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Birth of the Array Part 8: The French Connection (Correction)

So what for the next 20 years? You could be excused for thinking that the preceding BOTA chapters have been leading inexorably to a big punch line, like a laborious joke or a daytime soapie where the suspect-looking, nonconformist weirdo, dramatically unmasks the villain who previously appeared to be a paragon of virtue. There's no villain here but there is a nonconformist, and also a happy ending. Get comfy, because it's a big read.

The crystal ball and the spherical wave

Until such time as somebody invents a single full-range transducer that can be assembled to any size and have a capacity for programmable cardioid dispersion, we will be stuck with cardboard cone/metal/polymer diaphragm driven multi way speaker systems.

There have been a few attempts at “the big panel” transducers but none of them have had enough going for them to take over from the good old cardboard piston bolted on to an acoustic transformer (horn) designed early last century. Just as car motors are super high-tech now, the same story applies to the old Benz design petrol 4 stroke of the late 1800's.

As far as cardboard cone technology and acoustic loading goes, it's pretty clear that the present market leader is the Nexo Geo, when applied to arrayed speaker systems. There are a couple of pretty clever competitors to the Nexo, who will have something to say about that sweeping statement but on balance, the Geo has more science and genuine patents per roadie mile than any other existing system.

Let's look back at some history for a moment.

So we see the problem for all live sound engineers… Projection of a sound source, across an expanse of space, to be received as duplication by an individual or assembled multitude. The key word here is duplication. When information is missing, musician instinctively heads for the volume control while a sound guy heads for the EQ. Neither will put the information there.

So if the Geo claims to “put all the information there”, is this really science or spiel? To quote another manufacturers line is it, “Better sound through research” or “better sound through marketing?”

Well rather than try to explain it without duplication, here is an edited (and adulterated) white paper from the Nexo web site. The whole work is very interesting and contains some useful information that can even assist with getting optimum results from a conventional array as well… First, a preamble.

Many of the world's great discoveries are related to the geometric study of cone related maths.

Not only for Nerds! Before we start the précis version of the Nexo Geo paper, remember the first couple of chapters of BOTA where we started with the Greek Mathematicians, the Greek amphitheatre and the early horns of Gaspaire P Schotton? Well let's revise some stuff that started in 11 Maths and ended with a Masters Degree.

Conic sections
Conic sections

Conic sections (see above) are among the oldest mathematically defined curves, and have been studied systematically and thoroughly since the time of Alexander the Great, whose Greek tutor Menaechmus (c.375-325 BC) seems to have discovered them. (His brother Eratosthenes , devised a method to create a square equal in area to a given circle using the quadratrix . quadratrix (from the Latin word quadrator, squarer). So it was in the family.

Menaechmus was “the man” when it came to resolve complex geometric problems studying conic sections. In the classic Greek world, mathematicians were more appreciated than they are today. No party was complete without one.
Menaechmus was “the man” when it came to resolve complex geometric problems studying conic sections. In the classic Greek world, mathematicians were more appreciated than they are today. No party was complete without one.

Conic sections were conceived in an attempt to solve the three famous problems of trisecting the angle, duplicating the cube, and squaring the circle. The conics were first defined as the intersection of: a right circular cone of varying vertex angle with a plane perpendicular to an element of the cone (an element of a cone is any line that makes up the cone).

Depending on whether the angle of intersection is less than, equal to, or greater than 90°, the curve generated by the intersection of plane cone is an ellipse, parabola, or hyperbola respectively. (See examples of conic sections above).

Apollonius the great Geometer; he was popular too. Popular enough for his picture to last over 2,000 years
Apollonius the great Geometer; he was popular too. Popular enough for his picture to last over 2,000 years.

Apollonius (c. 262-190 BC, known as The Great Geometer) consolidated and extended previous results of conics into a monograph of eight books with 487 propositions, entitled Conic Sections (Book VIII has been lost). Apollonius was the first to base the theory of all three conics on sections of one circular right or oblique cone. He was also the first to name the ellipse, parabola, and hyperbola.

