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DIY Active Cardioid Implementation Using Global Optimization Algorithm
- Thread starter P.L.
- Start date
You can only get perfect cancellation with ideal 1-D plane waves, which under the usual idealized conditions, does not attenuate with distance.
In the cases of spherical and cylindrical waves, in free space, the sound pressure amplitudes will be proportional to 1/r and 1/√(r), respectively. What it means is that, at a point in the 180° direction (directly behind), the rear source will be closer to the measurement point than the front source and will have less distance attenuation. If the sources are equal in strength, the cancellation will not be perfect.
Here is an example. The sources S_a and S_b are assumed to be omni-directional point sources in free space and there is no obstacle impeding the sound waves. The source are separated by 0.15 m. The are 2 receiver positions, R_1 is 1 m from the center point and R_2 is 2 m from the center point.
Considering R_1 first. If the sources have equal strengths, pressure from to source S_a is 1/1.075 and pressure from source S_b is 1/0.925. The residual pressure at R_1 will be 1/0.925 - 1/1.025 = 0.15. For perfect cancellation, the strength of S_b will need to be 0.925/1.075 = 0.86 that of S_a.
If we compare this residual pressure to that of a reference single point source of strength 1 (which will result in a pressure = 1 at R_1), the residual pressure will be equal to an attenuation to 0.15 = -16 dB.
Now consider R_2. Pressure from S_a will be 1/2.075 and pressure from S_b will be 1/1.925. To have perfect cancellation, S_b will need to be 1.925/2.075 = 0.93. This is a different number from the R_1 case, which means we can only EQ to provide perfect cancellation at 1 point in the 180° direction line.
In real life where the sources aren't omni-directional point sources and the speaker cabinet is a significant obstacle, we should expect significantly less cancellation (even when in anechoic conditions).
Very cool approach!
The use of multiple drivers is very flexible as it can be tuned very precisely, but it also costs atleast 2 extra drivers (one on each side) compared to a resistive slotted approach like in the D&D 8C. Have you considered doing optimization for that as well?
The use of multiple drivers is very flexible as it can be tuned very precisely, but it also costs atleast 2 extra drivers (one on each side) compared to a resistive slotted approach like in the D&D 8C. Have you considered doing optimization for that as well?
Not to forget additional amplification, excursion capabilities and enclosure volume. As mentioned, I highly appreciate the technical sophistication of active cardioid concepts, but sometimes I think to myself that their designers live in a land of plenty when it comes to all aforementioned reserves.
I think the left and right driver could use the same filtering and amplification if the cabinet is perfectly symmetrical.
Intuitively excursion is lower since there are now several drivers reproducing the same bandwidth.
Though that's just intuition and I have no mathemathical/measured evidence of that.
In theory and if impedances are complying, yes. In practice you easily come to a point where you need a lot of power from the amps, so having 4 channels 250 Watts each might be cheaper than 2 channels per 500 Watts.
Active cardioids are based on the idea of inverted phase signals and angle-dependent cancellation, so I am afraid excursion might not get lower to achieve the same SPL. Rather the opposite, as waves cancelling each other out, have to produced by drivers as well.
