Ccauv.a-k4 Final Report - Kcdb

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Final Report on the Key Comparison CCAUV.A-K4 Abstract The Key Comparison CCAUV.A-K4 has been carried out under the auspices of the Consultative Committee for Acoustics, Ultrasound and Vibration (CCAUV) of the International Bureau of Weights and Measures (BIPM). The participating NMI’s are the Instituto Nacional de Metrologia, Normalizacao e Qualidade Industrial (INMETRO, Brazil), the Centro Nacional de Metrología (CENAM, Mexico), the Laboratoire National de Métrologie et d'Essais (LNE, France), the National Metrology Institute of Japan (NMIJ, Japan), the Korea Research Institute of Standards and Science (KRISS, Korea), and the Physikalisch-Technische Bundesanstalt (PTB, Germany). The role of the Pilot laboratory was undertaken by the DFM and CENAM. The measurements took place between January 2007 and February 2008. The time schedule was organized in a single star configuration. Two LS2aP microphones were circulated. This report includes the measurement results from the participants, information about their calibration methods, and the analysis leading to the assignation of the degrees of equivalence. Prepared by Salvador Barrera-Figueroa, Lars Nielsen and Knud Rasmussen Danish Primary Laboratory of Acoustics Danish Fundamental Metrology Ltd. Matematiktorvet 307 DK-2800 Kgs. Lyngby, Denmark Andrés E. Pérez Matzumoto and José Noé Razo Razo Centro Nacional de Metrología Carretera a Los Cués km 4.5 El Marqués, Querétaro, México. CP 76246 Page 1 of 44 Content 1 Introduction 3 2 Comparison protocol 3 3 Travelling microphones 4 4.1. Calibration methods 5 4 Calibration methods and reported results 5 4.2. Microphone parameters 13 4.3. Microphone sensitivities 14 5 Analysis of the results 17 5.1. Degrees of equivalence 17 5.2. Equivalence and consistence of results 18 6 Results 20 6.1. Reference values 20 6.2 Degrees of equivalence per laboratory 20 6.3 Degrees of equivalence 25 7 Conclusions 27 8 References 27 Appendix A — Determination of the correlation coefficients 28 Appendix B — INMETRO corrections to reported results 29 Appendix C — Uncertainty budgets 30 Page 2 of 44 1 Introduction The CCAUV.A-K4 is a Key comparison realised under the auspices of the CCAUV-BIPM. The standards circulated among the laboratories were two LS2aP microphones of the type Brüel & Kjær 4180. Both microphones were also standards used for the CCAUV.A-K3. The microphones had to be calibrated using the reciprocity technique under free-field conditions in the frequency range from 1 kHz to 31.5 kHz (optionally up to 40 kHz), and the open-circuit free-field sensitivity level had to be reported at the nominal preferred 1/3rd octave band. The participating NMIs are the Instituto Nacional de Metrologia, Normalizacao e Qualidade Industrial (INMETRO, Brazil), the Centro Nacional de Metrología (CENAM, Mexico), the Laboratoire National de Métrologie et d'Essais (LNE, France), the National Metrology Institute of Japan (NMIJ, Japan), the Korea Research Institute of Standards and Science (KRISS, Korea), and the Physikalisch-Technische Bundesanstalt (PTB, Germany). The National Physical Laboratory (NPL, UK) and the National Institute of Standards and Technology (NIST, USA) were included in the original time schedule, however they resigned participating during the course of the comparison. The time schedule was organized in a single star configuration. The role of the Pilot laboratory was undertaken by the DFM and CENAM. The measurements took place between February 2007 and February 2008. This report includes the measurement results from the participants, information about their calibration methods, uncertainty budgets, and the analysis leading to the assignation of the degrees of equivalence. 2 Comparison protocol The September 2006 Draft technical protocol for the key comparison CCAUV.A-K4 was presented during the 5th meeting of CCAUV on September 2006, and the subsequently prepared October 2006 Draft was used for this key comparison. This protocol is based on the CCAUV.A-K3 protocol with some additional clarifications. It was emphasized that the calibrations had to be performed at the preferred nominal frequencies rather than the exact frequencies. It was also recommended that the laboratories should report the results using three decimals. In this report, results are presented in the same way they were declared. The microphones were transported in all cases by means of a courier company selected by each participant. The container used under the courier transportation was provided by DFM. The actual participants are listed in table 1: Table 1. Participants in the CCAUV.A-K4 key comparison Participant Acronym Country Country Regional Metrology code Danish Primary Laboratory for Acoustics. DFM Denmark DK Organization EURAMET Danish Fundamental Metrology LTD. Centro Nacional de Metrología CENAM Mexico MX SIM Korea Research Institute of Standards KRISS Korea KR APMP National Metrology Institute of Japan NMIJ Japan JP APMP Laboratoire national de métrologie et LNE France FR EURAMET and Science d'essais Physikalisch-Technische Bundesanstalt PTB Germany DE COOMET (EURAMET) Instituto Nacional de Metrologia, INMETRO Brazil BR SIM Normalizacão e Qualidade Industrial Page 3 of 44 3 Travelling microphones Two LS2 microphones, Brüel & Kjær 4180, serial numbers 1395455 and 1395456, were supplied by DFM and circulated among the participants. The DFM has monitored the microphones since the beginning of the comparison. The monitoring consisted of free-field reciprocity calibrations and also pressure reciprocity calibrations. The DFM also performed free-field reciprocity measurements from 1 kHz as stated in the protocol. Figure 1 shows DFM’s results of the control calibrations for some selected frequencies during the comparison span. Figure 1 also shows the difference with respect to a common average for the two microphones over the whole frequency range. No significant trend was observed in the control calibrations. Microphone 4180.1395455 Sensitivity difference (dB) 0.1 0 -0.1 -0.2 0 10 Normalised sensitivity (dB) Microphone 4180.1395456 1 0.2 0.1 0 -0.1 -0.2 02/07 06/07 09/07 12/07 04/08 date 0.2 0.1 0 -0.1 -0.2 0 10 Frequency (kHz) Microphone 4180.1395455 10 Normalised sensitivity (dB) Sensitivity difference (dB) 0.2 1 10 Frequency (kHz) Microphone 4180.1395456 0.2 0.1 0 -0.1 -0.2 02/07 06/07 09/07 12/07 04/08 date Figure 1. Upper charts: Difference of the sensitivity level obtained at each calibration at DFM with respect to their common average for each microphone as a function of frequency (DFM’s uncertainty bounds are shown). Lower charts: Changes in the sensitivity level of the microphones as a function of time. The sensitivity level has been normalized to the level of the first measurement. Blue line: 1 kHz; red line 2 kHz; black line 5 kHz; and magenta line 10 kHz. Page 4 of 44 4 Calibration methods and reported results 4.1. Calibration methods A description of the calibration methods and the reporting of results of each laboratory is given below as submitted by each laboratory. No editing of the contents but a small amount of reformatting has been performed. Consequently, table, equation and figure numbers and references do not follow the numbering of the report. DFM: Free-field calibration of LS2 microphones. The free-field sensitivity of LS2 microphones are determined by conducting a reciprocity calibration in accordance with IEC 61094-3 [1]. The calibrations were performed in a small, specially designed anechoic room of about 1.4 m × 1.50 m × 1.7 m free dimensions. The reflection coefficient of the lining material is below -40 dB above 1 kHz. Measurement method The electrical transfer impedance is measured in linear frequency steps of 120 Hz from 3 kHz (initially 960 Hz) to 51 kHz. Due to the unavoidable poor signal-to-noise ratio and reflections from the environment a special technique has been developed based on narrow-band filtering in both frequency- and time domain [2] Filtering in the frequency domain is applied by using a B&K Pulse Analyzer in the SSR-mode when measuring the transfer impedance. To enter the time domain by applying an inverse FFT-technique to the measurement result, the missing low frequency values down to 0 Hz are estimated as follows: The average pressure response (normalized at 250 Hz) has been determined for a large number of BK type 4180 microphones. The free-field to pressure sensitivity diffraction has been calculated as well using the Boundary Element Method [3]. The missing values of the transfer impedance from 120 Hz to 3 kHz (resp. 1kHz) are then estimated from the above normalized responses, the absolute pressure sensitivity of the involved microphones at the actual environmental conditions and assuming an acoustic centre of 4.74 mm. To avoid sudden jumps in