  Morris made math “real” to thousands of engineering students.
Morris made math “real” to thousands of engineering students.

Professor Morris Kline (1908 – 1992) has stated "As an achievement [Apollonius' Conic Sections] is so monumental that it practically closed the subject to later thinkers, at least from the purely geometrical standpoint." Apollonius' Conic Sections and Euclid 's Elements together represent the quintessence of Greek mathematics. No, we're not going to visit Euclid today.

Conic sections is a topic that has spurred many developments in mathematics. During the Renaissance, (c. 1,400 –1,650?) mathematicians pushed conics to a high level. Kepler's law of planetary motion, Descartes and Fermat's coordinate geometry, and the beginnings of projective geometry in the work of Pascal and others are all based in the study of conics. Many later mathematicians including Isaac Newton have also contributed through the study of conics, especially in the development of projective geometry where conics are fundamental objects as circles are in Greek geometry.

GEO reflective wave sources are:

1. Very accurate capable of perfect array coupling

2. Very compact extremely versatile

This excerpt from the original white paper will discuss the GEO design process and some of the first results to come out of it. First, however, we want to put the GEO project in the context of professional sound reinforcement.

This is Big… Really big. Remember the horn?

Traditional coercive waveguides attempt to force the more or less spherically expanding acoustic pressure wave into a conical section of the sphere. They do this by putting boundaries around the airspace. Their “impedance matching” function is accomplished by the horn acting as a resonant chamber: the listening area is excited by the horn's mouth instead of the driver's exit tube.

If sound pressure is equal across the horn's mouth, the wave will develop in that shape after exiting the horn. Small pressure differentials at the horn's mouth are magnified as the pressure wave expands to fill the listening area. Unfortunately, sound doesn't behave like toothpaste: it's not easy to constrain it using a container. The horn walls reflect and sometimes diffract the wavefront as well as coercing it towards the desired pattern. In the throat, pressure asymmetries can cause distortion*.

Boundaries such as the horn mouth, or the transition between the narrow throat section and the horn flare, cause diffraction: the sound bends around the edge instead of following the direction of the boundary.

* Air pressure in an unbounded container (such as a waveguide) can range from 0 to 2 atmospheres. Because of the asymmetry in its behavior as a medium, air always distorts the waveform at extremely high pressure levels, such as often occur in the throat of a horn or near the surface of a phase plug. NEXO has an international patent on signal processing algorithms that correct this.

Birth of the Array Part 8: The French Connection (Correction)

We've all seen this before. It's the good old constrictive horn. It amplifies (transforms) and directs acoustical energy but by the nature of the way it works, it is not even transformation across all wavelengths. An alternative way to couple the driver to the air is… Reflective wavesource technology using geometrical transformation of conicoids. That's maths speak for bouncing and shaping waves off conic sections.

The ideal objective of the line array is to generate a uniform cylindrical wavefront, which will travel further before loosing energy than the classic spherical wave, generated by a conventional system (Remember the early Birth of the Array chapters)? For a conventional system, the trouble starts before the mouth of the horn.

What we want is a uniform phase “ribbon” at the mouth of the horn that stays coherent as it moves through the air as pictured. Theoretical ideal "isophase ribbon" Equal sound pressure across the mouth of the horn = idealized polar pattern of defined horizontal angle.

Birth of the Array Part 8: The French Connection (Correction)

In practice, coercive horns distort the acoustical waveform in the process of shaping it. Internal reflections, diffraction effects and pressure asymmetries produce variations across the horn mouth, and in the coverage pattern.

1/3 octave smoothed polar plots of a contemporary “constant directivity” horn using boundary walls to control dispersion.

The result, when translated into familiar polar plots, looks something like this: Shown above are 1/3 octave smoothed polar plots of a contemporary “constant directivity” horn using boundary walls to control dispersion. The –6 dB points that define “directivity” are reasonably consistent across the measured frequency range of almost four octaves. However, at each measured frequency the overall shape of the dispersion is quite different from those on either side (or above and below in the frequency domain).

