Thoughts and Ideas behind the design of Line arrays.

 

This article was written in about 2005. It was to provide additional information to an ongoing discussion on the Harmony Central web forum, taking place at the time, concerning the feasibility of a DIY line array. It generated more enquiries than all the other articles combined and was also the most linked to article.

It has since been copied and appeared on a few commercial websites presented as their own technical white papers. This is the original source.

 

Since setting up this web site I've had requests for information about designing line array loudspeakers. This page is to explain some of my thoughts on the topic. If you still have any questions or want to discus further thoughts and issues feel free to contact me. The idea of this page is to give some of my thoughts on what I have been asked. If you don't agree that is fine by me. Please remember that this is not a theoretical text and that I've tried to keep the maths to a minimum. The concepts are more rule of thumb than accurate formula.

Before starting please be aware that any images, diagrams and quotations taken from manufacturer's web sites belong to the respective companies and I have used them purely for educational (I hope), instructional and illustration only. For the sake of ease of layout I'll credit the guilty parties at the end. Please don't take any of my comments about any of the commercial designs mentioned here to mean that they are no good. The main aim of this article is to show that most of the designs out there are not perfect but still work well despite that, and that it is possible for individuals to construct a system of their own.

So to answer the basic question of whether it is possible to build a line array; in general terms, yes, assuming that you have sufficient knowledge and ability plus the willingness to put in some time, effort and money, building a line array is a distinct possibility. Whether any particular individual who emails me is capable of building a line array I simply don't know. Don't ask me questions about rigging or suspending loudspeakers. Whilst I don't think that it is something no-one should attempt, as a safety point if you need to ask then you don't fully understand the issues involved and are best sticking to floor stacked speakers.

A lot of hype surrounding commercially produced line arrays is simply that. The number one priority for the manufactures is to make money. To this end they use a lot of smoke and mirrors in the form of marketing and pseudo- science to try and convince us that their product as the edge.

Most of the science seems to be directed at coupling the high frequency horns to produce "virtual line sources" or "isophasic wave fronts". This is usually accomplished by some patented, proprietary device. One reason for this maybe because if the low frequency section comprises of a bunch of 8", 10" .. 15" drive units stacked vertically it is difficult to claim any originality or advantage over the next person's line array with similar drive units stacked exactly the same way. Hidden behind the horns and slots it is easy to claim all manner of great attributes for you device.

Whilst some manufactures claim to use revolutionary new technology others just use more conventional horn designs stacked up one above the other. That all these systems work as line arrays and all have fans who prefer each system above another suggests that producing some new patented high frequency waveguide is not an absolute prerequisite of building a line array.

If you look at line arrays they are almost universally hung vertically. They would work in exactly the same manner if orientated horizontally or any angle between. Rivers and the ocean shore are examples of natural line arrays in a horizontal format. The reason that line arrays are hung vertically is that we live in a horizontal world with ears on the sides of our head. This makes us more sensitive to variations in sound, such as lobing caused by interference between drive units, in the horizontal plain. By configuring a loudspeaker stack vertically the lobing is less noticeable than using conventional horizontal arrays.

Given the above I think that the best way to design a line array is to forget the line and concentrate on the horizontal directivity of each individual cabinet. Using better quality components will obviously help, but using a design that maintains an even and smooth (if not constant) directivity is the key to a good design.

The previous page, where I outlined my design, explains how I went about trying to achieve this. If you look at some of the commercial designs you will see a similar goals. The original modern line array the Vdosc uses two 15" drive units in a cabinet 1.3m wide. If the distance between acoustic centres is taken to be 0.75m and the half wavelength rule is applied, the cross over frequency should be 226Hz. The actual cross over frequency is 200Hz. Similarly the crossover frequency between the mid and high frequency sections occurs where the half wavelength is similar to the dimension of the mid range drive units. With the smaller two way cabinets some compromise has to be reached and the Nexo geo, which uses an 8" bass driver crosses over at 1.8KHz a frequency whose wavelength corresponds approximately with the diameter of the bass drive unit. I suspect that 1.8KHZ was the lowest frequency the manufacturers felt was safe to ensure reliability. Interestingly the smaller dV-DOSc loudspeaker uses a lower cross over frequency (800Hz) than its bigger brother possibly because it uses a slightly larger cones for the bass/mid. It does illustrate well the need to pay attention to cross over frequencies and horizontal dispersion.

 

 

The diagram shows a stack of V DOSc cabinets.
The small (relative to wavelength) radiating area of each frequency band can clearly be seen.