the transfer impedance the calculated values are blended into the measurement results over a frequency range of 1200 Hz. Above 51 kHz the measurements are extended to 70 kHz by a linear extrapolation of the measurement results from 48 – 51 kHz in order to avoid an abrupt high-frequency cut-off when applying the inverse FFT-technique. Next, in the time domain, a time window of 0.9 ms is applied to eliminate the unwanted part of the signal and the remaining signal is converted back to the frequency domain. The final free-field sensitivities are then calculated in accordance with IEC 61094-3 using the above manipulated transfer impedances. Page 5 of 44 Acoustic centres The acoustic centres used are derived from a linear regression analysis of the above manipulated transfer impedances at four distances (corrected for air attenuation). This has been done for a large number of microphones and the average value has been expressed as a polynomial slightly different from the values in reference [4]. Correction to reference environmental conditions In general, calibrations will be performed at the following environmental conditions: + + + a static pressure of 101.325 ± 3 kPa a temperature of 23 ± 1 °C and a relative humidity of 50 ± 15 %RH The calibration results are corrected to reference environmental conditions by applying the individual static pressure- and temperature coefficients valid for the pressure sensitivity, i.e., the additional influence of the radiation impedance has been neglected. Correction to nominal frequencies The correction of the measured sensitivities in steps of 120 Hz to the required nominal frequencies has been performed by a simple linear interpolation between the measured sensitivities. References [1] IEC 61094-3, 1995. Measurement microphones – Part 3: Primary method for free-field calibration of laboratory standard microphones by the reciprocity technique. [2] S. Barrera Figueroa, New methods for transducer calibration: Free-field reciprocity calibration of condenser microphones, PhD thesis, Ørsted•DTU, Technical University of Denmark, 2003. [3] S. Barrera Figueroa, K. Rasmussen, and F. Jacobsen, On experimental determination of the free-field correction of laboratory standard microphones at normal incidence, Metrologia 44, pp 5763 (2007). [4] S. Barrera Figueroa, K. Rasmussen, and F. Jacobsen, The acoustic center of laboratory standard microphones, Journal of the Acoustical Society of America 120, pp 2668-2675 (2006). CENAM: a) Procedure: 510-AC-P.105: “Calibración primaria de micrófonos patrón mediante la técnica de reciprocidad en campo libre” (Primary calibration of standard microphones by the reciprocity technique in free-field). b) Instrumentation: + + + + + + Microphone B&K Type 4180, SN: 1627796 Microphone B&K Type 4180, SN: 1893458 Reciprocity apparatus B&K Type 5998, SN: 2040462. Polarization voltage meter B&K Type 5981, SN: 1468333. Signal Analyzer B&K Type 3560D/3110, SN: 2415164. Measuring Amplifier B&K Type 2610, SN: 919975 Page 6 of 44 + + Calibrator Fluke Type 5700A, SN: 6230304. Environmental Monitoring System CENAM –SN 063. c) Measurement: c.1) Determination of the free-field sensitivity modulus The open circuit sensitivity is determined by means of the reciprocity technique according to IEC 61094-3, [1], using a set of three microphones of the same type, {1, 2, 3}. The microphone under test is sequentially acoustically coupled in pairs, {1-2, 1-3 and 2-3}, at known distances within the two microphones in a field essentially free of acoustic reflections (free-field). The sensitivity of the microphone is obtained from the measurements of the electrical transfer impedance function, and the calculation of the acoustical transfer impedance between the three pairs of microphones. Electrical transfer impedance is measured in the frequency range from 1 152 Hz to 52 992 Hz with a 128 Hz resolution, using a dual channel digital signal analyzer. A cleaning procedure, based on time selective window, is applied to reduce acoustic reflections, microphone interference and cross-talk between the measurement channels. Sensitivity levels for 1/3 octave frequencies above 3 kHz are calculated by linear interpolation from the set of measurement results in the frequency range given above, according to: M f , freq = M f , f low + M f , f high − M f , f low f high − f low ( freq − flow ) (1) where: freq : frequency of interest in [Hz]; flow: frequency immediately below freq , in [Hz] in the set of measurement result; fhigh: frequency immediately above freq , in [Hz] in the set of measurement result; Mf,freq: sensitivity level corresponding to the frequency freq , in [dB re 1V/Pa]; Mf,flow: sensitivity level corresponding to the frequency flow , in [dB re 1V/Pa] Mf,fhigh: sensitivity level corresponding to the frequency fhigh , in [dB re 1V/Pa] Free-field sensitivity levels for frequencies below 3 kHz are calculated through a free-field correction, determined from measured free-field and pressure sensitivity levels. A ninth degree polynomial fitting is calculated for each free-field correction, obtained from repeated measurements. For frequencies below 500 Hz it is assumed that both sensitivity levels, free field and pressure, are equal. Then the free-field correction calculated, through the polynomial fitting, for frequencies from 1 kHz to 3 kHz is used to determine the corresponding free-field sensitivity level. Four different separation distances, between each pair of microphones, are used in each measurement; these are given in table A: Table A: Separation distances used during the electrical transfer impedance measurements, for each pair of microphones. Number Distance / mm 1 160.03 2 189.83 3 220.03 4 249.40 Corrections for the position of the acoustic centre are applied, and the corresponding correction factors for static pressure and temperature are used to obtain the sensitivity at reference conditions (101.325 kPa and 296.15 K (23 ºC)). Polarizing voltage of 200 V ± 0.04 V is applied to both, transmitter and receiving, measuring channels. Page 7 of 44 c.2) Acoustic centre and environmental coefficients Positions for acoustic centre are obtained from reference [2]. Static pressure coefficients are determined for each microphone using the pressure sensitivity levels obtained by the reciprocity technique for five static pressures from 81 kPa to 101.4 kPa. Later a linear regression fitting is used to obtain the corresponding coefficient for frequencies from 125 Hz up to 31.5 kHz. Temperature coefficient is calculated using the typical value given by the manufacturer and the polynomial approximation given in [3]. The Environmental conditions of measurement are shown in table B Table B: Environmental conditions of measurement for each standard Microphones 4180.1395455 4180.1395456 Static Pressure: 80.97 ± 0.35 kPa 81.00 ± 0.31 kPa Temperature: 22.47 ± 1.89 °C 22.02 ± 1.44 °C Relative Humidity: 32.50 ± 9.55 % 36.30 ± 7.09 % d) Results a e) Uncertainty: The expanded measurement uncertainty is obtained multiplying the standard combined uncertainty by a coverage factor, k = 2, which gives a confidence level of al least 95 %, under the assumption that the probability distribution function for the measurand is approximately normal. The measurement uncertainty is estimated according to the Mexican National Standard NMX-CH140-IMNC-2002: “Guía para la Expresión de la Incertidumbre en las Mediciones”, which is equivalent to the “Guide for the Expression of Uncertainties in Measurement: BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML (1995)”. The uncertainty value given in this certificate, does not take into account the contributions due to long term stability, drift and transportation for the calibrated instrument. f) Traceability: Calibration results are traceable to the kilogram (kg), Kelvin (K), second (s), metre (m) and ampere (A), base units of the SI, through the Mexican National Standards for Barometric Pressure (CNM-PNM-24), Temperature (CNM-PNE-2), Time (CNM-PNE-1), Length (CNM-PNM-2) and Intensity of Alternating Current (CNM-PNE-10), maintained by CENAM. References: [1] IEC International Standard 61094/3. Measurement microphones – Part 3: Primary method for freefield calibration of laboratory standard microphones by the reciprocity technique”. a Note: CENAM results are presented in the next sub-section. Page 8 of 44 [2] Salvador Barrera-Figueroa, Knud Rasmussen and Finn Jacobsen, “The acoustic center of laboratory standard microphones,” J. Acoust. Soc. Am. 120 (5), 2668-2675 (2006). [3] Brüel & Kjær. Technical Review No. 1- 2001. Properties and calibration of laboratory standard microphones & Uncertainties in microphone frequency response. ISSN 0007-2621. 