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Ambisonics explained


Starting of by discussing the difference between a velocity mic and a pressure mic Eric Benjamin the other day offered a really good explanation of the basic consepts of ambisonics at the sursound mailing list. I’m quoting it all below in order to be able to store it for later reference:

A sound wave has both pressure and velocity (or ‘particle velocity’) components. This is all just jargon until you understand what it means. If you put up a pressure microphone (which has omnidirectional polar patterns) it only senses the pressure of the sound waves. As the wavefront passes the microphone the pressure will go up and down and the signal from the microphone will go up and down in a corresponding way. But the microphone doesn’t ‘know’ what direction that wave came from.

Think of the old expanding ripples in a pond analogy. If a rock is dropped into the pond the ripples expand outwards in every direction until they hit the edges of the pond – but we will imagine that the pond is infinite. If we observe a leaf floating in the pond as the wave goes by it just goes up and down. From observing the leaf we can’t tell anything about the direction of the wave. But as observers from above we can see that the wave does have direction to it. From the position of the leaf we can point back to where the wave started – where the rock was dropped in.

The motion of the leaf is like the output of the omnidirectional pressure microphone. It has no direction only up and down.

Now imagine a hair suspended vertically in the pond. As the wave goes by the hair will be deflected. And it will be deflected In The Direction of The Wave! It gives an indication of the direction of the wave propagation. Note that that direction depends on the position of the observer. Its an “it came from over there” sort of thing and depending on where you happen to be sitting the direction could be different.

I used the analogy of the hair deflected by the wave because that’s how insect’s ears work. Ours are pressure sensors. We can sense direction primarily because we have two ears. (even though persons who hear with only one ear can still manage to sense direction via other means.) We or rather our hearing look at the differences in the pressure signals at our two ears and from that determine the direction of arrival.

The method of the vibrating hair is like the ribbon microphone. The reason that the hair moves and the reason that the ribbon moves are the same. When the wave reaches the ribbon and flows around it it creates a small zone of increased pressure on the near side and a sort of shadow of decreased pressure on the far side. It is the difference in pressure between the two sides of the ribbon that makes it move and only when the ribbon moves can the fact that there was sound be sensed.

But wait! I thought that the ribbon was supposed to be a velocity sensor. And now we’ve decided that it’s pressure that makes it move. That’s true. It’s the difference in pressure between front and back mathematically described as a pressure gradient that makes the ribbon move.

To codify our terminology:

a pressure microphone senses pressure and as a result it has a fundamentally omnidirectional polar pattern. It can’t tell what direction the sound came from.

a velocity microphone senses the pressure gradient which is proportional to the acoustic particle velocity. The microphone has an output which is a cosine function (figure-of-eight) of the direction of the sound. Positive for sounds from in front zero for sounds from the sides and negative for sounds from the rear.

Two of these placed at right angles to each other give a full description of the acoustic particle velocity in the plane of the microphones. Three of them at right angles to each other give a full description of the particle velocity in three-dimensional space. Add an omnidirectional pressure microphone to the mix and you have a complete physical description of the sound field at a point in space.

What is this all about with regard to the velocity/pressure ratio? How are these things measured?

Now we know about acoustic pressure and particle velocity. And we know that our ears aren’t directly sensitive to particle velocity but we can still sense direction by measuring the pressure gradient between the two ears. And this is a big part of how we sense the direction of a sound.

So to get the reproduced sound right ideally we would want to get both the pressure and the particle velocity right. We would like for the pressure and the particle velocity at the listener’s position to be the same as the pressure and the particle velocity were in the recording venue. This is what Ambisonics can do and what 2-channel stereo can’t do. But obviously 2-channel stereo works pretty well. Otherwise we wouldn’t spend so much time listening to it.

In acoustics the pressure and particle velocity are wrapped up in a combination called acoustic intensity. There are devices made by Bruel and Kjaer and by one or two other companies that are called intensity probes and that is what they measure. In effect an intensity probe and a Soundfield microphone are really the same thing. It’s just that the first is a laboratory device intended for measuring things and the second is a recording microphone.

I assume that the figure-eight components of the B format remain pure velocity mics. Are there real world pure velocity mics that could be used to record B format directly (along with an omni pressure mic for W)? I’m not sure about the word “pure” in your question. The cardioid or subcardioid capsules in the Soundfield microphone have a mixture of pressure and pressure gradient sensitivity. When the capsule outputs are matrixed together what is recovered are the pressure and three pressure gradient components.

In that sense the output of the Soundfield microphone is exactly like the output of an omnidirectional (pressure) and three figure-of-eight (pressure gradient) microphones. But better because the Soundfield microphone has output signals that behave as though all four of those microphones were exactly coincident in space.

Are there real world pure velocity mics that could be used to record B format directly (along with an omni pressure mic for W)? Why sure! You can use your stereo ribbon microphone to recover the horizontal velocity components of B-format and add an omni to get the W component.

Thomas Chen and I wrote an AES paper (AES preprint 6621 The Native B-Format Microphone Part I) on this subject and boiled down the thrust of that paper is that you can record B-format in the way that you suggest. We were trying to encourage people to do just that. In some ways this technique is inferior to a Soundfield microphone for two reasons. One of them is that you can’t make the discrete microphones be truly coincident. The other one is that the polar patterns of real-world omnidirectional microphones aren’t all that omnidirectional! In some ways the “Native B-format microphone” is better. You get to use the microphones that you prefer.

Perhaps most important is that it may make the difference between having a B-format recording or not having a B-format recording. That argument supercedes a lot of the theoretical BS surrounding what is best.

For those who are interested in the subject of recording B-format with discrete microphones Thomas and I plan a second paper detailing the results of our listening tests. That paper is planned to be presented at the 120th AES in Paris this spring. Wish us luck. We have a lot of work to do.

Eric Benjamin


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