--- In Dan Dugan <> wrote:
> Reference, please.
The result of summing two coincident microphones depends on their
polar responses, the angle between the capsules, and their relative
amplitudes. For now, assume the relative amplitudes remain the same,
so the only variables are the polar response and the subtended angle
between them.
The result of summing two coincident omnis together at equal
amplitude will always be a single omni with 6dB higher sensitivity,
regardless of the angle between them.
The situation with bidirectional microphones is interesting. At 0
degrees, the result is a bidirectional with 6dB more sensitivity. As
we increase the angle between the capsules, the response remains a
bidirectional but the sensitivity and direction changes. When we
reach a subtended angle of 180 degrees the two responses cancel out,
resulting in no output at all.
You [Dan] asked about summing coincident cardioids...
The true cardioid polar response contains equal quantities of a
pressure component (omnidirectional) and a pressure gradient
component (bidirectional) response. To put it mathematically:
Cardioid =3D [pressure component x 0.5] + [pressure gradient component
x 0.5]
But to keep the following maths within the group vernacular, I'm
going to say that there are equal quantities of omni and
bidirectional (rather than 'pressure component' and 'pressure
gradient component'), and because they are in equal quantities I'm
going to use the straightforward value of 1 for each rather than 0.5
, to make the maths more obvious. Therefore I'm going to re-write
the cardioid definition as follows:
Cardioid =3D [omni x 1] + [bidirectional x 1]
(I hope there are no pedants out there taking issue with this, it is
purely relative.)
When adding two (or more) coincident cardioids, the resulting polar
response depends entirely on the angles between the bidirectional
components. The omni component will always be there, of course.
Consider the following three subtended angles between two cardioid
capsules:
A coincident pair of cardioids facing the same direction (i.e.
subtended angle =3D 0 degrees) and at the same amplitude will sum to a
single cardioid facing the same direction because the omni and
bidirectional components add equally. The bidirectional component of
each capsule is facing the same direction and therefore adds
completely. Mathematically:
Combined response =3D cardioid + cardioid
Substituting:
Combined response =3D ([omni x 1] + [bidirectional x 1]) + ([omni x 1]
+ [bidirectional x 1])
Therefore:
Combined response =3D [omni x 2] + [bidirectional x 2]
Combined response =3D Cardioid x 2
In other words, a cardioid facing 0 degrees with 6dB more
sensitivity.
If the subtended angle between the cardioid capsules is increased to
180 degrees (+/-90 degrees either side of centre) so they are back
to back, the result is an omni because the bidirectional components
subtract and cancel each other out. Mathematically:
Combined response =3D ([omni x 1] + [bidirectional x 1]) + ([omni x
1] - [bidirectional x 1])
Combined response =3D Omni x 2
In other words, an omni with 6dB more sensitivity.
For angles between 0 degrees and 180 degrees the combined response
of two cardioids will be somewhere between a cardioid (0 degrees)
and an omni (180 degrees), passing through wide cardioid (also known
as 'hypocardioid') along the way.
That's what happens when summing coincident cardioids - the combined
response depends on the subtended angle between them. The wider the
angle, the less directional they become.
- Greg Simmons
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