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By Lumer G.

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The pattern is described by which is plotted in Fig. 14(b). Although the cardioid microphone is not optimal in directional gain or front-to-back ratio, it is the most commonly manufactured differential microphone. 8 dB, the same as that of the dipole microphone and the 3 dB beamwidth is 131°. 5 dB. Hypercardioid. 3 of having the highest directivity index of any first-order microphone. 95). The 3 dB beamwidth is equal to 105° and the null is at 109°. 5 dB. 4 Supercardioid. The name supercardioid is commonly used for a first-order differential design which maximizes the front-to-back received power.

A general expression for the directivity factor can be defined as where the angles and are the standard spherical coordinate angles, and are the angles at which the directivity factor is being measured, is the pressure response of the array, and is the distribution of the noise power. The function is normalized such that Differential Microphone Arrays 23 For a cylindrical sound field, the equation for a general directivity factor can be written as Similarly, the distribution of the noise power is defined as In general, the directivity factor Q can be written as the ratio of two Hermitian quadratic forms [3] as where w is the complex weighting applied to the microphones and represents the complex conjugate transpose.

When dipole. At the microphone is an omnidirectional microphone with 0 dB directivity index. 12 shows the dependence of the front-to-back ratio F on The maximum F value corresponds to the supercardioid design. 13 shows the 3 dB beamwidth of the first-order differential microphone as a function of When the 3 dB down point is approximately at 180°. Higher values of correspond to designs that are increasingly omnidirectional and are sometimes referred to as subcardioid in the literature. 13 indicates Differential Microphone Arrays 41 that the first-order differential microphone with the smallest beamwidth is the dipole microphone with a 3 dB beamwidth of 90°.

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