Folded horn speaker design – explanation and calculator
How does a folded horn speaker design work?
The folded horn speaker design is a particular case of a normal horn design. Horn’s main purpose is to increase the efficiency of a speaker. You might of done it as kid : fold a piece of paper into a cone shape and shout through it, so it sounds louder. This is a rudimentary example of real life horn. Other, more sensible examples, are the trumpet or the trombone. These horns are easily made for high and mid frequencies, because the horns have acceptable sizes.
If you go down in frequency, the wavelength increases and so the dimensions of the horn. This is where the folded horn subwoofer comes into play. Folding the horn makes for an efficient use of space, and therefore makes the enclosure more acceptable size. A real life example would be the tuba, which is a brass instrument for the low notes. It is using a horn, but not a conventional one, like the trumpet. The tuba’s horn is not straight, it is a snail shape, to efficiently use space. A horn loudspeaker is designed to go from a small opening to a large opening. I can make it straight or folded, but the principle must remain the same.
Before we get into the folded horn speaker design, we first must understand the basic horn principles.
How does a horn loudspeaker amplify sound ?
The basic principle on which the horn relies on is impedance matching. The speaker is a mechanical system, which has a high impedance, versus the air, which has a low impedance. When a wave propagating in a tube, meets an abrupt change in acoustic impedance, part of its energy will be reflected back. Horns are not tubes. They have a certain taper. The duct or tube is progressively increasing in its cross section. Because of this taper or flare, the horns act like an impedance transformer (aka coupler). They make a smooth transition from the high impedance of the cone, to the low impedance of the air.
Now that we explained the principle on how the horn works, let’s enumerate the reasons why you would want to couple a horn to your speaker :
- Highly improved efficiency.
- Eliminating the resonance introduced by speaker boxes.
- Increased directivity. The sound doesn’t spread as much, like with normal radiating speakers. Depending on how the horn is designed, the sound is directed into certain areas. This can be a good or a bad thing, depending on the application.
- Reduction of speaker generated nonlinear distortion.
Parts of a horn speaker
The horn is composed of 3 main parts :
- The throat : which is the part that is connected to the speaker.
- The neck : which describes the length of the horn.
- The mouth or the bell : which describes the end part of the horn, “connected” to the air.
A horn will start expanding, starting from the throat and end at the mouth. The speaker will be connected at the throat of the horn, and radiate sound at the mouth of the horn. All of these parts influence how will the horn affect the overall sound. The flare and mouth design, the phase and direction of the particle velocity at the mouth, will all have an impact on the sound quality and directivity of the horn.
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One of the main characteristics of the horn is its shape. The horn has a certain taper, which is determined by the cross section expansion rate. The cross section area is determined by a function of distance, from the throat of the horn along its axis. This function will give the neck of the horn a certain shape. This means that the neck can have various shapes, but there a few shapes which are most common.
Here are some common horn profiles :
- Parabolic : Easy to design and construct, but poor impedance conversion.
- Conical : Easy to design and construct, but poor impedance conversion.
- Exponential : Good wide band impedance conversion, but some nonlinearity.
- Hyperbolic : Very good and high impedance conversion, but relative nonlinearity.
- Stepped : High impedance conversion. Nonlinearity depends on step resolution. This shape is not like the others. The horn is not growing in a smooth fashion, but in abrupt square steps (imagine a cube, then a larger cube, and so on. The speaker plays through these cubes)
When you are designing a horn, you will look for 3 things : Transfer function, acoustic impedance at the throat and nonlinear distortion. There are other things to worry about, like directivity, phase distorsion and resonance characteristics, but those are secondary. The latter properties can be determined by altering the length of the horn and the shape of the mouth. Because of this aspect, conical and parabolic shaped horns are not so popular.
On the other hand, exponential horn profiles are very popular, since they have good bandwidth, relatively low linear distortion and suitable throat impedance characteristics. Hyperbolic expansion gives a response down to a lower frequency value, compared to exponential, but the fall-off below that particular frequency is steeper. Also, because the expansion from the throat to the mouth is more gradual, pressure builds up inside and may cause distortion issues.
How to design a horn
Because of the impedance difference of the speaker system and that of the air, that transfer from the speaker to the air is very inefficient. The efficiency is somewhere around 1% or less. The horn is like an interface from the cone to the air, to match the impedance difference, and prevent internal reflections. A folded horn speaker design can improve efficiency by up to 80%
The design of a horn is complex, but I’m going to give the basic guidelines to keep it simple and easy to understand. No one wants to see walls of text with math formulas.
- When choosing the diameter of the throat, keep in mind that the shortest wavelength reproduced is twice the diameter of the throat. So for high frequency response, the throat needs to be as small as possible. Example :
- For 10 000 Hz -> the throat needs to be 17 mm maximum.
- For 15 000 Hz -> the throat needs to be 11.3 mm maximum.
- For 20 000 Hz -> the throat needs to be 8.5 mm maximum.
