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arrays

basics

advantages

drawbacks

lobing

measurings

One way to make high sensitivity loudspeaker system is to employ driver with very strong magnet and attach it into horn enclosure. Another, usually cheaper and easier to build is any combination of multiple drivers. This design can work in conventional enclosures (sealed, bass reflex,..) or can take advantage of acoustic transformers.

advantages

  Increase of sensitivity due to lower resistance

Each time the resistivity halves (i.e. goes from 8 ohm to 4 ohm, etc.), the sensitivity doubles, and quite vice versa. So, when connecting two 8-ohm speakers in parallel, the impedance drops to 4 ohm and the sensitivity increases 3dB because the amplifier develops more power into the lower impedance. If you would connect the two drivers in series, the impedance increases to 16 ohm. Ignoring for a moment the cone-area increase's effect, the sensitivity will drop 3dB because the amplifier produces less power into the higher impedance.
This is based on the following principle: when the impedance halves, the amplifier doubles it's output power, and hence the 3dB rise in output level. In a solid-state amp this works, but what about the valve amp. Their spec.sheet usually indicates the same power into 4, 8 or 16 ohms. So they do not add the 3dB increase.

Increase of sensitivity due to enlarged cone area

For each doubling of the cone area, the sensitivity rises 3dB, i.e. if you have one cone, adding a second one will add 3dB to the sensitivity (ignoring for the moment changes of impedance). Now with two cones, Sd must be doubled (total four cones) to add another 3dB to the sensitivity. To increase the sensitivity another 3dB, you need to add four cones, etc. ad infinitum.

Interaction between units

The advantage of using multiple drivers is that an increase of efficiency is achieved. The disadvantage is that the sound is coming from multiple points.

An array will have a gain increase due to the directivity of the whole speaker that increases. The advantage of an array is that total power is reproduced by more speakers = less distortion at higher listening volumes.

behavour of linear array compared to single point source

The sound pressure level from an ideal point source radiator (full space radiation) falls by 6 dB per doubling of distance. The intensity of sound from the point source falls off as the inverse square of the distance. This is known as the inverse square law. The energy radiated from the point source is evenly distributed over the surface of an expanding sphere. The surface area of the sphere is inversely proportional to the distance (radius of the sphere) squared.

The SPL from an infinitely long line source falls in more moderate fashion; with a rate of 3 dB per doubling of distance. The energy distribution is now over the surface of a cylinder, rather than a sphere as in the case of the point source. Because the surface area of the expanding cylinder is inversely proportional to distance, not distance squared, it follows that the energy density falls simply with distance from the source, rather than distance squared.

A finite line source will behave more as an infinite line when the observation point is very close to the line compared to its length. At greater distances the source looks more like a point radiator and the SPL will fall at 6 dB per doubling of distance.

As an empirical example consider the observed behavior of the noise pollution from a highway. Folks living near highways are the unfortunate victims of the highway noise only falling at only 3dB per doubling of distance from the highway. That's because the highway noise source precisely fits the model of an infinite line source.

Basically, the vertical line of drivers creates a cylindrical wavefront as opposed to the spherical wavefront of ordinary speakers. The cylindrical wave propagation focuses the sound into a narrower beam vertically, while maintaining a wide dispersion horizontally. This focusing of the sound allows it to reach the listener without reflecting around the room. In addition to the line array concept focusing the lower octaves, two other features serve to focus the upper octaves. First, the 1.4" cone diameter focuses the treble into a norrower beam than is common.

Since this is not a true linesource, but rather an array of discrete elements, the necessary distance between the drivers would cause phase problems with a flat baffle. Vertical listening area has been sacrificed for treble coherence by curving the front baffle with a 10 foot radius. This focuses all the treble inward, and is probably the feature which makes these speakers sound so nice. The sonic presentation of these speakers is quite "forward", like horns, but without the horn coloration.

disadvantages

  Any single loudspeaker may measure to have exceptional response, and the sound quality of a single loudspeaker may be nothing short of hi-fidelity, but that will not be the case once arrayed. With these direct-radiator packaged speaker systems grouped in a cluster, the individual drivers can not be positioned to minimize time delays between devices and the resulting destructive interference, cancellation and response variations. These variations are important because the coverage uniformity in the 1,000Hz to 4,000Hz range is critical for good intelligibility and uniform frequency response from 250Hz to 1,000Hz is important for natural sounding speech.

The problem is related to the physical distance between individual loudspeaker components. The special signal processor/crossover that comes with the loudspeaker can only correct for time offset of the signal between the low and high frequency drivers along a single speaker system axis. The signal delay in the processor cannot adjust for every possible off-axis listening angle, especially in the vertical plane, where the physical offset between high and low frequency devices changes the signal delay for various listening positions by fractions of a millisecond. The processor certainly can't fix the additional multiple signal delay variables thrown in by having additional boxes added to the mix.