Given that an array consists of multiple elements it is worth looking at how multiple sources form a wave front. The following gif gives the general idea.

The following diagrams show calculated interference patterns from various sources. You can either consider the sound sources as arrayed vertically so that you are looking from the side, or horizontally so that you are looking from above.

If you want to mess with interference patterns click on the link, but I'd finish reading this first and I'll remind you later (temporarily unavailable)

What the above diagrams show is that it is important to pay attention to the layout, coupling and interaction between drive units. It also shows that even an ideal line array is not perfect One way of reducing the side lobes of a line array is to use a tapered array. This is where the power to each element of the array is tapered off as you move out from the centre. The more modern name for this is shading. Intensity shading is similar to the principle mentioned above where the intensity or power to individual elements is varied. Frequency shading is the same thing only it is frequency dependent and effectively varies the length of the line according to frequency. Angular or divergent shading means pointing more or less elements at a certain point by either tightly packing the cabinets or angling them further apart to vary the relative intensity. This last technique is employed in the classic J shaped arrays.

Tapering or shading is nothing new and was described back in the 1950s the image below shows how a line-source was effectively made shorter at high frequencies by using wedges of fibreglass in front of the drive units.

The term isophasic comes up quite often with descriptions of line arrays the following diagram is taken from Acoustical engineering. Back in the 1950s the aim seems to be that of increasing the curvature of the isophase or phase contour rather than making it flat. What it illustrates is that all loudspeaker drive units produce isophases.

Another acoustic device that has been rediscovered is the lens. The small image is .... well I'll let the manufacturer describe it.

The SERPIS is a D.A.S. designed plane-wave adaptor which provides accurate high frequency summing and the generation of a flat, isophasic wave front. The complex design of the SERPIS adaptor eliminates the destructive interference associated with the high frequency sections of traditional multi-box "clusters". The result is improved over all sonic quality while maximizing the use of input power.

 

Sound waves on the scale of loudspeaker cabinets don't behave like the rays drawn on the diagram, but ray tracing can be useful to illustrate a point. Lenses do work and used to be a common site on PAs of old. Hopefully the similarity between the plane-wave adaptor and the lens can be seen. The large lenses on the old PA systems were supposed to have major sonic problems and inferior to the constant directivity horns that replaced them. No doubt the original short comings have been overcome.

If all the principles behind modern line arrays appear to originate from the 1950s then the following should dispel that notion. It is a quote from "Text Book on Sound" first published in 1908 and written by Baron Rayleigh

Definition
	The locus of all points just reached by a wave disturbance at any instant is called the wave front at the instant in question
Huyghens' Principle
	The wave front at any instant may be derived as the envelope of wavelets whose origins are all the points constituting the wave front which existed t seconds previously. In an isotropic medium at rest these wavelets are spherical and of radius vt, where v is the velocity of propagation of the waves in all directions in the given medium.

The above is better explained by a diagram.

Using his principle Huyghens (sometimes Huygens) was able to explain both reflection and refraction. The main deficit of the principle is that it fails to explain the directionality of the wave. If the wavelets expand in all directions the wave should also converge back to the origin. Subsequently, Augustin Fresnel (1788-1827) elaborated on Huyghens' Principle by stating that the amplitude of the wave at any given point equals the superposition of the amplitudes of all the secondary wavelets at that point (assuming that the wavelets have the same frequency as the original wave). Fresnel didn't actually resolve the question about "backward" propagation of waves, but was able to account for diffraction. Fresnel and diffraction are prominent in the work done by Heil on the V-DOSc. The diagram below hopefully demonstrates diffraction and why slot apertures feature in line arrays.

	A small opening or narrow slot acts like a point source in the dimension that is small compared to the wavelength.
	When the opening is approximately the same as 1 wavelength the sound propagates mainly in a forward direction
	Where the opening becomes large compared to 1 wavelength the sound diffracts around the edge of the slot.

If we now look at the polar plots for a couple of radial horns, we can see how the above comes into play. The diagrams are taken from Olson's Acoustical Engineering, and the first shows a 60 degree horn. This was chosen because the polar plots are given in relation to the radius and with a 60 degree horn the width of the mouth is equal to the radius.

Where the radius and hence mouth dimension is small relative to the wavelength there is no directional control. As the wavelength becomes comparable with the mouth width the dispersion pattern narrows. With an increasing frequency and shortening wavelength the radiation pattern approximates that of the horn walls.

With a 120 degree horn the width of the mouth is approximately double and the narrowing of dispersion pattern starts at the half wavelength point.

