! That's a thorough explanation. I'm going to have to read it a few times to absorb the info. Thanks.

#### Horn Fanatic

Wow! That's a thorough explanation. I'm going to have to read it a few times to absorb the info. Thanks.

I have barely touched in the subject.

I spent years writing a proprietary horn design program that has served me well. Perhaps if you let me know what driver you wish to use I can give you some design tips.

H.F.

BTW - The EICO cabinet was originally designed for Harman-Kardon by famed horn designer Stewart Hegeman, of Lowther. EICO changed the woofer to accommodate a horn tweeter.

#### Impunity

I have just built a pair of full range speakers using Alpair 7.3 drivers. I am still evaluating them as they are still in the run-in period. Initial results are very pleasing and so I would likely give them a try. Thanks for your offer.
John L.

#### knarfor

I have owned several pairs of these speakers (I still own one pair). A few years ago, I cracked one open and made a cabinet plan for it. I attached it here (it's in inches. I can't find the metric copy, but the conversions are easy enough).

The speaker's F3 was at about 47 Hz. It used a modified Philips 9750M driver. Given the 9750M's common specs, you could probably use this design for many different modern drivers with good results.

#### Attachments

• HFS-2 Cabinet.jpg
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#### knarfor

Slightly off-topic

I have barely touched in the subject.

I spent years writing a proprietary horn design program that has served me well. Perhaps if you let me know what driver you wish to use I can give you some design tips.

H.F.

BTW - The EICO cabinet was originally designed for Harman-Kardon by famed horn designer Stewart Hegeman, of Lowther. EICO changed the woofer to accommodate a horn tweeter.

I'm something of a Hegeman fanatic, so I have to comment here. Sorry that it's mildly off-topic.

The Citation X (the Lowther based speaker Hegeman designed that you referenced) was designed by Hegeman two years after he designed the EICO HFS-2. Both designs were derivatives of Hegeman's "Hegeman Professional Loudspeaker", which was a massive beast of a speaker (the horn loads two 8" drivers) that served as the "concept speaker" for the HFS-2 and Citation X.

The same design (the "Professional") was later reproduced by Shahinian Acoustics, with Hegeman's permission, as their famous "Contra-Bombarde Subwoofer."

I own a pair of all three Hegeman designs. The bass output of the "Professional" horn is impressive. In my room, it is flat to around 18hz. I wish I were brave enough to try reverse-engineering the design, but I've never seen another pair and I don't want to risk ruining them.

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#### DrBoar

The Eicos are not horn but quarter wave pipes, as the horn openings are constricted to very small openings. I presented my building of Decca Corner horns here in 2014. Sound really good with the Philips 9710 8 1/2" driver.

#### Dwightay

what is the difference between 1/4 wave pipes and horns

Thank You Dr. Boar,

I can see your point that the EICO back loaded section being a series of folded, expanding flat conduits is not a horn in shape. But does it matter? Pioneers have demonstrated that the throat can be subdivided into smaller throats, continue as separate conduits, and be recombined back into the mouth without noticeable (human limits) losses compared to a contiguous tube/pipe/horn. The EICO cabinet does not recombine the output into a whole but surrounds the driver to approximate a single point source. Also there are comments that square horn section are good as approximates to circular but slightly smaller horn sections, And, that in the case of reinforcing bass frequencies through a rear loaded tube/horn that the transition at the bends of the folded sections need not be shaped for the flow of low frequency sound.

As contributor ScotMoose joshes in his byline: the perfection says that is good enough, seems to say it all. After cobbling designs for backloaded horns/1/4 wave conduits/tubes it seems many have to resort to stuffing the back passage to get a sound more pleasant and in keeping with the driver front output.

So what is the consensus of design back loaded cabinets to boost less efficient driver bass output?
1. Try to approach a well engineered 1/4 wave exponential/tractrix horn profile, following an continuously expanding mathematical formulae to prevent reverberation/distortion/standing waves?
2. Shape the rear passages as close to a square or circular section as possible (is this important at all)?
3. Combine the output into a single focus, a point source output?

Or does any of this matter? Dwightay

#### freddi

I owned a Shahinian Contra-Bombarde - drove it with a Belles amp - worked well in a little room - don't think it handled my larger room very well - IIRC the exit area of the slots at the floor exit was fairly small - may have had custom Oaktron 8s ( -could not get its lid off) - the cabinet was certainly heavy and stiff.