Also note that the total power radiated into the listening area through this device does not change smoothly: for instance, dispersion is narrower at 8 kHz than at either 6.3 kHz or 10 kHz. These anomalies are indications of the difficulties encountered when “squeezing a spherical acoustic pressure wave through a rectangular funnel.” The result, when translated into familiar polar plots, looks something like this:

1/3 octave smoothed polar plots of a contemporary “constant directivity” horn using boundary walls to control dispersion.

Shown above are 1/3 octave smoothed polar plots of a contemporary “constant directivity” horn using boundary walls to control dispersion. The –6 dB points that define “directivity” are reasonably consistent across the measured frequency range of almost four octaves. However, at each measured frequency the overall shape of the dispersion is quite different from those on either side (or above and below in the frequency domain). Also note that the total power radiated into the listening area through this device does not change smoothly: for instance, dispersion is narrower at 8 kHz than at either 6.3 kHz or 10 kHz.

These anomalies are indications of the difficulties encountered when “squeezing a spherical acoustic pressure wave through a rectangular funnel. It's also worth noting that horn design has remained an empirically based process. Good designers know roughly what to expect from their first attempts at a new horn, but few if any would commit to a production model without repeatedly measuring the results and trying out various modifications to the first set of flares.


Limits on constant directivity #1

It is impossible to control wavelengths larger than 4x the horn mouth's height (for vertical control) or width (for horizontal dispersion) at all, and control begins to diminish at 2x the mouth size. Horns thus have an inherently limited operating band with the lower limit at a relatively high frequency. No solution has ever been proposed for this problem, because it is a factor of the physical laws of acoustics.


Limits on constant directivity #2

As the wavelength becomes small relative to the horn's throat, the pressure wave “detaches from the horn walls” and the driver's diaphragm begins to operate as a piston, rather than as a point source. When the pressure wave is expanding more slowly than the coercive horn, there's nothing to coerce. The high frequencies turn into a narrow “beam.” The “constant directivity” horn employs a dual flare rate intended to broaden the high frequencies via diffraction around the transition from a narrow throat to the wider nominal flare.

Coercive horn problem #3: Separation of the acoustic centers

This did not become apparent until multiple horns began to be arrayed next to one another. Because horns and drivers are physical objects, they can't occupy the same point in space at the same time. As a result, multiple coercive horns cannot produce tangent wavefronts, and never be as coherent as a single source. To make matters worse, the dual flare rate of CD horns separates their acoustic centers even further. Using the “vertical side” of the horn as the horizontal side, which puts the acoustic centers back at the throat rather than at the transition from narrow to wide flare, minimizes, but does not eliminate, the distance between sources. Other unavoidable construction details such as the size of the horn and the cabinet walls move adjacent acoustic sources even further apart, eroding coherency necessitating overlap and interference between non-tangent wavefronts.

Limitations of multi horn arrays

We have flogged this point to death in earlier chapters of BOTA, but just in case you missed it, here it is again: Horns, drivers and enclosures occupy physical space, which creates a path length difference between adjacent speakers. Sounds originating at the same time thus arrive at different times.

Physically separate sources produce non-tangent (overlapping) wavefronts that interfere with each other even when the horns match the cabinet angles (not always the case, even for array-able loudspeaker models)

Physically separate sources produce non-tangent (overlapping) wavefronts that interfere with each other even when the horns match the cabinet angles (not always the case, even for array-able loudspeaker models)
Physically separate sources produce non-tangent (overlapping) wavefronts that interfere with each other even when the horns match the cabinet angles (not always the case, even for array-able loudspeaker models).

Conventional horn design and geometry limit array performance

And there is the problem for all speaker system designers. Put up more than one speaker box in an array and you have interference and degradation of performance. It naturally follows that, the goal of optimized horizontal arrays of conventional horns is to approximate a point source by making the wavefronts radiated by multiple sources as close to tangent* as possible. With coercive horns, the physical dimensions of the drivers and horns limit the extent to which this is possible.