In the four box cluster we will show here, there was approximately 30" between the box centres, both horizontally and vertically, and this was the manufacturer's minimum interference configuration (That's a half wavelength at 225Hz, one wavelength at 450Hz, two wavelengths at 900Hz). At the crossover point, where the horn and the 12" bass speaker in each box are operating at equal levels, there are a total of eight devices operating at the same level with multiple wavelength spacing between all eight sound sources. This is the offset distance vertically, horizontally and diagonally between all devices. Where the coverage of the boxes overlap, there will be significant lobing of the coverage and comb filtering caused by these physical-offset-induced signal delays.

Below the crossover point, the 12" bass drivers gradually broaden their coverage angle until the boxes each become omnidirectional. In the frequency range between 250Hz and 1000Hz, very large variations in level will be found, with the highest level exactly on the centre axis of the cluster, and spurious lobes all around that centre hot spot. This produces plainly audible sound quality variations with seating position, and may produce feedback prone positions under the cluster.

Second one is related and that is uneven spl/power. Lines (even those made of single long elements) exhibit a much different "acoustical density" over distance, essentially falling off at half the rate of attenuation of a point source. (And the line itself becomes a point source at a frequency far above your subwoofer when you build a short line.) This means that your placement is going to be iffy in your room, and the mesh between driver(s) and driver banks will need a great deal of adjustment. The theory is understood but the setup still requires trial and error when you try to integrate lines and points.

Lastly, a little known phenomenon of lines is their corruption of transient information. Lines are 2-dimensional radiators (having no vertial dispersion when they are used standing upright) and thus cannot disperse sound in all directions like points. The transients are produced with artifacts, or "wakes". Kinergetics published a white paper some years ago detailing this if you can find it. In fact, I think it was Venderkoy who also published a paper discounting lines entirely for this and other reasons. Somebody please correct me if I misremember...

Having said all this, obviously, some lines are very entertaining and make big waves in some audiophile circles. While the jury may be out as to the absolute "accuracy" of these devices, listeners report an enormous image and big rock and roll factor.

It is also important to understand the effects of physically mis-aligned loudspeakers, and to be able to measure and adjust the time-offset of devices. The small packaged boxes described above may relieve the buyer of the need to think about the selection of devices, but that doesn't alter the final results as we've shown here. Cluster design can't be left to a manufacturer's marketing department!

What follows is a brief review of the behaviors of point, line, and plane sound sources.

jlm

There are a few notes here. The classic Series/Paralell connections will result in the Back EMF of the various drivers interfering to some degree with each other, it's unavoidable.

The other issue is the "Bessel" Effect which creates a comb-filter effect with multiple Driver arrays. A 1 X 2 or 2 X 2 Array is (IMHO) the largest that could be used succesfully without actually angling in the Drivers and applying other "extreme" measures.

If you want to play with larger groups, there are two options. Philips have a Patent for multiple driver Linesources that are on a flat Baffle, but use specific gain and phase coeficcients for each driver, combating the combfilter effect. It does require a lot of slip stick (or PC) work though.

The other option is mechanical and works (at least in practice) very well. As long as all drivers are placed on a baffle that offers a close approximation of a section of a sphere, having the same radius as the listening Distance.

This quite succesfully eliminates the problems with the "Bessel" Effect and presents a very coherent sound for vertical array without messing with overly complex crossover.

Measurements should prove much smoother responce from curved baffle linesource.

The more serious problem is with the frequency characteristics of multiple dirivers: as the frequency increases the wavelength decreases and when you get to the point where the wavelength is 1/2 the distance between driver centers you will get wave destructive interferance causing deep nulls in the response. Especially the off-axis response will suffer from this earlier than the on axis but generaly what you will get is a very sharp narrowing of the on axis response, i.e lobbing. Thus a wide frequency reproduction and even off-axis response from multiple drivers is not possible.

With an extended-range driver used in a line array, there is a significant chance that the beaming problem is really lobing - that is, multiple lobes at different angles, but of nearly equal loudness. For instance, a large array of sources spaced uniformly 6.75" apart (close to the str8-8 spacing) at 4kHz will have far-field peaks at 0 (on-axis), 30 degrees, and 90 degrees. There will be nulls between, at 14 degrees and 49 degrees. At higher frequencies, there will be even more beams, more closely spaced.

The best way around this is to move the drivers more closely together. Tweeters spaced 3,5 cm apart will work up to 20kHz, or approximately 7 cm apart will work to 10kHz, before becoming excessively lobed.

If multiple woofers and a single tweeter is used, than there is a problem with different pressure decays, woofers act like infinite line source, tweeter acts like a point source. With this kind of behaveur tweeter must be padded more when listening closer to the speakers, and less when listening far away. It's an interesting effect to walk up very close to the speaker. The highs get louder and louder, much more quickly than the mids.