# horn questions

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#### e-side

Hi,

i'm looking around on the web for info about horns. I visited www.melhuish.org and some other sites, but there are still a couple of things which i don't understand (maybe because my english is not so very well).

- compression chambers.. what's the function of them. Is it possible that rear loaded horns have rear compression chambers, or front loaded horns have front compression chambers ?

- I saw that there a small room between the driver and the throat of an RL horn. How do you calculate the volume this room?

- do rectangular horns need a minimal width?

#### GM

Greets!

Compression chambers are used only on front loaded horns (FLH) to reactance annull the horn's throat reactance, IOW equalize the pressure on both sides of the driver to 'force' the driver to be linear and maximize its gain near/at the horn's cut-off (fl).

The front chamber is a low pass filter chamber, so in a back loaded horn (BLH), this chamber is behind the driver, with the 'compression chamber' being the room, ergo no reactance annulling capability due to its acoustically large volume (Vb) unless some form of mass loading is used, with a small front horn usually the preferred option. Read Dinsdale's article for more info on this approach.

WRT calculating either and/or both chamber's Vb, Marshal Leach's formulas are accurate, though there are various ways to arrive at it, but DIY folks today usually just find it by trial and error using Hornresp.

WRT minimum aspect ratios, it is not a good idea to exceed a 9:1 ratio (width:height) or it becomes aperiodic (acoustically resistive) in nature.

GM

#### e-side

thanks! it's clear to me now!

#### e-side

At the moment i'm reading the Leach paper on horn modelling, and again i couldn't give myself answers at the following things:

1. I read somewhere that a front-loaded horn should have the smallest possible volume between the driver and horn, while there's a room between the driver and horn in leach's paper (Vf, front cavity). Which one is correct?

2. Are throat and mouth calculations for a front-horn the same as for the rear horn?

3. In Leach's modell you'll have determine Wl and Wh at eq. (14). Are these the same as the low and high cutoff frequency of the system? if so, what frequency for Wh is suited when the low cutoff frequency is 35 Hz?

best regards

#### GM

Greets!

1) The beauty of horns is their design/performance flexibility so there are few 'absolutes' in horn design. ML's default design is for an optimum compression horn for a given F3 (Fl, Fh), but is hardly the optimum for many apps. For instance you wouldn't normally design a 'fullrange' BLH with 10-12 dB of gain since baffle step requirement is only 3-6 dB.

2) ?? Yes, and no. I mean the math's the same, but what Fl, Fh you choose will be different and so may be the boundary.

3) Yes, though I work from Fl, Fh, which is Wl/(2pi), Wh/(2pi). It depends on the BW you want, so if you chose 3 octaves and the driver can handle it, then Wh = (35*2^3) = 280*(2pi) = ~1760 Hz.

GM

#### e-side

thank u very much GM, but i already have a new question

I searched for other material and so I downloaded Michael Zhang's software for calculating a horn based on ML's theory.
When the program designs the horn, it takes f0 ('Horn Cutoff Frequency') as the cutoff frequency (in my case 80,2 Hz), but i thought 35 Hz was the cutoff freq

Probably it's me who makes the mistake, but i just want to be sure before i design 'n build my new horn.

#### GM

Greets!

You're welcome! I'm aware of the program (he lives fairly close to me and I helped him some with learning horn design also), but I've never installed the program since it requires also installing Microsoft .NET.

Anyway, I don't understand your Q. What is 80.2 Hz, the driver's Fs? Or is it just a sample design? Or.....?

GM

#### e-side

Hello GM

I'll try to explain.

I would like to design a horn which has a Fl of 35 Hz and a Fh of 280 Hz (3 octaves). After I filled in the properties of my driver, ML's program calculates several values (as you can see in the first attachment).

As you can see, the Horn Cutoff Frequency (Fo) is 80,215 Hz. Leach says this is the frequency where 'reactance annulling' (?? I don't really understand what it is) can be achieved.

When I use the Horn Design function of the program, the Cutoff Frequency is set to Fo: 80,2 Hz . This results in a 'small' horn (see attachment 2).

I thought that this Cutoff Frequency had to be 35 Hz, beacuse Fo is to achieve reactance annuling.

Does the program use the right cutoff frequency (80,2 or 35 Hz) ??

BTW, if a horn can only cover 2 or 3 octaves, what about the frequencies above these octaves?
For example, my horn covers up to 280 Hz. Are the frequencies above 280 Hz, like 400 Hz, produced well by the system ?

I hope you understand my question now, since it's pretty difficult for me to explain in english

#### Attachments

• img1.gif
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#### e-side

And here's the second attachment.

best regards.

#### Attachments

• img2.gif
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#### paulspencer

I can't find that program ... has anyone got a link?

#### paulspencer

thanks ... in searching I found another one but it was in German!

#### GM

Greets!

Well, I guess it will have to do since I don't speak Dutch. Anyway, as they say, 'a picture is worth a thousand words', so now I understand (I think).

For my records, what make/model driver is this? Rest of the specs (measured?) or website?

Reactance annulling is the balancing of pressure on both sides of the diaphragm until they are ideally equal. Viewed another way, a compression driven horn optimized for max efficiency is an underdamped 4th order bandpass (BP) cab mated to a large, overdamped 'port' that nulls out each other's excess 'Q-ness'.