The graphs are for a curved mouth radial horn, but it does show the effect that the flare angle and mouth size has on the radiation pattern. Also interesting to note is that even with a single horn and drive unit, interference patterns show up on the diagrams. Keele found that this lobing or fingering, which was also present in constant directivity horns could be reduced by doubling the flare angle over the last 1/3 of the length of the horn.

It is now worth looking at a few more methods deployed by some of the manufacturers in their line arrays.

First of all there is the waveguide used in the grandfather of the modern line arrays. The following diagram shows the use of a sliced cone to produce a constant path length from the drive unit to the slot. The diagram underneath, criteria No 1 basically states that if you have a load of slot (similar to the bottom drawing in the diagram above where d>λ) sound sources, they behave as a continuous source as long as the gaps in between the slots is less than 20% of the total area.

Within the physical constraints of their size and operating parameters it would be interesting to compare one of the DOSC waveguide elements with the more traditional slot tweeters two of which are shown below.

 

Instead of using obstacles to force the sound waves round, some manufacturers use the principle of reflection; most notably Nexo. The diagram below is taken from their web site.

Despite its small size, an array of Geo S830s can produce a remarkable punch. Whether the parabolic reflector works as described, the cabinet has a good reputation.

Outline use a similar technique with their butterfly array.

The pictures look great and the concept seems like a neat idea except that as I mentioned before sound doesn't work like light in the scales that we are dealing with. Ray tracing is useful to give a general outline but it is worth remembering that the wavelength of visible light ranges from 400 to 700 nanometres. At the longest wavelength that is 0.0007mm. If you consider the diameter of a small torch, say 12mm across -that is 17,142 wavelengths (hope I've got all my decimal places correct). To give a similar ratio for a 2KHz audio wave whose wavelength is 0.172m, the reflector would need to be 2948 m in diameter; nearly 3 kilometres! To find out how light behaves with openings and obstructions that are comparable with the wavelength of light do a Google search for Young's slits or Newton's rings. If you do search, you will find that light can suffer from interference patterns similar to the comb filtering we get when arraying loudspeakers. Ray tracing, as shown in the diagrams above also predicts that the sound level outside the beam is zero, something that doesn't happen in real life. If this reflector technique works so well, why has no one mentioned it in relation to folded, or W, horns?

The JBL Vertec looks suspiciously like the V-DOSc.

The high frequency horn is more conventional but fits three drive units in one cabinet keeping the inter driver spacing to a minimum.

While most of the other manufacturers go to great lengths to explain how the wave front that their device produces is perfectly flat, JBL have acknowledged that in some instances a curved wave front produces better results and have included spacers between the drive unit and horn to achieve this.

The Apogee cabinet shown below doesn't appear to use any special lens, reflector or other wave sculpting device in its line array loudspeaker.

Martin produce one of the only horn loaded line arrays. As well as being horn loaded it uses an asymmetrical layout.

Unfortunately the plots are taken at octave intervals and the cross over frequencies fall in between those shown. Another way to smooth the results (I'm not suggesting that Martin may have done this) is to measure each pass band separately so that there is no interaction between each section. More importantly for those wanting to build their own line array is that from the photographs and drawings the horns appear to be the normal constant directivity type. The main problem with using the horn based approach is that even with a minimum stack of four cabinets, each cabinet needs to be large to give an effective mouth size at the lower frequencies.

I mentioned the Nexo Geo wavesource above. The Geo-T despite its unusual look is basically the same layout as the dV DOSc, with the high frequency section between two 8" bass units.

The biggest difference is not the shape, but that it uses an additional two rear facing drive units to control the directivity. The principle behind this technique is quite simple. The drive units are placed one quarter of a wavelength apart. The front drive unit is then delayed to effectively re align the drive units so that the sound adds together in phase. For a sound wave radiating backwards the effective separation is the quarter wavelength physical separation plus an additional quarter wavelength delay. The result is a sound source 1/2 wavelength or 180 degrees out of phase from that of the rear drive unit and when combined they cancel out. The effect is usable over a range of one octave centred on the frequency chosen.