2001. KRISS: The dimensions of the anechoic chamber used for the free-field calibration are 2.3 m (depth), 2.2 m (width), and 2.4 m (height). The microphones are mounted on 12.7 mm diameter vertical rods. The distance between two microphones is adjusted by a computer controlled servo motor and encoder with the resolution of 1 mm. The voltage ratio functions are measured using Reciprocity Calibration Apparatus (B&K 5998) and PULSE (B&K 3560C). The frequency is swept from 0.8 kHz to 51 kHz in linear frequency steps of 120 Hz. The number of measurement at each frequency is increased until the statistical uncertainty of the measurement response (i.e., twice the standard deviation) is less than 0.01 dB. A perfect free-field facility of no interference from walls and obstacles is not readily available in practice, so it has led to the use of signal processing techniques to eliminate the reflections from boundaries. In addition, an electrical interference noise due to imperfect insulation of measuring instruments, so-called cross-talk, should be eliminated with the same manner. The time selective windowing technique for effective removal of multi-path noises is widely utilized for reciprocity calibrations, but it is still short in overcoming the limitations imposed by overlapped signals, in particular at low frequencies. Based on FFT analysis, the leakage due to the limited frequency range makes the overlap problem worse, not to be perfectly separated. Instead of conventional low pass filter designed to have a flat response in the frequency range of interest, Chebyshev window shaped function is selected because of its low sidelobe levels. After multi-path noise removal, the voltage ratio functions are restored by compensation with inversing filtering. The free-field sensitivity level at the nominal preferred 1/3rd octave centre frequencies is calculated with the linear interpolation between those at two adjacent frequencies. The free-field sensitivity levels near 1 kHz are estimated by the interpolation technique between the pressure sensitivity levels at the low frequencies and the free-field sensitivities at the high frequencies. The distances between two microphones are varied from 100 mm to 300 mm with 50 mm step. The final results are the average of these five measurements. The acoustic centres used for the sensitivity calculation are the nominal values given in IEC 61094-3:1995. The acoustic centres for the higher frequencies were obtained by extrapolation method. NMIJ: The free-field sensitivity was determined in compliance with IEC 61094-3:1995, using a reciprocity calibration system developed by NMIJ. In the system, both the signal generation and the signal processing were executed by a dual-channel FFT analyzer, model CF-5220 of ON0 SOKKI Co. Signal to noise ratio was improved by the synchronous waveform averaging method. The insert voltage technique was used to cancel the effect of the gain and impedance of an electrical circuit. The calibration was performed by using software of our own making. Sound absorbing wedges made of glasswool are attached on the inside walls, ceiling and floor of an anechoic chamber. The inner space of the anechoic chamber is (W) 9.5 m by (L) 8.0 m by (H) 7.2 m. The cutoff frequency of the anechoic chamber is 40 Hz. The temperature and humidity inside the anechoic chamber are well controlled (23.0 ± 0.5 ºC and 50 ± 5 %, respectively). Page 9 of 44 The sensitivity was corrected to the reference environmental conditions by using K. Rasmussen's method [I]. At 31.5 kHz, only pressure dependency has been corrected because of no reliable temperature coefficients. At 40.0 kHz, neither pressure nor temperature dependency has been corrected because of no reliable pressure and temperature coefficients. The calibrations were normally carried out using only B&K type 4180 microphones. At low frequencies below 5000 Hz, however, type WS2 microphones (B&K type 4165 and type 4190) with cavity rings (B&K UA0825) were also used to achieve high signal to noise ratio because the sensitivity of these microphones was about 10 dB higher than that of type 4180 microphones. B&K type 4165 microphones were just used as the transmitter microphones and B&K type 4 190 microphones were used as the reciprocal microphones. To minimize the influence of sound reflection, the virtual pulse technique was applied [2, 3]. In this technique, firstly the voltage transfer function (VTF) between the input terminal of the transmitter microphone and the output terminal of the receiver microphone was measured by using swept-sine signal. The bandwidth of the swept-sine signal was 200 Hz (1 kHz - 1.6 kHz), 400 Hz (2.0 kHz - 5 kHz), 2 kHz (6.3 kHz - 12.5 kHz) and 4 kHz (16 kHz - 40 kHz), respectively. The centre frequency of swept-sine signal was equal to each measurement frequency. Secondly, the pulse response of VTF was computationally calculated by multiplying the virtual pulse signal by the VTF in the frequency domain. The influence of sound reflection could be minimized by the convolution of the pulse response and a window function [2, 3]. The acoustic centres were calculated from the VTFs by using least square method. In the VTFs measurements, the actual distances were set to 10, 15 and 20 cm (1000 Hz - 5000 Hz) and 15, 20 and 25 cm (6300 Hz - 40000 Hz), respectively. The microphones used for determining the acoustic centre were the same as the calibration. The influence of reflection was similarly minimized by the virtual pulse method [2, 3]. Values of the air attenuation coefficients were obtained according to IEC 61093-3 Annex B. Density of air was calculated in compliance with IEC 61094-2, Annex F.1 (Density of humid air). Reference [1] K. Rasmussen, "The static pressure and temperature coefficients of laboratory standard microphones," Metrologia 36 (1999). [2] T.Fujimori, "Free-field calibration of "1/2-in" microphone," 3rd. joint meeting of ASA and ASJ (1996). [3] T. Fujimori et. al, "Measurement of acoustic center position of LS2P Laboratory standard microphones," J. Acoust. Soc. Jpn. ( J ) 58, 579-585 (2002). LNE: According to the technical protocol of the key comparison CCAUV.A-K4 (October 2006), this report completes the two standard calibration certificates issued from LNE after the key comparison CCAUV.A-K4 in order to provide additional information on the calibration method. All the pieces of information required in the technical protocol (§ reporting results) are listed below in the following paragraphs. Page 10 of 44 The environmental conditions during the calibrations. Pressure : 1000.0 to 1004.5 hPa Temperature : 22.8 to 23.2 ° C Relative humidity : 44 to 50 % The actual distance(s) used between the microphones during the calibrations. The results given in the calibration certificate correspond to the mean values of three calibrations obtained using three distances. The used distances between microphones body (not including frontal cavity depth) are: 25 cm, 30 cm and 35 cm. Values of the temperature and pressure coefficients of the microphones used in the calculations. The temperature and pressure coefficients of the microphones are calculated using the polynomial constants given by the manufacturer (technical review N° 1 – 2001) and using a constant microphone resonant frequency of 23 kHz. A summary of the uncertainty calculation and the overall uncertainties calculated for a coverage factor of k=2. The budget was sent before the comparison starts. The effect on the reported results. Air density is calculated using the polynomial formula given in Report PL11b, 1997 DTU. The effect on sensitivity calculation seems to be lower than 0.0015 dB. Air attenuation coefficient is calculated using the polynomial formula given in Report PL11b, 1997 (DTU). The effect on sensitivity calculation seems to be lower than 0.0005 dB. The values of the acoustic centres used in the calculation. Acoustic centres used in calculation are those given in IEC 61094-3:1995. For frequencies greater than 20 kHz, this value is set to 0 mm. Calibration results using three decimals (if not already given in the certificate). Calibration results are given with 3 decimals in the calibration certificate and with a full resolution in the additional results spreadsheet. The interpolation technique used if the actual measurements are not performed at the required frequencies. None interpolation technique is used: calibrations are carried out at the required frequencies. The technique used to estimate the free-field sensitivity at low frequencies if a direct calibration is not available. Free field calibrations are carried out at the all the nominal preferred 1/3-octave frequencies from 1000 to 31500 Hz. However in order to provide acoustical disturbances filtering, calibration requires additional frequency points which are measured for frequencies greater than 950 Hz and estimated above. That estimation involves the individual pressure sensitivity of each microphone and the diffraction correction given in IEC/TS 