Instrumentation for Noise Measurement and Analysis
3.1 MICROPHONES
3.1.5 Field Effects and Calibration
Reference to Equation (3.19) shows that the output voltage of a microphone is directly proportional to the area of the diaphragm. Thus the smaller a microphone of a given type, the smaller will be its sensitivity. As the example shows, the output voltage may be rather small, especially if very low sound pressure levels are to be measured, and the magnitude of the gain that is possible in practice is limited by the internal noise of the amplification devices. These considerations call for a microphone with a large diaphragm, which will produce a corresponding relatively large output voltage.
In the design of a good microphone one is concerned with uniform frequency response, besides general sensitivity as discussed above, and the demand for high- frequency response recommends against a microphone with a large diaphragm. The problem is that, at high frequencies, the wavelength of sound becomes very small.
Thus, for any diaphragm, there will be a frequency at which the diameter of the diaphragm and the wavelength of sound are comparable. When this happens, large diffraction effects begin to take place which will make the microphone response to the incident sound quite irregular, and also sensitive to the direction of incidence. This may be undesirable when the direction of incidence is unknown.
Unfortunately, the problem of diffraction cannot be avoided; in fact diffraction effects begin to be apparent when the wavelength of the measured sound is still as much as 10 times the diameter of the microphone, and this is always well within the expected measurement range of the instrument. At still higher frequencies and shorter wavelengths the response of the microphone becomes quite sensitive to the angle of incidence of the measured sound, as illustrated in Figure 3.3. In the figure the increase or decrease in sound pressure level due to the presence of the microphone, relative to the sound pressure level that would exist in the absence of the microphone, is shown.
Thus for a microphone characterised by the diffraction effects shown in the figure, and for a microphone diameter to wavelength ratio of 0.63, a normally incident sound will produce a sound pressure at the microphone which is 8 dB higher than the same sound will produce at grazing incidence.
Essentially, what is affected is the phase as well as the amplitude of the sound pressure distribution over the diaphragm of the microphone. Since the problem of
DF R 0
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60 90 180 120
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0.16 0.25 0.4 0.6 3 1.0 1.6
-1 0 0 10
Sensitivity (dB)
d/λ
Figure 3.3 Microphone free-field correction: the sound pressure level on the diaphragm relative to the free-field level in the absence of the microphone, as a function of angle of incidence. Angles are measured relative to the normal to the diaphragm. DFR is the diffuse-field response, i.e. sound pressure level on the diaphragm in a diffuse field (random-incidence calibration); adapted from Bruel and Kjaer, 1973.
diffraction cannot be avoided for practical reasons of sensitivity, as has been explained, it is necessary to take account of the expected angle of incidence of sound upon a microphone during use. This has led to the so-called free-field calibration, which is a function of angle of incidence. Alternatively, if sound is assumed to be incident from all directions at once, then the properly weighted average of the free- field calibrations produces the random-incidence calibration. Such a weighted average is shown in Figure 3.3 as the diffuse-field response (DFR).
Yet another possibility exists. If a uniform pressure is imposed on the diaphragm (done in practice electrostatically), then a pressure response can be determined. The latter response is affected by the design of the backing electrode, the size and shape of the backing cavity, and the mass and tension of the diaphragm. It is thus possible to shape the high-frequency pressure response to compensate for the effective increase in pressure at the diaphragm due to diffraction. For example, if the pressure-response roll-off is shaped by design to just compensate for the increase of the free-field pressure at normal incidence, giving a combined response which is fairly flat for normally incident sound, then a free-field microphone is produced. Alternatively, the pressure response roll-off can be adjusted to compensate for the free-field increase at any angle of incidence, or it can be adjusted to compensate for the random incidence response, in which case a random-incidence or diffuse-field microphone is produced.
In summary, three types of calibration are recognised. These are free field, random incidence and pressure sensitivity. Microphones are commonly sold as (1) free field, generally meaning flat response for normal incidence, or (2) as random incidence, meaning generally flat response in a diffuse sound field characterised by sound of equal intensity incident from all directions. Alternatively, some sound level meters provide a filter network to allow simulation of diffuse field response for any
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0.01 0.1 1.0 10 100
Frequency (k Hz)
Sensitivity (dB re 1V Pa) ABC
Figure 3.4 Free-field condenser microphone sensitivities. Diaphragm diameters:
curve A, 25 mm; curve B, 12 mm; and curve C, 6 mm.
particular microphone. In some applications where diffraction is not present (such as when the microphone is mounted flush with the wall of a duct to measure turbulent pressure fluctuations), the pressure-response calibration only is used.
Both free-field and diffuse-field microphones are used for industrial noise measurement. When it is obvious from which direction the noise is coming, then a free-field microphone is used and pointed directly at the source. When it is not obvious where the noise is coming from or when there are noise sources all around the microphone, then best results are obtained by using a diffuse-field microphone and pointing it straight up into the air. In this case most sound will then be incident at 90E to the microphone axis, and as the diffuse-field response is reasonably close to the 90E incidence response for many microphones the measurement error is minimised. For more accurate results, the actual error can be compensated by using the microphone characteristics for a particular microphone, similar to those shown in Figure 3.3.
All microphones must trade sensitivity for frequency response. Frequency response is inversely related to the microphone diaphragm diameter D, while the sensitivity is directly related to the fourth power of the diameter, as may be inferred by reference to Equations (3.19) and (3.21). It can be seen that good high-frequency response is obtained at the expense of a rapid deterioration in sensitivity. The effect is illustrated in Figure 3.4, where the respective sensitivities of three free-field microphones, having diameters of approximately 25, 12 and 6 mm, are shown.
Fortunately, in the audio-frequency range, which is of interest here, it has been possible to produce, and make commercially available, microphones which have sufficient frequency response and sensitivity for most purposes; amplifiers are available which can adequately cope with their small output signals. Recent advances in microphone technology have resulted in 12 mm microphones that are 10 dB more sensitive than shown in Figure 3.4. Thus, 25 mm diameter microphones are not used very often any more as 12 mm microphones with similar sensitivity and better frequency response are available.