Hi all,
I've not been very active on the forums and with the audio hobby for some while, but the last few months I had an idea in the back of my head that wouldn't go away. So together with one of my audiophile friends I started a project again: building a 2nd order cardioid. The last few months I've created a model in Excel based on simple point sources (download here, I originally created it to simulate interaction of source types with a wall behind the source).
As an introduction, I'll 'dissect' the model. We'll start with the simple dipole, which is modelled as two point sources of opposite polarity, separated by a distance D (plotte response for D = 0,343 m):
If we delay the rear source with T = D/c (c = 343 m/s), we'll get a cardioid source:
For a 2nd order cardioid we have two equal dipole sources, each with separation distance D1, positioned at a distance D2 from each other and out of phase, analogous to the simple point sources in the 1st order cardioid. The rear dipole is thus delayed with T = D2/c.
The radiation pattern will be narrower than a 1st order cardioid, but it's low frequency response will also drop with 12 dB/octave instead of 6 dB/octave. The practical advantages and usefulness are not evident even from a theoretical point of view, but I wanted to try it anyway.
So we started with two 8" A&D drivers, mounted on a minimal frame. No baffle and an electronic delay, to approach the theoretical model as close as possible:
The distances D1 and D2 are equal for this first test configuration (0,21 m). The simulated response for 1 m distance:
The measured response resembles the model pretty well:
And the beamwidth is indeed very narrow! Probably it is a little wider in reality because of the short measuring distance, but it will probably do ~ -12 dB at 90 degrees. The polar also follows the model reasonably well:
The first on-axis dip is pretty sharp because the "baffle" of both drivers is round and thus the dipole separation does not vary. Moreover, it is very low in frequency, about 800 Hz. That can be improved by setting the distance between both drivers exactly half of the dipole separation of each source. That's logical, because for both dipoles the first dip occurs at D/λ = 1, while for a cardioid, which you superimpose on it, the first dip is at D/λ = 0.5 (see also simulated responses above).
That gives the following result:
Interesting is that a number of mild dips have been introduced. Perhaps this is caused by some resonance between both drivers (after all they're mounted very close together). But again, the measurements follow the simulation reasonably well!
In the upcoming weeks, we want to research how to improve this concept further. First step will probably be to introduces (rectangular) baffles to minimize the on-axis dips at high frequencies and improve polar response in that region. Step two is to investigate if this can be made to work with a resistance enclosure, analogous to a first order cardioid resistance box.
I've not been very active on the forums and with the audio hobby for some while, but the last few months I had an idea in the back of my head that wouldn't go away. So together with one of my audiophile friends I started a project again: building a 2nd order cardioid. The last few months I've created a model in Excel based on simple point sources (download here, I originally created it to simulate interaction of source types with a wall behind the source).
As an introduction, I'll 'dissect' the model. We'll start with the simple dipole, which is modelled as two point sources of opposite polarity, separated by a distance D (plotte response for D = 0,343 m):
An externally hosted image should be here but it was not working when we last tested it.
If we delay the rear source with T = D/c (c = 343 m/s), we'll get a cardioid source:
An externally hosted image should be here but it was not working when we last tested it.
For a 2nd order cardioid we have two equal dipole sources, each with separation distance D1, positioned at a distance D2 from each other and out of phase, analogous to the simple point sources in the 1st order cardioid. The rear dipole is thus delayed with T = D2/c.
The radiation pattern will be narrower than a 1st order cardioid, but it's low frequency response will also drop with 12 dB/octave instead of 6 dB/octave. The practical advantages and usefulness are not evident even from a theoretical point of view, but I wanted to try it anyway.
So we started with two 8" A&D drivers, mounted on a minimal frame. No baffle and an electronic delay, to approach the theoretical model as close as possible:
The distances D1 and D2 are equal for this first test configuration (0,21 m). The simulated response for 1 m distance:
An externally hosted image should be here but it was not working when we last tested it.
The measured response resembles the model pretty well:
And the beamwidth is indeed very narrow! Probably it is a little wider in reality because of the short measuring distance, but it will probably do ~ -12 dB at 90 degrees. The polar also follows the model reasonably well:
An externally hosted image should be here but it was not working when we last tested it.
The first on-axis dip is pretty sharp because the "baffle" of both drivers is round and thus the dipole separation does not vary. Moreover, it is very low in frequency, about 800 Hz. That can be improved by setting the distance between both drivers exactly half of the dipole separation of each source. That's logical, because for both dipoles the first dip occurs at D/λ = 1, while for a cardioid, which you superimpose on it, the first dip is at D/λ = 0.5 (see also simulated responses above).
An externally hosted image should be here but it was not working when we last tested it.
That gives the following result:
An externally hosted image should be here but it was not working when we last tested it.
Interesting is that a number of mild dips have been introduced. Perhaps this is caused by some resonance between both drivers (after all they're mounted very close together). But again, the measurements follow the simulation reasonably well!
In the upcoming weeks, we want to research how to improve this concept further. First step will probably be to introduces (rectangular) baffles to minimize the on-axis dips at high frequencies and improve polar response in that region. Step two is to investigate if this can be made to work with a resistance enclosure, analogous to a first order cardioid resistance box.
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Nice work! I'm looking forward to what you come up with.
I tried this with 15" woofers but iirc it wouldn't go high enough, and the lf roll off was more than I was willing to accept at the time. That said I do want to look into this some more.....maybe next year.
I tried this with 15" woofers but iirc it wouldn't go high enough, and the lf roll off was more than I was willing to accept at the time. That said I do want to look into this some more.....maybe next year.
So could you get a pair of omnidirectional speakers mounted next to each other and steer the output around be moving the second speaker?
Chris
Chris
Hi Chris,
I'm not sure I get your question. Do you propose to use two small closed-box speakers, putting one out of phase and delaying it and then steer output by moving the cancelling speaker? In that case you would create a first-order cardioid, which is simpler but less directional that what I've created here.
And yes you could create some kind of steerable array if you would use multiple drivers and change the delay and phase of individual drivers. Note that with small distances low frequency output will be low and you might also encounter lobing and on-axis comb filtering with such a system.
I'm not sure I get your question. Do you propose to use two small closed-box speakers, putting one out of phase and delaying it and then steer output by moving the cancelling speaker? In that case you would create a first-order cardioid, which is simpler but less directional that what I've created here.
And yes you could create some kind of steerable array if you would use multiple drivers and change the delay and phase of individual drivers. Note that with small distances low frequency output will be low and you might also encounter lobing and on-axis comb filtering with such a system.
Have you seen this? http://www.diyaudio.com/forums/multi-way/14697-second-order-gradients.html
I'm thinking I'd like to try this with a resistance box like you suggested in the op, with the rear driver hi-passed to transition to cardioid at lf to minimize the roll off.
Or maybe an all pass filter to get the delay on the rear driver that would transition to bipole on the low end. Might have some lower amplitude side lobes though, which wouldn't be that big of a deal to me below 300hz.
I'm thinking I'd like to try this with a resistance box like you suggested in the op, with the rear driver hi-passed to transition to cardioid at lf to minimize the roll off.
Or maybe an all pass filter to get the delay on the rear driver that would transition to bipole on the low end. Might have some lower amplitude side lobes though, which wouldn't be that big of a deal to me below 300hz.
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