live sound_ electronic versus physical_ an analysis of shaping array directivity - pro sound web

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3/13/13 Live Sound: Electronic Versus Physical : An Analysis Of Shaping Ar ray Directivi ty - Pro Sound Web

www.prosoundweb.com/article/print/shaping_array_directivity

Figure 1: Loudspeakers

equidistant to listeners (1a);

loudspeaker B moved back

(1b); and loudspeaker B

electronically delayed (1c).

Electronic Versus Physical: An Analysis Of ShapingArray DirectivityElectronic modification of an arrays directivity is not always a substitute for goodold mechanical arranging or aiming. Here's a look at the differences

January 26, 2012, by Joe Brusi

Modifying the directivity characteristics of loudspeaker arrays

through electronic delay has become increasingly popular.Whereas 20 years ago the only option was expensive

dedicated digital delay units, and a few years later the original

BSS Omnidrive was a luxury, the advent of inexpensive digital

processing has changed the game.

The design of complex arrays using a relatively high number of

processing channels, as required to electronically modify the

directionality of an array, is now affordable and widely

implemented.

However, virtual (electronic) modification of an arrays

directivity is not always a substitute for good old mechanical

arranging or aiming, as the two methods have widely differingradiation characteristics off-axis (i.e., to the back and sides).

Lets look at the differences in the two approaches, how they differ across a number of array types,

and suggest applications where each of them should be used with subwoofers.

Arrival Times

The reason why physically moving a loudspeaker backward is different from delaying it electronically

may not be intuitively obvious, but is easily shown graphically.

Figure 1a shows two loudspeakers (A and B) located left and right at equal distance from both a

listener positioned in front and another listener positioned behind.

Leaving aside subtleties such as the location of the time origin of the

loudspeakers, since it does not influence the basic concept being discussedhere, sound from loudspeakers A and B will arrive at the same time to both

listeners.

If we move back loudspeaker B (Figure 1b), then loudspeaker A is closer to

the front listener, so sound reaches that listener earlier. Behind the

loudspeakers, of course, the opposite occurs.

If we return the loudspeakers back to their original positions, and then apply

electronic delay to loudspeaker B (shown in Figure 1c as a diverted path length to the listeners), we

see that the output of loudspeaker A arrives earlier than B in both cases (in front and behind).

Thus, it is graphically clear that physically moving enclosure B produces a significantly different result
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Figure 2: 3D balloon f ormechanically tilted array at

100 Hz (2a); vertical polars

for mechanically tilted array at

80, 100, 125 and 160 Hz (2b).

Figure 3: 3D balloon for array

w ith delay steering at 100 Hz

(3a); vertical polars f or arrayw ith digital delay steer ing at

80, 100, 125 and 160 Hz (3b).

Figure 4: Room mapping of

mechanically tilted array (4a)

and an electronically steered

array (4b), both at 125 Hz.

to electronically delaying it.

Focus On The Effect

Lets now look at the implications within the context of a vertical array of loudspeakers, and predict the

coverage of a column of omnidirectional sources.

I often prefer to display results via polar plots, because with plane mappings

its often difficult to understand the behavior at distances other than those

close to the system being modeled.

Also note that Ill use mostly omnidirectional sources instead of real-world

sources (with a certain degree of attenuation at the back, i.e., not perfectly

omnidirectional) to focus on the effect that the arrangement is causing on the

directional response of a single loudspeaker.

In Figure 2a and 2b, we have physically tilted a 12-element array that is 23

feet (7 meters) long downward by 30 degrees.

The front part of the radiation points down 30 degrees, and the back part points up 30 degrees, while

left and right (i.e., 90 degrees to the sides) are pointing straight, as if the array had not been tilted at

all.

Figure 2a shows a three-dimensional directivity balloon resembling some sort of flying saucer at an

angle, while Figure 2b shows polar plots for the third octave bands between 80 and 160 Hz (the main

lobe gets narrower as frequency increases).

In Figure 3a and 3b, the sources are delayed so that the main radiation is (electronically) steered 30

degrees down (by applying increasingly larger delay times from top to bottom).

