7.14 The electret microphone: sensitivity to variations in properties. One of the parameters involved in the output of the electret microphone is the permittivity of the electret. a. Calculate the sensitivity of the output to the relative permittivity of the electret. b. What is the error in the expected reading if the permittivity of the electret decreases by 5% due to aging or due to variations in manufacturing? Use the data in Example 7.6. Example 7.6: The electret microphone: design considerations Consider the design of a small electret microphone for use in cellular phones, made in the form of a cylinder 6mm in diameter and 3mm long to fit in a slim telephone. Internally, the designer has considerable flexibility as to the choice of materials and dimensions as long as they fit within the external dimensions. Assuming the protective external structure requires a thickness of 0.5mm, the diaphragm cannot be larger than 5mm in diameter. The thickness of the diaphragm depends on the material used. Assuming a polymer, a reasonable thickness is 0.5mm, and a tension of 2N/m can be easily supported by the structure. Polymers have relatively low permittivities, so we will assume a relative permittivity of 6 . The gap between the electret and the lower conducting plate will be taken as 0.2mm (the smaller the gap, the more sensitive the microphone). The ratio of specific heat in air is 1.4 (varies somewhat with temperature, but we will neglect that since the variation is rather smalli). The polymer can be charged at various levels, but the surface charge density cammot be very high. We will assume a charge density of 200C/m2. With these finction between the output voltage and the change in pressure using (7.30) : (retion between the output voltage and the change in pressure using (7.30): V=0s+s1ss1((P0/s1)+8T/A1)P. In this relation, if P0 is in pascals, P must also be in pascals. Numerically, V==8.85410120.5103+68.85410120.21032001060.2103(1.4101,325/0.2103+82/((0.0025)2)1)P3.733103P[V]. This is a sensitivity of 3.733mV/Pa. For a normal level of speech (45dB to 70dB), the pressure is 3.5103Pa to 6.3102Pa (see Example 7.1), producing an output of 13V to 235.2V. In general terms, the sensitivity can be improved by increasing the surface charge density or the area of the diaphragm or decreasing the gap, the permittivity, the thickness of the electret, or the tension in the diaphragm. However, one must be careful. With the given values, the electric field intensity in the gap as calculated from (7.27) is 2.657106V/m, which cannot be increased much since breakdown in air occurs at 3106V/m. Decreasing the gap will have the same effect as increasing the charge density. The results given here represent the upper limit on sensitivity that can be obtained. 7.14 The electret microphone: sensitivity to variations in properties. One of the parameters involved in the output of the electret microphone is the permittivity of the electret. a. Calculate the sensitivity of the output to the relative permittivity of the electret. b. What is the error in the expected reading if the permittivity of the electret decreases by 5% due to aging or due to variations in manufacturing? Use the data in Example 7.6. Example 7.6: The electret microphone: design considerations Consider the design of a small electret microphone for use in cellular phones, made in the form of a cylinder 6mm in diameter and 3mm long to fit in a slim telephone. Internally, the designer has considerable flexibility as to the choice of materials and dimensions as long as they fit within the external dimensions. Assuming the protective external structure requires a thickness of 0.5mm, the diaphragm cannot be larger than 5mm in diameter. The thickness of the diaphragm depends on the material used. Assuming a polymer, a reasonable thickness is 0.5mm, and a tension of 2N/m can be easily supported by the structure. Polymers have relatively low permittivities, so we will assume a relative permittivity of 6 . The gap between the electret and the lower conducting plate will be taken as 0.2mm (the smaller the gap, the more sensitive the microphone). The ratio of specific heat in air is 1.4 (varies somewhat with temperature, but we will neglect that since the variation is rather smalli). The polymer can be charged at various levels, but the surface charge density cammot be very high. We will assume a charge density of 200C/m2. With these finction between the output voltage and the change in pressure using (7.30) : (retion between the output voltage and the change in pressure using (7.30): V=0s+s1ss1((P0/s1)+8T/A1)P. In this relation, if P0 is in pascals, P must also be in pascals. Numerically, V==8.85410120.5103+68.85410120.21032001060.2103(1.4101,325/0.2103+82/((0.0025)2)1)P3.733103P[V]. This is a sensitivity of 3.733mV/Pa. For a normal level of speech (45dB to 70dB), the pressure is 3.5103Pa to 6.3102Pa (see Example 7.1), producing an output of 13V to 235.2V. In general terms, the sensitivity can be improved by increasing the surface charge density or the area of the diaphragm or decreasing the gap, the permittivity, the thickness of the electret, or the tension in the diaphragm. However, one must be careful. With the given values, the electric field intensity in the gap as calculated from (7.27) is 2.657106V/m, which cannot be increased much since breakdown in air occurs at 3106V/m. Decreasing the gap will have the same effect as increasing the charge density. The results given here represent the upper limit on sensitivity that can be obtained