> 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 ?

A detailed explanation would be a spherical harmonic one
... and possibly not what you want ...

A simplistic one is that 'W' is a sum, whereas 'X', 'Y', 'Z' are
differences.
So (ignoring any misgivings about using six capsules, and
presuming their directional sensitivities are such that this
will work, ....):
W = Xf + Xb + Yl + Yr
X = Xf - Xb
Y = Yl - Yr
(I am also ignoring normalisation, and dropping 'Z' to keep
it simple.)
( f,b,l,r = front, back, left, right)

So to feed a 'front' loudspeaker:
F = W + X
and a 'back'
B = W -X
or
F = 2Xf + Yl + Yr
B = 2Xb + Yl + Yr

This is hideously over-simplified, but with all its errors
I hope it demonstrates how using a sum (W) and
differences (X,Y,..) allows reconstitution.

For a better (accurate) appreciation, you need to tackle spherical
harmonics.

Michael


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