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Electronic Versus Physical: An Analysis Of Shaping Array Directivity

The differences in electronic and mechanical modification of array's directivity

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.

Figure 3: 3D balloon for array with delay steering at 100 Hz (3a); vertical polars for array with digital delay steering at 80, 100, 125 and 160 Hz (3b).

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 mechanical tilting 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 we’ve 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.

Figure 4: Room mapping of mechanically tilted array (4a) and an electronically steered array (4b), both at 125 Hz.

The 125 Hz octave band was used for the room predictions; while it is probably 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.)

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