While out of phase or phase shift radiation can be minimized and placed outside the listening area, it cannot be eliminated using the conventional horn design. This is true for both horizontal arrays and vertical line arrays. “True” line array speakers avoid this by using waveguides whose vertically flat wavefronts can be combined to form a continuous ribbon across all frequencies .

*Tangent: touching a curve or line at one point only and not intersecting

The patented GEO wavesource design process

GEO takes an entirely different approach to pattern control. By using an acoustically reflective surface rather than a rectangular funnel, GEO wavesources are able to create any kind of pattern and to locate the acoustic center outside the physical enclosure. As we will see, this has very important benefits in producing tangent wavefronts that maintain coherency with multiple acoustic sources.

So what's so different and revolutionary about the GEO tangential waveguide?

The parabolic reflector and a flat wave front, that's what.


In case you forgot the name Apollonius, we note a few points about the above diagram, which was probably drawn first by Alexander the Great's tutor Menaechmus c.350 BC. (Remember that amphitheatre?)

The parabola reflects rays in parallel when those rays diverge from a common source located at its focal point. All path lengths are equal, so a listener at point L would hear everything in phase. Although the basic mathematical construct is far from new, its application to the control of acoustic radiation is. If it were possible to build a vertical array of paraboloid reflectors, we would be able to create a true line source of any desired length by stacking or hanging multiple enclosures. Now I hear you say, “so what. I've seen sonic reflectors before”. Well this gets more complex in a minute.


Hyperbolic reflector: Convex wavefront

The hyperbola produces a divergent curved convex wavefront that is more like those produced by ordinary coercive horns. Where the parabola has only one focal point (in front of the reflector), the hyperbola has two foci*: a real one in front and a virtual one behind the reflective surface. Thus with an hyperboloid reflecting surface the acoustic center [S (Virtual) ] can be located outside of the enclosure even though the actual transducer [S (Real) ] is inside. With a coercive horn the acoustic center is always located somewhere inside the physical structure of the horn.

*Foci: Plural of focus. A fixed point used in determining a conic section. A parabola has one focus while an ellipse or a hyperbola has two foci).


Although it's of little practical interest, we include the ellipse here for theoretical completeness. The two foci of the ellipse are both in front of the reflecting surface: the diverging rays of the real source are reflected to produce a curved concave (convergent) waveform that reaches a point at the second focus of the ellipse.

So how do we get from a CD horn to this “laser like” acoustic device?

GEO wavesources are designed using patented principles. Although the underlying mathematics are simple, the practical design is quite complex. To maintain the desired degree of precision and control over the end result, we use CAD (computer aided design) software to design the molds that are used to produce GEO wavesources. What follows is a simplified description of the steps of the CAD process.

We start with the same goal as the coercive waveguide: radiating sound into a section of a sphere. The design places no constraints on the cross-section: it could be an oval, a bean shape, or anything at all. For illustrative purposes, we'll use the traditional curved ribbon, since it is a useful tool for distributing sound to selected areas of typical buildings (auditoriums, arenas, etc.).


Instead of attempting to “cut a piece out of the sphere” using horn walls, GEO design begins by locating S (Virtual) at the center of the sphere. Note that if the radius of the sphere is infinite the result will be a flat instead of a convex ribbon (a parabola instead of a hyperbola).

The shape of the ribbon and the size of the sphere define a beam

The shape of the ribbon and the size of the sphere define a beam that looks like the illustration above. The width and height of this beam define the horizontal and vertical angles of the coverage pattern.


Now we choose a location for the real acoustic source. It could be almost anywhere, but, as we'll see later on, we can achieve significant practical benefits by placing the real source somewhere near the mouth.

Next we create a conicoid by rotating a conic sectional curve (parabola, hyperbola or ellipse) around the axis S (R) – S (V) .


Rotating an ellipse around the axis between real and virtual sources would produce an ellipsoid acoustical mirror that would focus a concave wavefront on a point in front of the loudspeaker.