61094-7. Page 11 of 44 The effect of the diffraction correction is lower than 0.01 dB on the free-field sensitivity at 1 kHz and negligible for the other frequencies. PTB: “Methodology for free field calibration CCAUV-A-K4 The calibration was performed as a reciprocity calibration according to IEC 61094-3 in an electrically shielded anechoic chamber with a net volume of about 15 m3 and free dimensions of about 2.0 x 2.0 x 3.7 m3. The microphone mounts were vertically placed half-inch hollow tubes holding the receiver preamplifier (B&K 2645) and the transmitter housing. An essentially constant voltage of approximately 6 V (rms) was directly fed to the terminals of the transmitter housing and measured by one channel of a dual channel FFT analyzer type Ono Sokki 6400 which also provided the transmitter voltage and performed a phase-locked averaging of the input signals. The other channel of the analyzer was connected to the receiver chain, consisting of the preamplifier type B&K 2645, a measuring amplifier type B&K 2636 and a third-octave filter type B&K 1617. The gain of the receiver chain, including the loading of the receiver microphone by the preamplifier, was determined using the insert voltage technique. The analyzer measured the ratio of the FFT spectra of both channels. In order to calculate the transmitter current, the effective capacitance of the transmitter microphones was measured for all frequencies by means of a capacitance bridge type QuadTech 7600 using a specific microphone housing. The electrical transfer impedance was then calculated from the spectral ratio, the receiver channel gain and the effective transmitter microphone capacitance. The polarization voltage for the transmitter microphone was provided by a modified microphone front-end type Norsonic 336, for the receiver microphone it was generated within the B&K 2636 measuring amplifier. The polarization voltages were checked by a differential voltmeter type Fluke 893A. For each measurement frequency several electrical transfer impedance measurements were performed in linear distance steps, distance ranges and number of steps are given in the certificates. The electrical transfer impedance per frequency was finally derived from a linear regression analysis of the electrical transfer impedance over the microphone distance. The open circuit free-field sensitivity was calculated using the formulae and data given in the current edition of IEC 61094-3 and transformed to the reference conditions, see certificate. Because all calibrations were performed at the required frequencies, no interpolation technique was applied. INMETRO: The basic procedure to calibrate microphones in free-field is described in the international standard IEC 61094-3. The calibration method used by INMETRO employs digital signal processing techniques to identify and to minimize the effect of the components that interfere in the determination of the sensitivity of the microphones. Among these components, crosstalk, multiple backscattering and sound reflections inside the anechoic chamber are considered. The crosstalk was suppressed using the subtraction technique. A correction file including the magnitude and phase response of a dummy microphone with similar capacitance to the B&K4180 is first Page 12 of 44 obtained. Then, all voltage measurements of the receiver microphone are corrected by the subtraction of this correction file. This procedure allows the suppression of this specific component, which interferes most strongly in the result of the reciprocity method in free field. The multiple backscattering between the microphones and the other sound reflections present in the impulse response of the voltage output of the receiver microphone were suppressed by using a time-selective signal processing technique. A hybrid non-symmetric time-window function formed by the combination hanning-rectangular-hanning with width of respectively 2 ms, 11 ms, 0.85 ms was used for the time-selection of the direct sound. The measurements of the electrical impedance were carried out at the distances between the microphones of 170 mm, 200 mm, 240 mm and 300 mm. The analyzer was configured for a resolution of 1.47 Hz between frequency bins. The interpolation technique used to obtain the sensitivities at the preferred nominal frequencies was the simple arithmetic mean between the results measured at the adjacent lower and upper frequency bins. Table 1 presents the values of the used acoustic centres for the determination of the sensitivity of the B&K4180 microphones serial numbers 1395455 and 1395456. Table 1 – Acoustic centres in metres. a The measured sensitivities at the environmental conditions of the laboratory were corrected to the reference environmental conditions. The correction method used is the one described in IEC 610943 (1995) for measurements up to 31.5 kHz. This same correction method was also applied up to the frequency of 40 kHz. INMETRO used the values [of the temperature and static pressure coefficients] described in Rasmussen, Metrologia 36 (1999). 4.2. Microphone parameters Besides the open-circuit, free-field sensitivities of the microphones, the protocol requested that the laboratories should submit additional microphone parameters: Values of the temperature and pressure coefficients used in the calculations, and values of the acoustic centres used in the calculation, The values of the temperature and pressure coefficients reported by each laboratory are given in the following tables 2 and 3. The values of the acoustic centre are given in the table 4 below. Table 2. Microphone parameters 4180.1395455 DFM Front cavity depth (mm) CENAM KRISS NMIJ LNE PTB INMETRO 0.488 0.502 0.516 N.R. N.R. N.R. 0.421 Temp. coeff. at 250 Hz (dB/K) -0.0015 -0.002 -0.00546 -0.002 -0.0012 -0.0012 -0.0012 Static press. coeff. at 250 Hz (dB/kPa) -0.0057 -0.00578 -0.00116 -0.006 -0.0052 -0.0052 -0.0052 21800 21603 22000 N.R. 23000 21400 N.R. Resonance frequency (Hz) a Note: This table is omitted here. The acoustic centres are presented in the following section. Page 13 of 44 Table 3. Microphone parameters 4180.1395456 DFM Front cavity depth (mm) Temp. coeff. at 250 Hz (dB/K) Static press. coeff. at 250 Hz (dB/kPa) Resonance frequency (Hz) CENAM KRISS NMIJ LNE PTB INMETRO 0.514 0.508 0.539 N.R. N.R. N.R. 0.500 0.0004 -0.002 -0.00546 -0.002 -0.0012 -0.0012 -0.0012 -0.0059 -0.00613 -0.00116 -0.006 -0.0052 -0.0052 -0.0052 21200 21191 22000 N.R. 23000 21400 N.R. Table 4. Acoustic centre (in mm) as a function of frequency reported by each laboratory. Frequency (Hz) 4.3. DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 4.56 4.42 5.00 4.50 5.00 — 5.00 1250 4.50 4.37 4.90 4.40 4.90 — 4.90 1600 4.41 4.28 4.80 4.30 4.80 — 4.80 2000 4.30 4.18 4.70 4.20 4.70 — 4.70 2500 4.14 4.04 4.40 4.00 4.40 4.00 4.40 3150 3.92 3.84 4.20 3.80 4.20 4.80 4.20 4000 3.61 3.57 3.90 3.50 3.90 2.10 3.90 5000 3.23 3.23 3.60 3.20 3.60 2.70 3.60 6300 2.74 2.80 3.20 2.80 3.20 3.10 3.20 8000 2.15 2.28 2.80 2.40 2.80 2.60 2.80 10000 1.57 1.76 2.30 1.90 2.30 1.90 2.30 12500 1.03 1.27 1.80 1.30 1.80 1.40 1.80 16000 0.60 0.83 1.20 0.70 1.20 0.90 1.20 20000 0.37 0.51 0.50 0.40 0.50 0.60 0.50 25000 0.01 0.03 -0.3 -0.30 0.00 0.20 -0.01 31500 -0.92 -0.88 -1.2 -1.10 0.00 -1.00 -0.87 40000 -1.42 -1.30 -2.2 -2.40 -1.20 -1.37 — Microphone sensitivities Each laboratory reported their results after their own measurement round. Once all data was gathered, a preliminary analysis was made, and it showed that there were some discrepancies among laboratories. A few laboratories were asked to review their submission, and to resubmit if it was necessary, with an explanation of the reason for the review. All but one laboratory (NMIJ) declined to resubmit. NMIJ sent the reviewed data with the following explanation. “NMIJ found two errors and corrected the free-field sensitivity levels and acoustic centres accordingly. (1) As described in Sec. 4.1, NMIJ used the virtual pulse method to minimize the influence of sound reflection. At 16 kHz and above, the delay time to separate the direct sound from the reflected sound was wrongly set to be 5 ms instead of correct 0.5 ms. Therefore, the influence of sound reflection among the transmitter and receiver microphones still remained in the VTF (voltage transfer function). Acoustic centres were also incorrect due to the same reason. (2) At 31.5 kHz, unintended data were acquired from the FFT analyzer because the frequency was specified by mistake. The following tables show frequency dependence of free-field sensitivity levels for each microphone and values of the acoustic centres before and after correction.” Page 14 of 44 The open-circuit, free-field sensitivity level reported by each laboratory for each microphone at each frequency is given in the tables 5 and 6 below. The sensitivity level is given in dB re 1 V/Pa. The uncertainties