The balloon looks a bit like a fat cone, showing that the 30-degree downward angle is taking place all

around the array, not just in front of it.

This behavior is emphasized by manufacturers of electronically controlled

(digitally steerable) column loudspeakers, correctly emphasizing that the

use of their products yields better coverage than a single, down-tilted

conventional enclosure.

Pointing Lobes

To provide another example illustrating the differences between mechanicaltilting and delay steering, we modeled one of each in a room, this time using

loudspeaker data with realistic nonperfect omnidirectionality.

The resulting pressure maps have been plotted onto the walls as well as the floor, and weve also

drawn lines, at different horizontal angles, that represent the direction in which the main lobe is

pointing.

In Figure 4a (mechanical), the lines follow the shape of a disk, which means that some of the lines are

pointing to the walls, and the mapping indeed shows that significant SPL is being radiated towards

the walls.

In Figure 4b (electronic), the lines form a cone and sound is mostly focused on the floor.

The 125 Hz octave band was used for the room predictions; while it isprobably somewhat unrealistic of typical subwoofer bandwidth, the narrower

coverage is helpful to exaggerate the effect for clarity.

It can also be seen that the covered area is roughly rectangular for the

mechanical case and rounder for the electronic one. (Some may recognize

the CADP2 graphics. What a beautifully elegant piece of software that was!

RIP.)

Exploring Arcs

From the explanation earlier in this article, we can guess that an electronic arc (where input signal is

increasingly delayed as one goes from the center to the edges of the array) will display identical front

and rear radiation for omnidirectional sources.
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Figure 5: Horizontal polars for

six-element physical arc in the

near field (5a); mid field (5b);

and far field (5c).

Figure 6: Side view of stage

show ing the diff erence

betw een mechanically aimed

arrays (6a) and electronically

steered arrays (6b).

Figure 7: Top view of s tage

show ing the diff erence

betw een mechanically aimed

arrays (7a) and electronically

steered arrays (7b).

A physical arc, in the far field, also provides symmetrical front and rear behavior but - at close

distances, rear levels will be higher.

This is because circular arc sources arrive simultaneously at the circles center, i.e. the arrays virtual

origin. Accordingly, physical arc best practices should avoid any arc that displays an inconvenient

center, particularly at center stage.

Figure 5a, 5b and 5c present polars for a physical arc of eight subwoofers spanning 120 degrees with

a radius of 10 feet (3 meters).

In the near field (Figure 5a), the buildup of sound pressure at the back can be

observed, with the array being an average of around 6 dB less sensitive atthe front for theoretical omnidirectional sources (though this number changes

widely with frequency as seen on the plots).

This translates approximately to the same level back and front for a typical

real-life subwoofer (with a certain degree of directionality). Also, in the near

field, the rear pattern is narrower at the back.

As we get farther from the array though (Figure 5b), the polars become symmetrical, with the same

levels being radiated to the back and front. This was calculated at a distance of 98 feet (30 meters)

from the center of the array.

Figure 5c shows the far-field results, made up of equidistant enclosures that would virtually follow the

same arc as the physical arc above.

Unlike the physical arc, the electronic version shows the same levels back and front both up close and

far away from the array.

In general, an electronic arc is preferred because it does not suffer from

pressure build-up behind the array, and it requires less space in front of the

stage.

And unlike array steering, where each element requires a different delay

time, we can use an even number of elements, so that pairs can share the

same delay, meaning one amplifier channel can power two boxes if needed.

Given todays prices, an extra DSP unit dedicated to subs does not seem

too much of a luxury. Mathematically, calculating required delay times for astraight line array of equally spaced boxes may be complicated.

However, a piece of string can be used to mark a circular arc on the floor as

physical reference for measuring virtual distances for pairs of subs.

Case Study A: Flown array of subwoofers on an open-air concert. When

flying a subwoofer array, if the array is mechanically tilted, the rear radiation

lobe will point upward (Figure 6a) and minimize trouble.