- The diameter of the mouth will dictate the low frequency response. For the horn to radiate a certain low frequency, the mouth needs to be half the size of the wavelength of that particular frequency. So for good bass response the mouth needs to be as big as possible.Also, the lowest frequency played by the horn sets the resonance frequency for that horn. Example :
- For 100 Hz -> the mouth needs to be 1.7 m minimum.
- For 50 Hz -> the mouth needs to be 3.4 m minimum.
- For 20 Hz -> the mouth needs to be 8.5 m minimum.
Length of the neck
- This length is given by the mouth of the horn. If you want the mouth to have a certain diameter, the horn’s neck will have a set length. Here is a formula, how to calculate the length of the neck, considering the growth of the cross section area is exponential :
- A = aria of the mouth (cm2).
- a = aria of the throat (cm2).
- f = lowest frequency.
- L = length of the neck.
Example : Let’s say I have an 8″ (20 cm) woofer and I want it to go down to 50 Hz
- Let’s say, for argument’s sake, that the throat is equal to the diameter of the woofer, so the area will be πR2 = 3.14 * 102 = 314 cm2.
- The diameter of the mouth needs to be 340 cm, so it can reach 50 Hz, so the area of the mouth will be 3.14 * 1702 = 3.14 * 28900 = 90746 cm2.
- f = 50 Hz.
- Length = (log(90746) – log(314)) *4000 / (0.4343 * 50) = (4.96 – 2.50) * 4000 / 21.72 = 453 cm.
Sometimes the area in front of the driver may be smaller than the actual size of the driver. This means that this area will start to narrow, to provide a small throat, for better high frequency response, and then it will start to progressively get bigger. Because of this, a region with high pressure is born. This pressure is equalized by the sealed chamber behind the cone, which reduces non-linear distortion.
Folded horn speaker design
We have determined that the size of the horn is in direct correlation with the frequencies we want to play. This means small and medium sized horns for the high and mid frequencies, and large horns for the low frequencies. It is impractical to build a horn with a mouth of 3.5 m in diameter, because it will probably fit nowhere. So for those horns, which we want to go low, below 100 Hz, a folded or coiled designed must be adopted.
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Low frequency horns have to be extremely large, so folding the length of the horn makes the enclosure fit into a more practical space. By folding the horn, you will compromise the high frequency of the system (mid-bass). However, this aspect should’t be an issue for subwoofers, since they play only the low octaves anyway.
Common folded horn subwoofer designs
The folded horn speaker design has an endless amount of possible internal layouts. The main focus is to increase the area of the flare at an exponential rate. How you fold the horn is up to your imagination. However, the folded horn speaker design is not something new. There are a few types which are quite popular :
- The W-Bins – This type of folded horn has a few variations of it own. Like any other low frequency folded horn, it has a limited frequency range and a degraded smoothness of frequency response (published specs usually smooth out the ripples in the curves). Nevertheless, the “compact” size of the W configuration is worth this drawback.
- The Scoop – this type of folded horn is similar to a transmission line. The front waves are direct radiating and the back waves are coupled to fairly long folded horn. The mouth of the horn is firing in the same direction as the front waves. This has a very good low frequency response, because of the long horn, and an extended response few octaves above, because of the direct radiating front waves.
- Bent horn – this is another typical style horn but with a shorter length.
The folded horn speaker design is a popular choice for outdoors or for very large rooms. The main reason is because they have very high efficiency and the designer can control the directivity of the sound. The size of the enclosure is not much of a problem, since they are for outside use. However, home audio is no stranger to folded horn speaker design. A rear loaded design, with a folded passage of increasing area formed behind the driver. Construct the passage using wooden panels in various configurations, to make the area exponentially larger.
Place the enclosure in a corner, and the room walls and floor serve as the final part of the flare, thus eliminating the need of making the box huge. The enclosure is not perfect, as the progression is roughly exponential and the length is short, so internal reflections can occur. Even so, efficiency of 40% is not unlikely with a folded horn speaker design. This is much more, compared to typical infinite baffle enclosure, which has around 0.5% efficiency.
Using a horn as coupler to a speaker, will bring several advantages, like : allowing good control of wavefront properties, easy to manipulate the direction of sound, and high acoustic power over a wide frequency range. On the bad side of things, horns will present a resonant, dispersive, and nonlinear wave propagation. Because of these negative points, horns aren’t very popular in the present day. Their high efficiency is not so attractive either, since amplifier power is easy to come by these day (cheap watts). However, they are still popular on outdoor audio systems, where efficiency and directivity are important factors.
- Newnes Audio and Hi-Fi Engineer’s Pocket Book by Vivian Capelm (Elsevier, 2016).
- Electroacoustic Devices: Microphones and Loudspeakers 1st Edition by Glen Ballou (Focal Press, 2009).
- The Sound Reinforcement Handbook 2nd Edition by Gary Davis and Ralph Jones (Yamaha, 1988).
- Image source : link.