in dB declared by each laboratory are listed in table 7. Table 5. Free-field sensitivity level of the microphone 1395455 in dB re 1 V/Pa Frequency (Hz) DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 -38.364 -38.386 -38.390 -38.351 -38.356 — -38.375 1250 -38.317 -38.347 -38.350 -38.319 -38.299 — -38.260 1600 -38.236 -38.272 -38.280 -38.250 -38.205 — -38.313 2000 -38.120 -38.159 -38.180 -38.128 -38.093 — -38.137 2500 -37.938 -37.981 -38.020 -37.957 -37.923 -38.017 -37.875 3150 -37.650 -37.689 -37.750 -37.676 -37.644 -37.815 -37.599 4000 -37.218 -37.233 -37.310 -37.243 -37.207 -37.206 -37.258 5000 -36.578 -36.575 -36.680 -36.619 -36.594 -36.659 -36.532 6300 -35.572 -35.593 -35.740 -35.603 -35.587 -35.701 -35.531 8000 -34.100 -34.148 -34.240 -34.145 -34.140 -34.239 -34.191 10000 -32.312 -32.378 -32.500 -32.362 -32.360 -32.425 -32.274 * 12500 -30.364 -30.428 -30.570 -30.411 -30.428 -30.513 -30.204* 16000 -29.100 -29.077 -29.300* -29.197 -29.146 -29.235 -29.169 20000 -30.111 * -30.220 -30.132 -30.101 -30.174 -30.131 25000 -33.103 -32.964 -33.070 -33.048 -32.993 -33.153 -33.154 31500 -37.101 * -36.960 -37.043 -37.018 -37.139 -37.183 40000 -42.392 -42.121 -42.080 -42.321 -42.517 -42.426 -30.010 -36.880 — * Note: The values marked with * have been excluded from the calculation of the Key Comparison Reference value (see 5.2) Table 6. Free-field sensitivity level of the microphone 1395456 in dB re 1 V/Pa Frequency (Hz) DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 -38.359 -38.417 -38.370 -38.356 -38.345 — -38.350 1250 -38.313 -38.383 -38.340 -38.320 -38.297 — -38.250 1600 -38.231 -38.315 -38.270 -38.234 -38.206 — -38.307 2000 -38.114 -38.206 -38.170 -38.133 -38.092 — -38.121 2500 -37.939 -38.026 -38.000 -37.963 -37.927 -37.965 -37.857 3150 -37.671 -37.731 -37.730 -37.683 -37.653 -37.752 -37.593 4000 -37.235 -37.255 -37.290 -37.236 -37.200 -37.136 -37.229 5000 -36.574 -36.579 -36.670 -36.590 -36.560 -36.536 -36.471 * -35.569 -35.548 -35.556 -35.457 6300 -35.560 -35.582 -35.720 8000 -34.054 -34.103 -34.170 -34.076 -34.068 -34.070 -34.073 10000 -32.202 -32.268 -32.370 -32.230 -32.227 -32.182 -32.079 * 12500 -30.171 -30.225 -30.370 -30.194 -30.207 -30.172 -29.909* 16000 -28.853 -28.819 -29.040* -28.908 -28.881 -28.840 -28.856 20000 -29.951 * -30.040 -29.970 -29.937 -29.929 -29.977 25000 -33.092 -32.987 -33.060 -33.056 -32.994 -33.114 -33.230 31500 -37.196 * -36.994 -37.100 -37.152 -37.123 -37.185 -37.385* 40000 -42.468 -42.231 -42.220 -42.403 -42.487 -42.606 -29.852 — * Note: The values marked with * have been excluded from the calculation of the Key Comparison Reference value (see 5.2) Page 15 of 44 Table 7. Expanded uncertainties in dB using a coverage factor of k=2, as declared by the participant laboratories Frequency (Hz) DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 0.07 0.86 0.24 0.08 0.24 — 0.13 1250 0.07 0.52 0.20 0.08 0.19 — 0.13 1600 0.07 0.35 0.19 0.08 0.16 — 0.13 2000 0.07 0.20 0.18 0.07 0.13 — 0.13 2500 0.07 0.13 0.17 0.07 0.11 0.55 0.13 3150 0.07 0.10 0.17 0.07 0.10 0.49 0.12 4000 0.07 0.10 0.16 0.07 0.09 0.32 0.11 5000 0.07 0.10 0.16 0.07 0.08 0.20 0.11 6300 0.07 0.10 0.16 0.06 0.08 0.21 0.13 8000 0.07 0.10 0.16 0.06 0.08 0.21 0.14 10000 0.07 0.10 0.16 0.06 0.10 0.21 0.15 12500 0.07 0.10 0.16 0.07 0.13 0.22 0.19 16000 0.08 0.10 0.16 0.09 0.16 0.26 0.19 20000 0.09 0.10 0.16 0.10 0.21 0.18 0.20 25000 0.10 0.11 0.18 0.10 0.26 0.18 0.20 31500 0.12 0.15 0.25 0.10 0.31 0.19 0.22 40000 0.20 0.30 0.40 0.10 0.22 0.24 — Page 16 of 44 5 Analysis of the results 5.1. Degrees of equivalence The nature of this comparison, with seven participants following a single loop with two travelling standards, should make it possible to use simple methods for estimating the comparison reference value such as those used in the comparisons CCAUV.A-K1 and CCAUV.A-K3. The methodology used in this report is similar to the one used in the Key Comparison CCAUV.A-K3 [1]. In general, a linear model described by E( y ) = X ⋅ a has to be solved for each frequency. In the model a is a vector of parameters of the model, E(y) is the expectation of the measurements and X is the design matrix; these values are the values that should have been measured in absence of uncertainty. The vector y is conformed by the n measurement values provided by the participants on at least one of the circulated measurement objects. The elements of the design matrix are known a priori with zero uncertainty. The parameters a1… ak, k ≥ 1, are unknown and have to be estimated from the n measurement results provided by the participants y, and the associated covariance matrix Σ. The covariance matrix Σ is the sum of two matrixes: Σmeas, which contains the square of the uncertainties claimed by the participants (diagonal elements) and the covariances between the provided measurement results (off-diagonal elements), and Σobject, which contains only diagonal elements that describe the estimated variance of the value of the measurand due to random instability of the circulated objects. Once these matrices have been built, the unknown parameters in the model and the reference values of the comparison can be estimated following the rest of the procedure described in reference [2]. In the analysis presented in this report it has been assumed that the correlation for two results yi and yj provided by different participants is equal to 0. In the case of two results yi and yj provided by the same participant, a common correlation coefficient for all participants has been assumed. The common correlation coefficient ρ was determined by the pilot laboratory using its own data, as described in Annex A. Additionally, the circulated measurement objects were considered stable, so that Σobject = 0 in the analysis. The covariance matrix and the matrix of the results of the participants are constructed using the data supplied by the participants. Because no further linking to any existing comparison is to be made, no additional matrixes with data from such a comparison are built. The model looks then as ⎡E ⎢ ⎢ ⎢E ⎢ ⎢E ⎢ ⎢ ⎣⎢ E (y1,1 )⎤ M y1, 7 y2,1 ⎡1 0 ⎤ ⎥ ⎢ ⎥ ⎥ ⎢M M ⎥ ⎥ ⎢1 0⎥ ⎡ a1 ⎤ ⎥=⎢ ⎥ ⋅ ⎢ ⎥, ⎥ ⎢0 1 ⎥ ⎣ a2 ⎦ ⎥ ⎢M M ⎥ ⎥ ⎢ ⎥ ⎦⎥ ⎣⎢0 1⎦⎥ ( ) ( ) M y2, 7 (1) ( ) where E(yi,j) is the expected value of the i-th standard being measured in the j-th laboratory in the loop. The elements of the vector ai are the parameters to be estimated for the standard i. The covariance matrix is a 14 x 14 matrix that contains the declared uncertainties from each laboratory. The correlation value for measurements carried in the same laboratory is frequency dependent, and it was determined from the measurements made at the pilot laboratory. See Appendix A for a detailed explanation of the calculation of the correlations. Page 17 of 44 Once these matrices are complete, the estimates of the unknown parameters of the model can be calculated using: aˆ = CX Tr Σ r−1 y r , ( C = X Tr Σ r−1 X r ) −1 (2) , where yr and Xr are obtained from y and X given in (1) by deleting the rows associated with the laboratories excluded from the calculation of the reference values, and Σr is the covariance matrix associated with the reduced data set yr The reference values of the comparison and the associated covariance matrix should be calculated using: yˆ = Xaˆ , (3) V (yˆ ) = XV (aˆ ) X T . The degrees of equivalence are obtained using: D ii = A T (y − yˆ ), (4) V (D ii ) = A T V (y − yˆ )A, where Dii is the degrees of equivalence per laboratory, A is an averaging matrix. The interlaboratory degrees of equivalence can be estimated using [1]: Dij = Dii − D jj , (5) V ( Dij ) = uii + u jj − uij − u ji , where Dij is the inter-laboratory deviation. The uxx elements are obtained from equation (4). 