JOSEPHSON ENGINEERING • C700 USERS GUIDE
Appendix B -- For the mathematically inclined
The omni or W microphone signal behaves as a monopole scalar pressure transducer, unaffected by
direction (at low and mid frequencies, where the size of the microphone housing isn’t a significant fraction of
a wavelength). The figure-8 (X and Y) microphone signals behave as dipole transducers with a response that
varies with cosine of the arrival angle. In the C700S, we use a combination of the two figure-8 signals X and
Y to yield a new figure-8 pattern D pointed at a defined angle
θ
. We use capital letters to refer to the signals
themselves and lower-case to refer to the proportions of each signal in a mixture.
For these formulas, consider the output as a combination of W and D signals where w+d=1. Some common
ratios are
Omni: all W
Subcardioid/hypocardioid/wide cardioid: 0.66W+0.33D
Cardioid: 0.5W+0.5D
Hypercardioid: 0.33W+0.66D
Supercardioid: 0.25W+0.75D
Figure-8: all D
Steering or rotation of D is achieved by adding X and Y signals. The main axis of the pattern is located at an
angle
φ
relative to the front of the microphone.
φ
changes linearly from 0 to 90
°
by varying the ratio of X to
Y signals in the mix. For a ratio of x and y such that x+y=1,
φ
=-90y.
φ
X Y
90º left 0 1
45º left .5 .5
0 º 1 0
45º right .5 -.5
90º right 0 -1
φ
is not restricted to the front quadrants. By reversing the phase of the X signal, it can be pointed to the rear.
φ
lies within one of the four quadrants depending on the phase of the X and Y components. In the C700A
there is no Y signal, so
φ
is fixed at 0 or 180
°
depending on whether X or –X is used.
The response
r
at azimuth angle
θ
(where
θ
is the angle from the main axis of D) is found with the formula
r
(
θ
) = w + d cos (
θ
).
Summary of Contents for C700
Page 1: ...C700 Users Guide ...