This cross section will intersect the beam from the virtual source to the desired radiating section of the sphere. For a convex conical wavefront, we rotate a hyperbola around the axis S (R) – S (V) to create a hyperboloid reflecting surface. To produce a flat wavefront we would rotate a parabola around the axis, creating a paraboloid. The shape of the acoustic reflector is defined by the intersection of the hyperboloid conic cross section, and the beam originating at S(V).


Now we have one half of the waveguide: the envelope joining the mirror (red) to the mouth (yellow).

 The other half of the waveguide is the envelope joining the mirror to S(R).
The other half of the waveguide is the envelope joining the mirror to S(R).

Finally, one small compromise is made in the design to accommodate the mechanics of acoustical transducers. The driver is a physical device, not a mathematical point, so it has dimension. We need a small adapter to convert the point at the end of the envelope from the mirror to S(R) into a roughly 1 inch throat that can be bolted to a compression driver. In contrast to coercive horn design, which is largely an empirical process, the GEO design is entirely calculated on the basis of rigorous geometric principles and transformations. From the front, the CAD-generated design looks like this:

GEO design is entirely calculated on the basis of rigorous geometric principles and transformations. From the front view of CAD-generated design looks like this

The acoustical mirror is now defined: it is the intersection of the coverage beam and the conicoid curve.


 Acoustical Mirror viewed from above
Acoustical Mirror viewed from above

Two views of the S805's GEO wavesource connected to a compression driver. This particular wavesource is designed to produce a 5° pattern in the coupling plane, with a variable-dispersion diffraction slot in the non-coupling plane. The whole package is very precise and sophisticated. You won't be knocking this up in your backyard on a Sunday Afternoon.

The wave emitted from this device is laser precise. A group of them can be aligned and stacked like “slabs of air”. The whole air mass behaves like it is being energized by a single sound source.

That's unheard of in the vertical plane. But how does it behave in the horizontal plane?

Front view showing part of the mirror and the diffraction slot exit. Removable flanges mean both symmetrical and asymmetrical patterns can be achieved.
Front view showing part of the mirror and the diffraction slot exit. Removable flanges mean both symmetrical and asymmetrical patterns can be achieved.

The natural consequence of this form of wave propagation is that there will be a coupling plane and a non-coupling plane .

Definitions: Coupling plane and non-coupling plane

We could define both the coupling and non-coupling planes using the reflective acoustical reflector.


In practice, the diffraction slot technique offers advantages in many applications.


As noted above, the GEO wavesource's acoustical mirror is defined, in part, by a spherical section. The plane of the illustrated ribbon's longitudinal axis (x) is the “coupling plane.” If we divide the sphere's circular cross section into equal segments of A°, we can form an omni directional source by combining 360/A loudspeakers based on the resulting wavesources. Since all of these wavefronts are tangent, they will produce a perfectly circular wavefront with whatever vertical beam we have defined.

The latitudinal direction (y) in this illustration is the “non-coupling plane.” The illustration shows a much smaller angle and therefore a narrow opening with same radius as in the longitudinal (x) direction. A narrow opening such as the one shown will act as a diffraction slot up to the frequency l = c÷2h (l = frequency, c = the velocity of sound).

This technique is used in the familiar “constant directivity” horn to broaden high frequency dispersion. The actual coverage angle in this non-coupling plane could be determined by the acoustical reflector, but the horn mouth for a usefully wide angle would be quite large. In many applications it is preferable to use the diffraction slot technique.

Using a diffraction slot, we can alter dispersion in the noncoupling plane by providing screw-on flanges that alter the wavesource's exit flare in the non-coupling plane. The coupling plane could just as easily be the latitudinal direction (y), in which case the non-coupling plane would be the longitudinal direction (x).