5.2. Equivalence and consistency of results As the participating laboratories are measuring the same item, it can be assumed that the reported results are drawn from a normal distribution. This hypothesis is tested by means of an observed χ2distributed estimator, as described in [2]. The degrees of freedom of the χ2 distribution are ν = n-k, where n is the number of measurements (14 for most frequencies) and k the number of standards (2 LS2aP microphones). To accept the hypothesis with a significance of 5 %, the probability P{ χ2 (ν)>χ2 obs} has to be larger than 5 %. During the course of the comparison, any anomalous results need to be identified by the pilot laboratory. Any laboratory whose results show deviations judged to be irregular must be contacted in order to have an opportunity to revise their results. Details of this process are given in section 4.3. Identifying discrepant measurements Once all data was collected, and the participants reported any problem with their measurement, the analysis method in [2] was implemented. This method uses the normalized deviations that were calculated for every frequency and measurement. The method assumes that the normalized deviations are distributed as N(0,1). Therefore, if the modulus of a particular normalized deviation is Page 18 of 44 greater than 2, the corresponding measurement can be considered discrepant with a significance of 5 %. Handling of discrepant measurements If a measurement has been judged to be discrepant, it should be excluded from the least squares calculation of the reference values. Otherwise the calculated reference values cannot be considered to be proper estimates of the SI values of the quantities represented by the circulated objects. If there is a discrepant measurement yij in a key comparison and the uncertainty assigned to this measurement is very small, the key comparison reference value will be attracted to this discrepant result. As a consequence the remaining results might appear to be discrepant as well even if they are mutually consistent. Since one discrepant measurement will always have a value |dij| larger than the values |dkj|, i≠k of two or more mutually consistent values, the value yij with the larger value |dij| should be excluded first. A repeated least squares adjustment of the reference values will then show if there are further discrepant results. The procedure of excluding discrepant results one by one can be summarized as follows: 1. 2. 3. 4. Identify the result yij with the largest value |dij|>2 in the (reduced) set of results. Exclude the result yij from the reduced set of results. Repeat the least squares adjustment of reference values for the reduced set of results. If the results in the reduced set are not mutually consistent, continue at point 1. It has to be emphasized, that the discrepant results are excluded only from the calculation of the reference values and not from the key comparison as such. It is therefore still necessary to calculate the deviations of the discrepant results from the reference values and the uncertainties of these deviations. Reference [2] gives a detailed explanation of the procedure. Page 19 of 44 6 Results 6.1. Reference values As in previous comparisons, there is not a single key comparison reference value, but one per frequency associated with each one of the standards circulated. The reference values are listed below in table 8. These values were obtained using the procedure described in the previous section. Some discrepant results were found at some frequencies. In all cases where a discrepant measurement was found, this measurement result or results have been excluded from the determination of the reference values (see tables 5 and 6 in section 4.3). Table 8. Reference values for the comparison. Free-field sensitivity levels Mf in dB re 1V/Pa and expanded uncertainty U (k = 2) in dB. Freq. (Hz) 4180.1395455 Mf U 4180.1395456 Mf k=2 U k=2 1000 -38.362 0.047 -38.357 0.047 1250 -38.312 0.046 -38.309 0.046 1600 -38.250 0.045 -38.243 0.045 2000 -38.127 0.041 -38.126 0.041 2500 -37.945 0.039 -37.949 0.039 3150 -37.663 0.037 -37.676 0.037 4000 -37.234 0.036 -37.233 0.036 5000 -36.594 0.035 -36.569 0.035 6300 -35.596 0.034 -35.561 0.035 8000 -34.143 0.034 -34.076 0.034 10000 -32.354 0.036 -32.224 0.036 12500 -30.403 0.041 -30.192 0.041 16000 -29.133 0.047 -28.863 0.047 20000 -30.136 0.054 -29.966 0.054 25000 -33.059 0.051 -33.065 0.051 31500 -37.073 0.064 -37.172 0.065 40000 -42.343 0.074 -42.424 0.074 6.2 Degrees of equivalence per laboratory The deviation of the measurements, that is, the reported measurements in table 5 and 6 minus their respective reference value in table 8 are plotted in figure 2. Page 20 of 44 Figure 2. Deviations of the free-field sensitivity levels of each microphone reported by the participant laboratories: (a) microphone 4180.1395455, and (b) microphone 4180.1395456. The degrees of equivalence per laboratory were determined as mentioned in the previous section (equation (4)). Figure 3 below shows average deviation in dB per laboratory as a function of frequency. Tables 9 and 10 present the degrees of equivalence and their uncertainties in tabular form. Figure 3. Average deviation in dB per laboratory and frequency. Page 21 of 44 Table 9. Degrees of equivalence per laboratory as function of frequency: deviations (dB). Frequency (Hz) DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 -0.002 -0.042 -0.021 0.006 0.009 - -0.003 1250 -0.005 -0.055 -0.035 -0.009 0.012 - 0.055 1600 0.013 -0.047 -0.029 0.004 0.041 - -0.064 2000 0.009 -0.056 -0.049 -0.004 0.033 - -0.003 2500 0.008 -0.057 -0.063 -0.013 0.022 -0.044 0.081 3150 0.009 -0.040 -0.070 -0.010 0.021 -0.114 0.074 4000 0.007 -0.011 -0.067 -0.006 0.030 0.062 -0.010 5000 0.005 0.004 -0.094 -0.023 0.005 -0.016 0.080 6300 0.012 -0.009 -0.152 -0.008 0.011 -0.050 0.084 8000 0.033 -0.016 -0.095 -0.001 0.006 -0.045 -0.022 10000 0.032 -0.034 -0.146 -0.007 -0.004 -0.014 0.113 12500 0.030 -0.029 -0.173 -0.005 -0.020 -0.045 0.241 16000 0.022 0.050 -0.172 -0.055 -0.016 -0.040 -0.015 20000 0.020 0.120 -0.079 0.000 0.032 -0.001 -0.003 25000 -0.036 0.086 -0.003 0.010 0.069 -0.072 -0.130 31500 -0.025 0.187 0.094 0.026 0.054 -0.038 -0.160 40000 -0.046 0.207 0.233 0.021 - -0.119 -0.133 Table 10. Degrees of equivalence per laboratory as function of frequency: uncertainty k =2 (dB) Frequency (Hz) DFM CENAM KRISS NMIJ LNE PTB INMETRO 1000 0.049 0.808 0.221 0.061 0.221 - 0.114 1250 0.050 0.487 0.183 0.062 0.173 - 0.114 1600 0.050 0.326 0.174 0.062 0.144 - 0.115 2000 0.053 0.184 0.165 0.053 0.116 - 0.116 2500 0.054 0.117 0.156 0.054 0.097 0.516 0.117 3150 0.056 0.087 0.156 0.056 0.087 0.459 0.107 4000 0.056 0.088 0.147 0.056 0.077 0.299 0.098 5000 0.056 0.087 0.145 0.056 0.067 0.182 0.097 6300 0.057 0.087 0.146 0.046 0.067 0.192 0.116 8000 0.057 0.087 0.145 0.046 0.067 0.192 0.126 10000 0.051 0.079 0.132 0.041 0.079 0.175 0.123 12500 0.048 0.077 0.140 0.048 0.104 0.183 0.164 16000 0.054 0.073 0.137 0.063 0.126 0.211 0.152 20000 0.060 0.095 0.125 0.070 0.169 0.143 0.160 25000 0.076 0.086 0.153 0.076 0.226 0.153 0.171 31500 0.095 0.153 0.226 0.072 0.284 0.167 0.199 40000 0.153 0.239 0.324 0.055 - 0.171 0.188 Page 22 of 44 The degrees of equivalence calculated for the frequencies, 2.5 kHz, 4.0 kHz, 8.0 kHz, and 20.0 kHz are shown in figure 4. Page 23 of 44 Figure 4 – Inter-laboratory degrees of equivalence at 2.5 kHz, 4 kHz, 8 kHz, and 20.0 kHz. Table 11 shows the results of the χ2 test applied to the comparison results for specified values of the correlation coefficient between results provided by the same laboratory. As demonstrated in [1], when high correlation coefficients are used, the test tends to fail. This is simply because a high correlation forces the differences to be the same for the two standards, and that may not be the case. Although at some frequencies the result of the χ2 test is low, in general this test has been considered satisfactory when the correlation between measurements of the same laboratory takes the values tabulated in Appendix A. Table 11. Results of the χ2 test as described in [2]. The correlation coefficients used in the calculations are shown in the table in Appendix A. Frequency (Hz) P{ χ2 (ν)>χ2 obs} 1000 100.0% 1250 100.0% 1600 99.6% 2000 99.7% 2500 95.6% 3150 94.0% 4000 98.7% 5000 74.5% 6300 57.1% 8000 87.5% 10000 45.7% 12500 90.7% 16000 84.6% 20000 99.1% 25000 76.0% 31500 94.8% 40000 41.1% Page 24 of 44 6.3 Degrees of equivalence inter-laboratory Tables 12, 13, 14 and 15 contain the inter-laboratory degrees of equivalence of this comparison. Table 12. Inter-laboratory degrees of equivalence at 2.5 kHz. The upper triangle contains the differences (dB); the lower triangle contains the uncertainties k =2 (dB) 2.5 kHz DFM CENAM KRISS NMIJ LNE PTB INMETRO - 0.065 0.072 0.022 -0.014 0.053 -0.072 CENAM 0.139 - 0.006 -0.044 -0.079 -0.012 -0.138 KRISS 0.173 0.201 - -0.050 -0.085 -0.019 -0.144 NMIJ 0.093 0.139 0.173 - -0.035 0.031 -0.094 LNE 0.123 0.160 0.190 0.123 - 0.066 -0.059 PTB 0.521 0.531 0.541 0.521 0.527 - -0.125 INMETRO 0.139 0.173 0.201 0.139 0.160 0.531 - DFM Table 13. Inter-laboratory degrees of equivalence at 4.0 kHz. The upper triangle contains the differences (dB); the lower triangle contains the uncertainties k =2 (dB) 4.0 kHz DFM CENAM KRISS NMIJ LNE PTB INMETRO - 0.017 0.073 0.013 -0.023 -0.056 0.017 CENAM 0.115 - 0.056 -0.005 -0.040 -0.073 0.000 KRISS 0.164 0.177 - -0.061 -0.096 -0.129 -0.056 NMIJ 0.093 0.115 0.164 - -0.036 -0.068 0.004 LNE 0.107 0.127 0.173 0.107 - -0.033 0.040 PTB 0.308 0.315 0.336 0.308 0.313 - 0.072 INMETRO 0.123 0.140 0.183 0.123 0.134 0.318 - DFM Table 14. Inter-laboratory degrees of equivalence at 8.0 kHz. The upper triangle contains the differences (dB); the lower triangle contains the uncertainties k =2 (dB) 8.0 kHz DFM CENAM KRISS NMIJ LNE PTB INMETRO - 0.048 0.128 0.033 0.027 0.077 0.055 CENAM 0.113 - 0.079 -0.015 -0.021 0.029 0.006 KRISS 0.162 0.175 - -0.095 -0.101 -0.051 -0.073 NMIJ 0.085 0.108 0.158 - -0.006 