Gus: You wrote: > invert the phase of one of the channels and then add them to get the X,Y,Z
There are two ways to approach the construction of such a microphone. One of them is to use cardioid microphone capsules facing outwards at the six sides of your cube. The other is to use omnidirectional capsules and place them on the surface of a rigid object such as a sphere. I don't know which approach you're taking so I'll discuss both. Using a cubic array is intuitively simple for a microphone that is going to have outputs which are directed along the Cartesian axes, such as is the case for Ambisonic B-format. As you already know, in B-format the W signal is equivalent to an omnidirectional microphone located at the center of the array. X is a dipole or figure-of-eight microphone pointed along the X-axis. Since a dipole has two lobes, one positive and one negative, it must have a precise orientation to conform with X. X is a front-back signal, Y is a left-right signal, and Z is an up-down signal. Cardioid microphone capsules have a directivity that is heart-shaped, hence the name. They theoretically have maximum sensitivity in the front direction and zero sensitivity in the rear direction. They can be modeled as being the sum of a monopole (omni) and a dipole (figure-of-eight), and that is why it is easy to recover those components by adding or subtracting capsule signals. If you have two cardioid capsules, on a line and facing opposite directions, when you add the two microphone signals the two dipole components, being of opposite polarity to each other, cancel out. That is assuming that the microphones are identical, of course! If you subtract one of the microphone signals from the other, the two monopole components, being identical, cancel out, but the dipole signals now add to each other. So the sum gives a monopole and the difference gives a dipole. Note that it only takes two of the capsules to get a monopole. But you will have 6 capsule signals and you can sum all of them to get a monopole signal that is, at least in some ways a better omni than you get with just two. The process is the same, of course, with the other two axes and deriving Y and Z. Now, if your capsules are omnidirectional microphones the analysis is somewhat different. There really should be some sort of a baffle on which to mount the microphone capsules although it's certainly possible to have them just sitting in free space. But let's assume that they are mounted on (actually, in) the surface of a sphere. If we add all six omni capsules together we get another omni. Simple. But if two of the opposite-facing omni capsules are subtracted, we get a dipole. That may not be immediately apparent. It is the separation in space that makes it so. The simplest analysis is that, if the two omni capsules are identical, when you subtract the two signals you will get nothing. And that's partly true. But since the capsules are separated by some small distance there will be a small difference between the two signals. If a sound wave is approaching along the line separating the two capsules then it will reach one capsule first and the other one second. Assuming that the sound source is distant from the microphone array there will be no attenuation in level between the two microphone positions, although there may be some difference in level due to the spherical baffle. Mostly there is a difference in the phase of the two signals. When the two are subtracted, one from the other, a difference signal appears that is proportional to the phase difference. But that phase difference is proportional to the frequency of the sound! That is, at low frequencies, say 100 Hz, the wavelength of sound is about 3.4 meters. And high frequencies, say 10 kHz, the wavelength is 3.4 cm. If our capsules are separated by 1 cm (just to make the arithmetic easy), then that is 1/340 of a wavelength at 100 Hz and 1/3.4 of a wavelength at 10 kHz. So there will be a minute difference in phase at 100 Hz and a large difference in phase at 10 kHz. The result is that the frequency response of such an array is differentiated; it rises at 6 dB/octave from the lowest frequencies to the highest frequencies. That slope will need to be corrected by equalization. Furthermore, if the spacing were increased, say from 1 cm to 10 cm, the amount of signal will be increased by a factor of 10. But a sound with a wavelength of 3.4 cm, like our 10 kHz sound, will be ambiguous. It gets quite complicated. I have simplified things to make the explanation tractable. Typical spherical microphone arrays have diameters of about 5 to 10 cm, depending on what bandwidth is needed in the final design. One other comment; You could use a different orientation of the array than what I have assumed above where the capsules lie on the Cartesian axes. You could, for instance, rotate the array so that the axes run along the bisector between two of the capsules, or along the trisector between three of the capsules. That makes a difference in what you call 'front', of course, but also in the behavior of the array at the highest frequencies. I hope this helps. Eric Benjamin ----- Original Message ---- From: Augustine Leudar <augustineleu...@gmail.com> To: sursound@music.vt.edu Sent: Thu, May 24, 2012 2:57:44 AM Subject: [Sursound] Why do you invert the phase of one channel of multi capsule microphones ? Hello all, I am building a six capsule ambisonic microphone. I have been told that with the opposite capsules (ie up/down, left/right, forward/backwards) I should invert the phase of one of the channels and then add them to get the X,Y,Z for the ambisonic b format. I've been struggling to find a good explanation - I was wondering if anyone could explain why this is in detail ? _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