Yet it might be tempting to go with a clean hang and implement electronic

steering, in order to digitally down-aim low-frequency (LF) radiation.

Doing this, however, means that corresponding rear radiation will also be aimed downward,

presenting potential noise problems with nearby housing, as shown in Figure 6b.

Case Study B: Opening up left-right subwoofers. Invariably, when left and right subwoofers are used,

interference creates the notorious power alley, where LF system response is audibly louder.

Additionally, bass coverage is not uniform since interference patterns change with frequency.

One way to minimize left-right interference is to aim subwoofer arrays away from each other in order to

reduce overlap.

If we aim the array physically (Figure 7a), the back radiation lobe will point to the stage, increasing LF

spill (again, the extent of this will be reduced through the use of cardioid subs, be i t off-the-shelf

cardioid models or array elements made up of a cardioid arrangement).


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Figure 8: 3D view of

a flow n 360-degree

array.

Figure 9: Horizontal and

vertical polars of 360-degree

array at 100 Hz.

Figure 10: 3D balloon for 6

element array w ith delay

steering at 160 Hz (10a);Vertical polars f or a six-

element array w ith delay

steering (10b) and w ith

mechanical aiming (10c) at 80,

100, 125, 160, 150 and 250

Hz.

However, if electronic steering is used (Figure 7b), the back lobe will point away from the stage.

This is actually the same as Case Study A, except for the fact that we are dealing

with horizontal, not vertical, coverage.

Case Study C: 360-degree subwoofer array. Certain arena applications might

call for 360-degree horizontal subwoofer coverage, as well as some degree of

downward firing toward the seating.

Achieving this with mechanical aiming is just plain impossible, but it can be

accomplished through the electronic realm.

The suggested design makes use of a somewhat unusual configuration. Since real

subwoofers are not entirely omnidirectional (a typical 18-inch subwoofer box may

show 4 to 6 dB less at the back relative to the front), to achieve the same level at

both back and front, we use a face-to-face deployment.

And it might seem a bit counterintuitive, but a physically phase-aligned pair can

also be achieved if the correct spacing is used between the two.

To avoid flying too much weight, we could alternate every other element in the array

as seen in Figure 8, an arrangement that also minimizes obstructions to the

expansion of the wavefront.

This two-column arrangement with electronic steering

would generate the directivity balloon seen in Figure 3a

(except that the sides would be slightly squashed), with

the horizontal and vertical polars that can be seen in Figure 9.

As with any low-frequency array, a longer array generates a narrower

radiation pattern, which means that different venues would require different

lengths to suit their geometry.

From the point of view of level consistency, the arrangement in Figure 8, with

real non-perfectly omnidirectional sources, would send slightly less SPL to

the sides (in our case, around 3 dB less for a real single 18-inch front-loaded

subwoofer), which would be desirable on a rectangular arena to compensate

for the difference in distance to the closest and farthest tiers.

On the other hand, given the uniform downward profile, this configuration would be ideally suited,

angle-wise, for circular venues such as a bullfighting ring or a Mexican Palenque.

Watch That Space

As we know from line array laws there is a maximum spacing between sources for any given

frequency.

If that spacing is exceeded, the array loses the ability to control directivity,

with higher frequencies showing lobes at the wrong angles and eventually

losing directivity control. This is even more so for an electronically steered

array, which requires a tighter element density.

Figure 10a shows a three-dimensional representation of the directivity

balloon of an electronically steered array with excessive spacing (4.5 feet).

A significant top lobe can be seen that will surely create reverberation issues

at that frequency in an indoor venue.

Figure 10b presents 80 to 250 Hz one-third octave polars for the same array

where the three highest frequencies have gone haywire across the top part of

the curve.

In contrast, a mechanically tilted array of subs (Figure 10c) with the same spacing only shows

misbehavior at 250 Hz, which corresponds to a wavelength that correlates roughly to the spacing

between sources, so i ts no surprise.

Jos (Joe) Brusiis an independent electroacoustical consultant. And thanks to Joan La Roda for


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the field phase measurements of the alternate face-to-face subwoofer configuration.

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