The horizontal dispersion of the sound wave can be focused in both symmetrical and asymmetrical patterns depending of the needs of the acoustic environment and without compromising the isophase ribbon…

In the coupling plane, coverage is determined by the mathematical model of the design, starting with the longitudinal ribbon we decide to carve out of the sphere. In the non-coupling plane, coverage is based on the diffraction slot/exponential flare model: the flares on either side of the diffraction slot can be easily configured with a screw-in device. The red plot shows nominal 120° coverage from 2000 Hz to 10 kHz with two configuration devices installed. The blue trace, with the coverage configuration device removed, shows 80° coverage from 2000 Hz right through 20 kHz. Asymmetrical coverage might be achieved by installing the configuration device on one side of the diffraction slot and not on the other. Again, this is a small-format horn, roughly 250mm x 150mm, designed for use in a loudspeaker that includes an 8 inch cone driver.

So at the other end of this process, we have total control over the shape and coverage profile of the emitting wave in a way that has not before been possible.

Here it is again. Because the reflective wavesource has a virtual as well as a real acoustic source, we can use this design technique to produce patterns that ordinary coercive horns cannot. The parabola can produce a perfectly flat wavefront (which might be useful as a line array element). The elliptical reflector can focus sound on a point in front of the loudspeaker. As shown below.


We have seen this image earlier in BOTA. It has a mathematically theoretical model overlaying the actual Geo HF plot.
We have seen this image earlier in BOTA. It has a mathematically theoretical model overlaying the actual Geo HF plot.

Actual coverage of a 30° coupling plane GEO reflective wavesource as compared with a theoretical “ideal isophase ribbon” of the same length and angular arc. While the GEO wavesource does not perform major miracles (note that beamwidth is still proportional to frequency), we can see that it reproduces the ideal isophase ribbon with a high degree of accuracy. The pattern produced is as close to the mathematical ideal as the actual device is to the mathematical model.

Note that 30° coverage is achieved at 2000 Hz, even though this horn is sized for use alongside an 8-inch diameter cone woofer. Also note the smoothness of the coverage vs. frequency, indicating that the power response will have an equally smooth taper.

More conventional polar plot: pure sine wave (not smoothed) measurements of the 5° GEO S805 wavesource (blue traces) vs. the theoretical 250mm 5° isophase ribbon (represented by the red traces). The geometrical model is an extremely accurate predictor of real world performance.
More conventional polar plot: pure sine wave (not smoothed) measurements of the 5° GEO S805 wavesource (blue traces) vs. the theoretical 250mm 5° isophase ribbon (represented by the red traces). The geometrical model is an extremely accurate predictor of real world performance.

The first really genuine array


The goal of array-able loudspeaker design is the design of multiple high output broadband sources whose wavefronts can be made tangent. Real sources have physical dimensions, so they can never occupy the same position at the same time – their wavefronts can be separate or can overlap, but cannot be tangent.

The GEO wavesource, however, has both real and virtual sources. Using a parabolic or hyperbolic reflector, we can locate the virtual source of one reflector along the edge of the arc covered by its neighbor. Now multiple wavefronts can be truly tangent. As long as they are virtual, these multiple sources can occupy the same space at the same time, as in the special case illustrated below, where both wavesources have the same coverage angle. Note also that the path lengths from S1 and S2, the real sources, to the horn mouths are identical at the coupling points, so that the two wavefronts combine with 0° of phase shift.

Beyond state of the art

GEO wavesource design uses reflection rather than coercion to determine the shape of the wavefront. The acoustical reflector used in a GEO wavesource is a mathematically calculated hyperboloid. This allows GEO wavesources to create a virtual acoustic source that is outside the enclosure and can be made precisely tangent to its neighbors, achieving an absolutely coherent wavefront and mathematically ideal arrayability.

Measurements of GEO wavesources show a high degree of correspondence between mathematical predictions and real world results. For the first time, designers have a robust mathematical model that can be applied to the design of pattern control devices and multi-enclosure arrays.

It is a long story but this is not all there is.