 

Another design that uses additional drive units to modify the directivity is the Meyer

Using four 15" drive units with a large gap between the forward facing ones to accommodate the horn this loudspeaker appears to defy all the principles that go to make a good line array. Closer inspection reveals that all four 15" drive units only operate up to 140Hz. The half wavelength for this frequency is 1.2m which is about the width of the cabinet. Above 140Hz just one 15" drive unit radiates up to 500Hz where the horn takes over. The distance between the centre line of the horn and centre of the 15" drive unit is again about the same as one half wavelength at the crossover point. Based on the principle mentioned above and the bass/mid cross over frequency of 140 Hz, the directivity control provided by the rear facing speakers will be effective from 70Hz to 140Hz (the octave below the cross over frequency. Taking the a halfway point of about 105 Hz the quarter wavelength is about 80cm. This should set the front to back distance of the cabinet. The actual measurement is 77cm.

The pictures above show the Renkus Heinz line array cabinet. The slot, or Isophasic Plane Wave Generator exits straight on to the front baffle without the additional flare used by other manufacturers. This should give a very wide dispersion pattern and allows the 10" drive units to be placed closer together. Even with the close spacing baffles are used to improve dispersion. To quote the literature

The PN102/LA and PNX1102LA's unique diffractor baffle provides mid range diffraction loading . It eliminates mid range narrowing of the horizontal dispersion to provide consistent wide angle coverage across the entire frequency range.

The down side to using the slot to produce wide dispersion angles is that the abrupt change in cross sectional area at the mouth is accompanied by an abrupt change in acoustic impedance. This results in some of the sound being reflected back down the wave guide towards the drive unit. These reflections cause a frequency dependent change in the acoustic load on the diaphragm which results in a frequency amplitude response than is less smooth than with a gradually flaring horn. This applies to any design, including most constant directivity horns that use abrupt changes in flare angle to control dispersion. The above Renkus Heinz horn is about as extreme as you can get.

I think that about covers everything that I have been asked. Hopefully it will be of some use. Finally don't forget to experiment with the interference patterns.

Diagrams are from
Acoustical Engineering	Harry Olson
L'Acoustics
DAS
JBL
Outline
Martin Audio
Nexo
Renkus Heinz
Meyer

 

Update

This article has proved to be extremely popular, so much so that a couple of businesses have been presenting it on their own websites as a technical paper. There still seems to be, however, a lot of controversy as to whether individuals have the ability to construct waveguides that will work as effective line arrays at high frequencies. I thought that it might be interesting to add some illustrations showing how manufacturers deal with the problem. The drawings are taken from patents and are thus freely available online if you wish to investigate further.

This diagram is from a patent put forward by Harman. It is basically a converging lens fitted inside the horn rather than being attached to the front of it. It works exactly like the lenses mentioned above. I tried a similar thing in some midrange horns but using a diverging lens. The series of horns I was using all used a curved front and were 1m wide. This resulted in a narrowing of the dispersion at about 350Hz. The lens was to try and prevent the narrowing of the dispersion. Every design that uses multiple channels to equalise the path length to the mouth of the horn is basically the same.

 

This design is by Meyer. If it works, it is good news for home constructors. It uses grating lobe mitigation fins in the flared section of the horn which are substantially parallel to the propagation axis of the horn (Meyer's description), the length of the grating lobe mitigation fins being selected to achieve a desired level of suppression of the grating lobes produced by said aligned array of acoustic power sources. The acoustic  centres of the drive units look close together anyway, but if the "fins" work a column of stacked horns should work better than expected.

 

Meyer again. This time the path from the compression driver throat exit is split into four pipes of equal length and have their exits aligned in a line.. I tried a system using equal length hose pipes. The principle was the same but it was more similar to the following design.

 

The sound passes through the holes and along curved passages. This is an Adamson patent.

 

Another patent from Adamson. This uses a coaxial design for the mid and high frequencies.  What is not clear from the above diagram is that the high frequency wave guide uses a plug similar to that used in the Vdosc.

 

The canny folk at Bose give nothing away, but I suspect it is simply a column of small cones.

 

Move along folks there's not much new to see here in this Clair patent. It is just a variation on the JBL design. The potential output from the cabinet becomes clearer in the next diagram. Definitely a candidate for most drive units in a cabinet.

 

 

This next diagram has got me puzzled.

This is from a patent by Guido Noselli, Stefano Noselli and Michele Noselli. The problem is, if the waveguide in diagram A is large enough to provide dispersion control as shown, then the addition of the extension waveguide wall in diagram c won't make any difference. in the diagrams with the additional cone drive units the sound waves are not shown to be eminating from the cones. The following altered diagram should show what I mean.

 

This next diagram is from a patent by Anthony Andrews. The diagram is described as a front view of the system constituting an embodiment of the invention. The unusual thing about this design is that it places the high frequency section outside the midrange section.