Microphone Technology 653rβγcos ,θ (22.22)where r is the radial distance from the origin and has a maximum value of 1, β and γ are
fractional coeffi cients with β γ 1, and θ is the angle of incident sound relative to
principal axis of microphone.
Although β and γ are arbitrary within the constraint that they sum to unity, there are
particular values that have proven to be quite useful. This information is listed in Table 22.2.
Some practitioners prefer to employ directional microphones because such microphones
respond to reverberant acoustical power arriving from all directions with reduced
sensitivity as compared with the same acoustical power arriving along the principal axis
of the microphone. This property is expressed by the entry labeled RE in Table 22.2.
RE stands for random effi ciency. The hypercardioid pattern, for example, has a random
effi ciency of ¼. The response to power distributed uniformly over all possible directions
is thus only ¼ that for the same total power arriving on axis.
The entry labeled DF in Table 22.2 compares the working distance of a directional
microphone to that of an omnidirectional microphone. TheDF for a hypercardioid
microphone is 2, meaning that the working distance for a source on axis for this
microphone can be twice as large as that for an omni in order to achieve the same direct
to reverberant sound ratio in the output signal.
These factors when considered alone would lead one to believe that higher gain before
acoustic feedback instability would be achievable through the employment of directional
Table 22.2 : Polar Pattern Parameters for Microphone Directional
Characteristics
Polar pattern βγ RE a DF a
Omni 1 0 1 1.0
Gradient 0 1 1/3 1.7
Subcardioid 0.7 0.3 0.55 1.3
Cardioid 0.5 0.5 1/3 1.7
Supercardioid 0.37 0.63 0.268 1.9
Hypercardioid 0.25 0.75 1/4 2.0
a Based on data from Shure, Inc.