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A Study of the Effect of Positional Offset on the Calibration Results of the Free-Field Comparison Method
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摘要: 参考传声器和待测传声器定位而引起的偏差被认为是引起自由场比较法测量不确定度的重要组成部分。为了评估位置偏移对灵敏度和频率响应校准结果的影响情况，在250 Hz到20 kHz频率范围，通过控制校准过程中参考与待测传声器位置的水平和轴向偏差，将灵敏度级的校准结果与位移偏差进行最小二乘法拟合，定量分析每个频率下灵敏度级受定位水平、轴向偏移的影响结果，给出相应拟合曲线。并对拟合结果进行统计检验，根据拟合曲线的斜率和检验得到的显著性水平表明：频率增加，灵敏度级的校准结果受水平偏移的影响显著提升，在20 kHz处达到最大斜率0.016 dB/mm；不同频率点处灵敏度级对轴向偏差的影响效果不同，部分频率对轴向偏差不敏感。Abstract: Positional offsets of the reference microphone (REF) and the microphone to be tested (DUT) are considered to be an important component causing measurement uncertainty in the free-field comparison method. To assess the effect of positional offset on the sensitivity and frequency response calibration results, this paper quantitatively analyzes the effect of positional offset on the sensitivity level at each frequency by controlling the horizontal and axial offsets of the REF and DUT during the calibration process. A least-squares fit of the calibration results of the sensitivity level to the displacement offset is performed in the frequency range of 250 Hz to 20 kHz, and corresponding fit curves are provided. Statistical tests were also carried out on the fitting results. According to the slopes of the fitted curves and the significance levels obtained from the tests, it is shown that with increasing frequency, the influence of horizontal offset on the calibration results of the sensitivity level increases significantly, reaching a maximum slope of 0.016 dB/mm at 20 kHz. The effects of axial deviation on the sensitivity level vary at different frequency points, with some frequencies being insensitive to axial offset.
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Key words:
- metrology /
- microphones /
- free-field comparison method /
- sensitivity /
- frequency response
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图 1 频率响应曲线的中高频部分波动
Figure 1. Fluctuations in the mid- and high-frequency sections of the frequency response curve
图 2 传声器自由场比较法校准示意图
Figure 2. Schematic diagram of microphone calibration by the free-field comparison method
图 3 传声器的原点位置和位置偏移装置
Figure 3. Microphone origin position and positional offset control structure
图 5 水平偏移下的频率响应校准结果
Figure 5. Frequency response calibration results with horizontal offset
表 1 水平方向偏移分析结果表
Table 1. Results table for horizontal offset analysis
频率(Hz) A1i(dB/mm) B1i(dB) 概率P>F R12 250 −0.001 −25.72 0.000 0.007 315 −0.009 −25.66 0.713 0.293 400 0.002 −25.77 0.011 0.070 500 −0.003 −25.70 0.248 0.111 630 −0.003 −25.68 0.139 0.062 800 0.001 −25.77 0.275 0.006 1000 −0.001 −25.70 0.730 0.008 1250 0.000 −25.68 0.692 0.001 1600 −0.004 −25.63 0.898 0.116 2000 0.010 −25.73 0.131 0.298 2500 0.004 −25.65 0.011 0.082 3150 −0.001 −25.49 0.209 0.013 4000 −0.002 −25.50 0.622 0.032 5000 0.005 −25.53 0.435 0.177 6300 0.010 −25.62 0.057 0.263 8000 −0.002 −25.61 0.017 0.085 10000 −0.008 −25.55 0.200 0.579 12500 −0.014 −25.47 0.000 0.814 16000 −0.007 −24.88 0.000 0.713 20000 −0.016 −25.71 0.000 0.818 
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表 2 轴向方向偏移分析结果表
Table 2. Results table for axial offset analysis
频率(Hz) A2i(dB/mm) B2i(dB) 概率P>F R2i2 250 0.012 −25.71 0.000 0.60 315 0.017 −25.73 0.000 0.57 400 0.008 −25.77 0.004 0.37 500 0.013 −25.71 0.000 0.48 630 0.005 −25.71 0.208 0.08 800 0.010 −25.69 0.001 0.44 1000 0.003 −25.68 0.266 0.06 1250 −0.006 −25.71 0.061 0.17 1600 0.008 −25.67 0.008 0.32 2000 0.020 −25.58 0.000 0.49 2500 0.008 −25.63 0.023 0.24 3150 0.018 −25.45 0.000 0.53 4000 0.007 −25.55 0.033 0.22 5000 0.029 −25.48 0.000 0.73 6300 0.016 −25.47 0.001 0.42 8000 −0.007 −25.60 0.003 0.38 10000 0.028 −25.59 0.000 0.76 12500 0.004 −25.78 0.364 0.04 16000 0.015 −24.95 0.000 0.53 20000 0.020 −25.83 0.000 0.58
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