0.044 0.021 LNE 0.098 0.119 0.166 0.093 - 0.050 0.028 PTB 0.205 0.215 0.245 0.202 0.208 - -0.022 INMETRO 0.145 0.159 0.197 0.141 0.149 0.234 - DFM Page 25 of 44 Table 15. Inter-laboratory degrees of equivalence at 20.0 kHz. The upper triangle contains the differences (dB); the lower triangle contains the uncertainties k =2 (dB) 20.0 kHz DFM CENAM KRISS NMIJ LNE PTB INMETRO - -0.100 0.099 0.020 -0.011 0.021 0.023 CENAM 0.112 - 0.199 0.120 0.088 0.120 0.123 KRISS 0.153 0.157 - -0.079 -0.111 -0.079 -0.076 NMIJ 0.112 0.118 0.157 - -0.032 0.000 0.003 LNE 0.190 0.194 0.220 0.194 - 0.032 0.035 PTB 0.167 0.171 0.200 0.171 0.230 - 0.003 INMETRO 0.182 0.186 0.213 0.186 0.241 0.224 - DFM Page 26 of 44 7 Conclusions The aim of the Key Comparison CCAUV.A-K4 is to establish reliable equivalence between National Metrology Institutes for free-field calibration of Laboratory Standard microphones of the type LS2aP. The initial plans involved nine participants. However, once the comparison was underway, two laboratories decided to decline from participating. Two LS2aP microphones were circulated among the participants in a single star configuration. All participants reported the free-field sensitivity and other microphone parameters such as acoustic centre, environmental coefficients, etc. The reported sensitivities have been analysed using a least-squares technique similar to the one used in the Key Comparison CCAUV.A-K3. All laboratories were included in the estimation of the reference values. There is no preceding comparison with which the obtained degrees of equivalence can be compared. 8 References [1] V. Cutanda-Henríquez, and K. Rasmussen, Final Report on the Key Comparison CCAUV.AK3, Centro Nacional de Metrología, México, Danish Primary Laboratory for Acoustics, Denmark, May 2006. [2] L. Nielsen, Identification and handling of discrepant measurements in key comparisons, Danish Institute of Fundamental Metrology, DFM-01-R28, 2002. Page 27 of 44 Appendix A — Determination of the correlation coefficients The correlation coefficients used in the analysis were determined from a relatively large set of freefield sensitivity data gathered at DFM from all the control measurements carried out on the travelling standards. The DFM’s own uncertainty budget was also used in the determination of the correlation coefficients. In principle, this calculation should only be valid for DFM’s correlation coefficients, but it has been chosen to use them for all laboratories. In the following, all operations are referred to this set of measurements. The covariance was determined as the sum of the contributors to the uncertainty of the measurement that affect the sensitivities of both microphones in a similar manner, including the reproducibility, that is, the type B contributors. Some of these contributors are: the environmental variables, the polarising voltage, the reference impedance, the effective distance between microphones, and the mathematical manipulations. Cov B ( M f 1 , M f 2 ) = ∑ ui2 , (A.1) where Mf1 and Mf2 are the free-field sensitivities of the microphones, and ui is the ith uncertainty type B component in the uncertainty budget. In order to have a more realistic estimate of the experimental reproducibility, the experimental correlation coefficient of the sensitivities of the two microphones, ρxy, was calculated, and used for determining the experimental covariance by means of: Cov A (M f 1 , M f 2 ) = ρ xyσ 1σ 2 , (A.2) where σ1, and σ2 are the standard deviations of the free-field sensitivity of each microphone. Finally, the correlation coefficient at each frequency was determined using the sum of all covariances divided by the product of the combined variance of the two microphones (which is the same for the two microphones): ρ= Cov A (M f 1 , M f 2 ) + Cov B (M f 1 , M f 2 ) u Mf 1 ⋅ u Mf 2 (A.3) . The correlation coefficients obtained by such a procedure are presented in the table below. Frequency (Hz) Correlation Frequency (Hz) Correlation 1000 1250 0.769 8000 0.716 0.769 10000 0.427 1600 0.769 12500 0.427 2000 0.769 16000 0.356 2500 0.769 20000 0.384 3150 0.769 25000 0.573 4000 0.769 31500 0.750 5000 0.716 40000 0.358 6300 0.716 Page 28 of 44 Appendix B — INMETRO corrections to reported results During the process of reviewing the draft A, INMETRO requested to introduce some corrections to the data originally reported. Table B1 contains the original and revised sensitivities of the two microphones. The reason given by INMETRO for this correction is the following: “The sensitivity results reported in the cancelled documents (i.e. calibration certificates DIMCI 0209/2008 and 0210/2008) where erroneously referred to the nominal centre frequencies of 3rdoctave band, as requested by the measurement protocol of the comparison CCAUV.A-K4. It was detected that these sensitivity results refer to the exact centre frequencies of 3rd-octave bands of base 2, which are obtained by the equation 1000*2N/3, where N is an integer. This situation implies that some frequencies match but others are different. A coincidence between the nominal and exact frequencies within the frequency range of the comparison is obtained at 1 kHz, 2 kHz, 4 kHz, 8 kHz and 16 kHz. Unfortunately, the INMETRO only perceived this fact after the confirmation sent to you. The mismatch between some of the frequencies reported and the ones requested in the protocol implies in significant differences that required this communication.” Table B1 Original and revised sensitivity level data for the two microphones. Sensitivity level (dB re 1 V/Pa) Freq. (Hz) 4180.1395455 4180.1395456 Original Revised Original Revised 1000 -38.375 -38.375 -38.350 -38.350 1250 -38.260 -38.328 -38.250 -38.319 1600 -38.313 -38.252 -38.307 -38.234 2000 -38.137 -38.137 -38.121 -38.121 2500 -37.875 -37.951 -37.857 -37.933 3150 -37.599 -37.678 -37.593 -37.671 4000 -37.258 -37.258 -37.229 -37.229 5000 -36.532 -36.628 -36.471 -36.565 6300 -35.531 -35.639 -35.457 -35.565 8000 -34.191 -34.191 -34.073 -34.073 10000 -32.274 -32.411 -32.079 -32.217 12500 -30.204 -30.469 -29.909 -30.178 16000 -29.169 -29.169 -28.856 -28.856 20000 -30.131 -30.124 -29.977 -29.960 25000 -33.154 -33.037 -33.230 -33.097 31500 -37.183 -37.021 -37.385 -37.215 40000 -42.426 -42.299 -42.606 -42.476 Page 29 of 44 Appendix C — Uncertainty budgets Uncertainty budgets were requested of all participants. The budgets are reproduced here as they were received from the participants. No editing of the contents but a small amount of reformatting has been performed. Table, equation and figure numbers do not follow the numbering in the report. Page 30 of 44 DFM The condensed uncertainty budget for a free-field reciprocity calibration of B&K type 4180 microphones are given in the table below. The free-field sensitivity is determined as the average of the results derived using four measuring distances between 170 – 320 mm for type B&K 4180. The background for the budget is given in the following remarks: 1. The figures represent the combined effects of the uncertainty on the distance between the microphone diaphragms (0.05 mm), front cavity depth (0.05 mm) and acoustic centres (0.5 – 1.0 mm) referred to the average distance of 240 mm. 2. The figures represent the combined effects of the measurement uncertainties on static pressure (50 Pa), temperature (0.5 K) and relative humidity (10 %). 3. The figures represent the combined effects of the measurement uncertainties on static pressure (50 Pa), temperature (0.5 K) and relative humidity (10 %). 4. The figures represent the effect of the basic uncertainty on the equations for calculating the absorption and density of humid air. 5. The figures represent the combined effects of the uncertainty on the measurement impedance and voltage ratios (3 ratios each derived from 4 voltage measurements). 6. The figures represent the uncertainty on the polarizing voltage (40 mV) and the non-linear relation between polarizing voltage and microphone sensitivity. 