The above may be a fine solution for a HF horn, but what about that row of cone driven speakers? Did I here somebody say, “So you've fixed the HF problem, what about the 1/4 wave interference between all the MF drivers?” Good question… And here is the answer; another patented Nexo device; Midrange Line Source Coupling. Midrange frequencies are usually reproduced using small-diameter cone transducers. The cones are fairly small in relation to the frequencies they radiate, so the direction the cone is aimed doesn't matter much.

The line will have a front firing lobe as long as the wavelengths are shorter than 1/2 the height of the line . Below that frequency it will transition to an omnidirectional point source. So the effect of curvature shading is simply to shorten the line slightly, thereby raising the frequency at which it loses directional control.


It's also critical to maintain intra-driver spacing that is smaller than 1/2 wavelength at crossover. Above that distance each driver will produce an individual lobe and the array will produce a series of main and side lobes rather than a coherent wavefront with curvature shading that fits the audience.

We've shown how conventional horns make it impossible to align multiple points of origin, and how the patented GEO wavesource uses hyperboloid acoustic reflectors to solve these problems. GEO S Series and T Series Tangent Array Modules use 8-inch cone midrange drivers to reproduce frequencies up to at least 1200 or 1300 Hz.

The relationship between wavelength, time and distance will always be an issue to overcome with any form of direct radiating speaker. It's just a question of “what frequency and how much interference”
The relationship between wavelength, time and distance will always be an issue to overcome with any form of direct radiating speaker. It's just a question of “what frequency and how much interference”

Of course, we can't expect to get 8-inch cones in adjacent enclosures any closer than 10 inches on centre. This means that they will be a full wavelength apart at 1300 Hz. Adjacent cones will start to become separate sources at 325 Hz (1/4 wavelength spacing) and will be developing individual lobes at 625 Hz: far too low to cross over into the compression driver.

The DPD is a simple phase plug that causes each 8-inch cone to behave acoustically like a pair of 4-inch drivers. By creating two acoustical centres with 5 to 6 inch spacing, the phase plug raises the upper frequency limit for line source coupling between adjacent midrange transducers. We don't lose the power handling or low frequency extension of the 8-inch cone driver in the process. The device looks this:

In the GEO-S Series, the DPD takes the form of a phase plug that is attached to the frame of the cone transducer. In the GEO-T Series, the DPD is part of the molding that also includes the Configurable Directivity Flange.
In the GEO-S Series, the DPD takes the form of a phase plug that is attached to the frame of the cone transducer. In the GEO-T Series, the DPD is part of the molding that also includes the Configurable Directivity Flange.


So far so good. We have previously unheard of pattern control and tangential directivity HF and midrange. What about Bass?

Glad you asked. This is only a very edited version of a collection of papers covering the Geo technology. But in a nutshell, here it is. It's another good read and we're back at the time, wavelength and distance problem again.

How to get an omni-directional wave to go where you want it to go. (And nowhere else)

Low frequency wavelengths are so long (a 20 Hz wave is about 17 metres or more than 55 feet between peaks or troughs), that they are not obstructed by objects the size of practical loudspeakers. Subwoofers are almost omni directional regardless of the driver loading technique: closed box, vented/reflex or horn.

A horn-loaded subwoofer can increase the efficiency with which electricity is converted into sound by providing better “impedance matching” between the woofer and the airspace. But the horn mouth is too small to provide any directional control over sub-bass frequencies: to exert any directional control over a 20 Hz sound wave, a horn would have to be at least 4.25 m wide (for horizontal control) or tall (for vertical control). A 14-foot horn is not easy to transport, hang, aim precisely, or keep out of the way of audience sightlines.

To add to the problem, because the subwoofers are omni directional, they tend to put as much sub-bass on stage as into the audience. The loud low frequencies on stage make it hard for performers to hear what's going on, necessitating louder floor wedge levels. Both the floor monitors and the sub-bass “spill” from the PA bleed into open microphones and make it harder to construct a clear mix. Omni directional sub-bass excites the reverberant field in an enclosed listening space, leading to “mushy” bass without transients.