'Fo' = F6. The rear chamber tuning frequency is Fc, so this design is for a SQRT(35*280) = ~99 Hz horn. To calc a 35 Hz horn, Fl needs to be 3 octaves below it, or 35/2^3 = 4.375 Hz. At this frequency it takes a negative pressure rear chamber to reactance annull it, so in reality you'd be making a slightly unequal pressure balanced BLH. This assumes though that you're attaching it to a M = 0.35 horn rather than a M = 1 expo that I assume you want to use based on the attachment, which will reduce the pressure on the front side somewhat, bringing the system closer to being annulled.

Use Hornresp to find the length that makes it acoustically a half WL long, terminating into a full size mouth when all the boundaries are factored in if you want it to load smoothly all the way to 35 Hz. Use it also to find the rear chamber Vb that makes it resonate at Fc if you want it to load (protect) the driver below it.

How much BW the horn passes beyond its passband is dependent on the driver, compression ratio (CR), 'M' factor, whether or not it has a phase plug and how effective it is. If folded, then how it's done will affect it also.

Speaking of 'M' factor, the program implies that it's a design variable, but it calc'd specs for a M = 0.436 (seriously hyperbolic), not M = 1 (exponential), so apparently this is strictly for designing the horn expansion, though of course you can mate it to any lens profile to get other alignments. Bummer, it would be nice if it calc'd everything based on the 'M' factor.

GM

#### DorinD

Phase plug

@GM
Please, could you indicate me a link with information about using phase plug on bass-horn driver to reach a higher bandwidt? Precisely, I need a phase plug to acomodate a rectangular thoath of 140 cm2 to a 10' driver. Thanks!

#### e-side

Thank u very much GM !

#### GM

Greets!

I'm only aware of AES papers on the subject. There may be others also, these are just the ones I've browsed. Like these folks and the pioneers of sound reproduction though, I learned most of what I know from experimentation:

[013] Title: Phase Plug Modelling and Analysis:
Publication: AES-P, No. 1140, Cnv. 55 (1976-10)
Author: Clifford A. Henricksen
Abstract: Mechanical modeling of a simple phase plug
yields an electrical-mobility equivalent circuit; a
single-frequency notch filter. This applies directly
to "normal" circumferential-slit configurations. The
analysis is then applied to a radial-slit phase plug,

[014] Title: Phase Plug Modeling and Analysis: Radial
Versus Circumferential Types
Publication: AES-P, No. 1328, Cnv. 59 ( 1978-02)
Author: C. A. Henricksen
Abstract: Mechanical modeling of a simple
two-dimensional phase plug and diaphragm yields an
electrical mobility equivalent circuit; a two-pole,
low-pass filter. At higher frequencies, this analysis
becomes incomplete, and a model presented by Merhaut
(1975) is us

[015] Title: An Application of Bob Smith's Phasing
Plug
Publication: AES-P, No. 1384, Cnv. 61 (1978-11)
Author: F. M. Murray
Abstract: The war of the phasing plugs still rages
after more than 25 years. Compression driver phasing
plugs have vacillated between annular rings, salt
shakers, teardrops, and now radial slots again. When
Bob Smith provided simple design criteria for

[016] Title: The Dual Coil Inductively Coupled
Loudspeaker System Performance Optimization and the
Application of an Acoustic Phase Correction Plug
Publication: AES-P, No. 2780, Cnv. 86 ( 1989-03)
Author: Boaz Elieli
Abstract: Analysis of the dual coil inductively
coupled loudspeaker system using an electrical
equivalent circuit is presented, and some of the
practical design aspects relating to the system
optimization are discussed. The application of an
acoustic phase correct

[017] Title: Ultimate Performance of Wide-Range
High-Frequency Compression Drivers
Publication: AES-J, Vol. 24, No. 8, pp. 639 (1976)
Author: Clifford A. Henricksen
Abstract: Performance equations are developed from an
electric mobility model of a typical electromagnetic
compression driver. The analysis is independent of
impedance and relates ultimate performance to
material, air, and phase-plug variables.

[018] Title: An Investigation of the Air Chamber of
Horn Type Loudspeakers
Publication: ASA-J, Vol. 25, No. 2, Pg. 305-312,
Mar-1953
Author: Bob H. Smith
Abstract: The front air chamber design is treated as
a boundary value problem which yields a solution of
the wave equation for the general case in which the
horn throat enters the air chamber in a
circumferentially symmetrical manner.

GM

#### GM

e-side said:
Thank u very much GM !

Apparently not since you didn't feel the need to 'pay' me what little I asked for in the way of a 'fee':

For my records, what make/model driver is this? Rest of the specs (measured?) or website?

GM

#### paulspencer

I have been modelling a number of different drivers in hornresp including AV12, AV15, a beyma 18" driver, the Apex 8" and the IB15 (AE speakers IB sub driver) and have found that a BLH tends to have a similar response but with less cone excursion! I take a design that works as a FLH and then set VRC to 0.

Why would this be the case? Some of the FLHs have a very sharp peak in cone excursion which looks like a problem, but the BLHs don't have this problem, the peak excursion is at dc, not at fc, hence it is not really a problem.

If this is how they perform, why would anyone build a FLH?

#### slowmotion

Hi Paul

I get less cone excursion with a back chamber, not more.
You can make a FLH with or without a back chamber , buy the way.
If you get problems with peaks, you can try to model a larger back chamber.

cheers

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