Standing waves and interference between two widely spaced omni directional sources (the left and right subwoofer stacks) usually create a “power alley” with too much bass down the center aisle and not enough near the side walls. (Depending on the size of the venue).

At mid-bass frequencies, where wavelengths are up to 2.25m/7.5 ft in length, multiple omni directional sources also create problems. Line arrays have to be very long to control 150 Hz in the vertical plane, and when they do manage to do so, they produce significant side lobes outside the intended coverage zone. Because of the low efficiency of omni woofers relative to horn-loaded mid- and high-frequency systems, most line array modules are forced to use direct radiating 15-inch woofers, which make up for their relative lack of efficiency by handling huge amounts of power. But they radiate lots of mid-bass off axis, with direction and intensity being dependent on frequency.

This is the cause of “mid-bass buildup” as well as the other problems mentioned above. Moreover, a 15-inch woofer requires an enclosure at least 18 inches tall. This makes it hard to create a smoothly articulated coherent wavefront at higher frequencies because the curve of the vertical array is divided into a small number of tall sections. A shorter array element would enable the designer to create a better approximation of the ideal smooth curve: one that delivers equal power to equal areas by increasing the angle between adjacent cabinets as distance decreases. The challenge for the loudspeaker designer is to provide an adequate amount of low frequency output from a short enclosure, and to control that output effectively. Ideally this control would be exerted in both the horizontal and vertical planes.

The cure? More physics lessons and another trip to the patent office?

The basic solution can be found at the other end of the signal chain. Microphones have long been designed with cardioid polar patterns. A cardioid loudspeaker can be simply described as a “cardioid mic in reverse.” Instead of using the interference between two arrivals of the same amplitude in order to create off-axis rejection, we use the interference between two sources of the same amplitude in order to radiate a cardioid polar pattern with off-axis attenuation. The basic concept is illustrated in the schematic below.

Even though one of the drivers is pointing toward the rear, proper implementation of the concept results in significant forward gain over an operating bandwidth of more than two octaves
Even though one of the drivers is pointing toward the rear, proper implementation of the concept results in significant forward gain over an operating bandwidth of more than two octaves.
The first NEXO loudspeaker to use this design principle is the CD12 Hyper-Cardioid Sub-bass. Except for the input plates, both ends of the CD12 have the same appearance: as the schematic shows, the enclosure holds two subwoofers driven in opposite polarity and with a frequency-dependent delay applied to the front woofer.
The first NEXO loudspeaker to use this design principle is the CD12 Hyper-Cardioid Sub-bass. Except for the input plates, both ends of the CD12 have the same appearance: as the schematic shows, the enclosure holds two subwoofers driven in opposite polarity and with a frequency-dependent delay applied to the front woofer.
Angular coverage is smooth and consistent within the operating band, as this MatLab-processed data from NEXO R&D's Brüel & Kjær acoustic analyzer shows.
Angular coverage is smooth and consistent within the operating band, as this MatLab-processed data from NEXO R&D's Brüel & Kjær acoustic analyzer shows.

Had enough?

Well that will be pretty heavy going for most people. Developing this work is thousands of hours of brain strain work that's for sure, by some pretty clever minds following a long tradition of mathematicians and physicists. But then, standing on the shoulders of giants affords a pretty good view.

There's More? You bet there is!

How about the mid bass? What happens when you stack a pile of these cardioid bass boxes together? How many feet apart must they be? What about some prediction and array software? How does it work in the real world?

For the real tech-hungry boffin, a trip to the Nexo site will reveal 10 Meg of the latest Geo paper that also contains the complete tech covering the programmable cardioid capacity of the Geo-T full-range + CD 18 sub and Geo-S CD 12sub. Consider the above as just a lengthy “tech teaser”.

Does this new technology mean that all concerts and theatre will always sound perfect in every seat?

Probably not, as it still takes “the man in the plan” to install the system, set it up correctly and another set of ears and mind to mix the show. And how many times has that last link in the chain been the snapping point. But that's another subject for a future BOTA…

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