7. The figures represent the possible errors introduced by the signal manipulations, such as digital filtering, inverse FFT-applications and subsequent removal of reflections in the time domain etc. 10. The figures represent the uncertainty on applying a correction for dependence of static pressure and temperature on the microphone sensitivity. (Uncertainty on resonance frequency, on low-frequency value of static pressure coefficient and on temperature coefficient, allowed deviation from reference conditions 3 kPa respectively 1 K). Page 31 of 44 Uncertainty budget for free-field reciprocity calibration of B&K 4180 microphones Components of type B uncertainties in dB*1000 Frequency kHz 10 15 20 25 30 40 3 5 22 19 1 0 40 2.2 18 5 22 19 2 1 40 2.2 7 5 22 19 8 2 20 2.2 2 5 22 19 15 4 20 2.2 2 5 22 19 18 6 20 2.2 2 5 25 19 17 9 20 2.2 2 5 29 19 12 11 30 2.2 2 5 39 19 20 20 40 2.2 2 5 30.5 29.0 21.2 22.5 23.4 24.4 28.3 37.9 Components of type A uncertainties in dB*1000 9 Allowed reproducibility 15 20 20 20 30 35 50 85 35.3 29.1 30.1 38.0 42.7 57.4 93.1 3 5 9 13 18 20 30 Overall uncertainty in dB*1000 at reference conditions (k=2) 34.1 35.4 29.6 31.4 40.2 46.3 60.8 97.8 0.068 0.071 0.059 0.063 0.080 0.093 0.12 0.20 0.12 0.20 * 1 2 3 4 5 6 7 8 Source Effective distance Density of air Air absorption Environmental equations Electrical transfer impedance Polarizing voltage Mathematical manipulations Rounding of results σB = ( ∑ u / 3) 2 1/ 2 Overall uncertainty in dB*1000 at measurement conditions ( σ = 2 σ 2A + σ B2 ) 1/ 2 34.0 Uncertainty on corrections to reference environmental conditions in dB*1000 10 Correction to reference conditions 2 Expanded uncertainty in dB Declared CMC values * 0.07 0.07 0.07 0.08 0.09 0.1 Not included in the CMC Page 32 of 44 CENAM Page 33 of 44 KRISS 1000 0.0029 0.0017 0.0020 0.0009 0.0004 0.0000 0.0003 0.0003 1250 0.0035 0.0026 0.0020 0.0009 0.0004 0.0000 0.0003 0.0003 1600 0.0035 0.0026 0.0020 0.0009 0.0004 0.0000 0.0003 0.0003 2000 0.0036 0.0026 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 2500 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 3150 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 4000 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 5000 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 6300 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 8000 0.0050 0.0044 0.0021 0.0009 0.0004 0.0000 0.0003 0.0003 10000 0.0069 0.0044 0.0052 0.0009 0.0004 0.0000 0.0003 0.0003 12500 0.0102 0.0087 0.0052 0.0009 0.0004 0.0000 0.0003 0.0003 16000 0.0102 0.0087 0.0052 0.0009 0.0004 0.0000 0.0003 0.0003 20000 0.0102 0.0087 0.0052 0.0009 0.0004 0.0000 0.0003 0.0003 25000 0.0102 0.0087 0.0052 0.0009 0.0004 0.0001 0.0003 0.0003 31500 0.0149 0.0087 0.0121 0.0009 0.0004 0.0005 0.0003 0.0003 40000 0.0149 0.0087 0.0121 0.0009 0.0004 0.0000 0.0003 0.0003 mm V 0.0307 0.0307 0.0005 0.0306 0.0306 0.0005 0.0306 0.0306 0.0005 0.0305 0.0305 0.0005 0.0304 0.0304 0.0005 0.0304 0.0304 0.0005 0.0302 0.0302 0.0005 0.0301 0.0301 0.0005 0.0299 0.0299 0.0005 0.0297 0.0297 0.0005 0.0295 0.0295 0.0005 0.0293 0.0293 0.0005 0.0290 0.0290 0.0005 0.0286 0.0286 0.0005 0.0282 0.0282 0.0005 0.0273 0.0273 0.0005 0.0256 0.0256 0.0005 0.0049 0.0048 0.0006 0.0000 0.0001 0.0049 0.0048 0.0006 0.0000 0.0001 0.0048 0.0048 0.0006 0.0000 0.0001 0.0048 0.0048 0.0006 0.0000 0.0001 0.0048 0.0048 0.0006 0.0000 0.0001 0.0048 0.0047 0.0006 0.0001 0.0001 0.0048 0.0047 0.0006 0.0001 0.0001 0.0047 0.0047 0.0006 0.0001 0.0001 0.0047 0.0046 0.0006 0.0002 0.0002 0.0047 0.0046 0.0006 0.0003 0.0002 0.0046 0.0046 0.0006 0.0005 0.0003 0.0047 0.0045 0.0006 0.0009 0.0004 0.0048 0.0045 0.0006 0.0016 0.0006 0.0053 0.0044 0.0006 0.0028 0.0009 0.0064 0.0300 0.0026 mm kPa K % 0.0006 0.0061 0.0019 0.0005 0.0287 0.0086 0.0006 0.0024 0.0006 0.1119 0.0029 0.1000 0.0012 0.0009 0.0500 0.0944 0.0029 0.0800 0.0012 0.0010 0.0500 0.0861 0.0029 0.0700 0.0011 0.0011 0.0500 0.0821 0.0029 0.0650 0.0011 0.0012 0.0500 0.0782 0.0029 0.0600 0.0011 0.0014 0.0500 0.0744 0.0029 0.0550 0.0010 0.0017 0.0500 0.0708 0.0029 0.0500 0.0009 0.0021 0.0500 0.0708 0.0029 0.0500 0.0007 0.0026 0.0500 0.0709 0.0029 0.0500 0.0003 0.0035 0.0500 0.0691 0.0029 0.0473 0.0006 0.0051 0.0500 0.0667 0.0029 0.0432 0.0020 0.0083 0.0500 0.0677 0.0029 0.0437 0.0032 0.0123 0.0500 0.0654 0.0029 0.0396 0.0004 0.0143 0.0500 0.0640 0.0029 0.0356 0.0107 0.0143 0.0500 0.0823 0.0029 0.0596 0.0261 0.0059 0.0500 0.1153 0.0029 0.0984 0.0308 0.0126 0.0500 0.1966 0.0029 0.1942 0.0292 0.0082 0.,05 Sum 0.1161 0.0994 0.0916 0.0878 0.0842 0.0807 0.0773 0.0773 0.0772 0.0755 0.0734 0.0746 0.0725 0.0710 0.0878 0.1232 0.1988 Expanded Uncertainty (k=2) 0.2323 0.1988 0.1831 0.1755 0.1683 0.1614 0.1546 0.1545 0.1544 0.1510 0.1468 0.1492 0.1449 0.1421 0.1757 0.2463 0.3976 Stated Uncertainty 0.24 0.20 0.19 0.18 0.17 0.17 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.18 0.25 0.40 Electrical Transfer Impedance Series Capacitor Voltage Ratio Inherent Noise Distortion Frequency Reveiver Ground Shield Transmitter Ground Shield Symbol C VR f Microphone Parameters Acoustic Center Polarizing Voltage Uo Measurement Conditions Distance between Microphones Static Pressure Temperature Relative Humidity l Ps T RH Processing of Results Rounding Error Repeatability of Measurements Static Pressure Corrections Temperature Corrections Sjgnal Processing Error Uncertainty Table Table Measured Measured Table B&K B&K Unit nF 1 0.0064 0.1 0.0137 0.1733 1.9370 0.0050 Table Table Table Hz dB Page 34 of 44 NMIJ Page 35 of 44 LNE Free field calibration of microphones by the reciprocity technique Uncertainty evaluation J-N Durocher, D. Rodrigues, LNE july 2007 Microphone sensitivity product The module of the microphone sensitivity product is given by (microphone 1 as receiver and 2 as emitter): αD ' M 1 .M 2 = With U 1 2 D' ⋅ ⋅10 20 I 2 ρ12 f U1 = Z e12 I2 is the measured electrical transfert impedance - f is the frequency - D’ is the distance between the acoustic center of the microphones D’=D-2δ where δ is the acoustic center position (relative to the diaphragm) and D the distance between the microphone diaphragms (δ is assumed independent of the microphone). - ρ12 is the air density during the measurement of Ze12 - α is the air absorbtion (assumed constant during the 3 Ze measurements) Expressed in dB, the above microphone sensitivity product become : L1 + L2 = 20 lg(M 1 M 2 ) = L12 + C D − C R12 + C f + αD '+ K sys with C D = 20 lg( D ' ) C R12 = 20 lg( ρ12 ) C f = 20 lg(2 / f ) And where Ksys corresponds to the systematic deviation from the ideal conditions (Ksys is a null correction only used for uncertainties calculation) K Sys = K polE + K polR + K ϑE + K ϑR + K Echos + K Elec + K Air - with : Polarization voltage of the two microphones Kpol Angular deviation of the two microphones from the main axis Kθ Acoustical disturbances Kecho Electrical disturbances Kelec unknown deviation Kunk Electrical transfert impedance measurement The elementary measurement is a voltage ratio measurement : And thus Z e12 = U R1 Ug = Cω 1 R1 U E2 I2 gE U1 U R1 g E = I 2 CωU E 2 g R1 Page 36 of 44 Where : - gR1 corresponds to the gain of the receiver microphone amplifier (insert voltage with the microphone n°1) and GR1= 20.lg(gR1) - gE corresponds to the gain of the emmiter microphone amplifier and GE= 20.lg(gE) - Ze12 corresponds to the electrical transfert impedance with the microphone microphone n°1 and n°2) and L12= 20.lg(Ze12) - C corresponds to the electrical capacitance used for the current measurement and CC is the corresponding correction (dB) CC = 20 lg(Cω ) The electrical transfert impedance expressed may be written in dB : L12 = 20 lg(Z e12 ) = G12 + GE − GR1 − Att − CC Where Att corresponds to the attenuation (dB) of the attenuator used for the insert voltage method. For the following microphone configurations 13 and 23 : L13 = G13 + GE − GR1 − Att − CC L23 = G23 + GE − GR 2 − Att − CC and thus, the electrical transfert impedance combination : L12 + L13 − L23 G12 + G13 − G23 GE G Att CC = + − GR1 + R 2 − − 2 2 2 2 2 2 Individual microphone sensitivity The sensitivity of the microphone n° 1 can be written as : L1 = L12 + L13 − L23 C R12 + C R13 − C R 23 C D + C f + αD'+ K sys − + + C proc 2 2 2 where Cproc is the equivalent correction to process the results. 2 L1 = (G12 + G13 − G23 ) + G E − 2G R1 + G R 2 − Att − C C − (C R12 + C R13 − C R 23 ) + C D + C f + αD '+2C proc + K sys Uncertainty budget : 2 4u 2 ( L1 ) = 7u 2 (G ) + 3u noise + u 2 ( Att ) + u 2 (CC ) + 3u 2 (C R ) + u 2 (C D ) + u 2 (C f ) + u 2 (αD ' ) + u 2 ( K sys ) + 4u 2proc Uncertainties evaluation Page 37 of 44 Basic parameters measurement Quantity Mean value Unit U k u Distance : D (between diaphragms) 0,3 m 1.10-3 3 0,58.10-3 Temperature : T 23 °C 1 3 0,58 Pressure : P 1013 hPa 1 3 0,58 Relative humidity : HR 60 % 5 3 2,89 Voltage ratio measurement : G - dB 0,01 3 0,0058 Noise component The effect of the acoustic noise depends on the frequency and on the distance between the microphones. For LS2 microphones, ⎛ D⎞ u noise (dB) = 0,133 ⋅ ⎜ ⎟ ⎝ 0,3 ⎠ the standard uncertainty unoise is estimated as : 2 FkHz where FkHz = f / 1000 Attenuator component The maximum uncertainty due to the attenuator is estimated as 0,01 dB. u att (dB) = 0,01 3 = 0,0058 Capacitor component The calibration of the capacitor gives C = 4744,0 pF ± 0,01 % ± 0,1 pF (k=2) It results : uC = 0,0012 / 2 = 0,00061 dB Air density component Using the formulation of the air density given in IEC 61094-2 Annex F and the usual air conditions, we obtain : u (C Rmn ) = (8,57.10 ) .u −3 2 2 ( ) 2 ( ) 2 ( PhPa ) + 2,93.10 − 2 .u 2 (T ) + 9,15.10 − 4 .u 2 ( Hr ) dB Page 38 of 44 and using the uncertainties given in 1 : u (C Rmn ) = 0,018 dB Distance between microphones component Using equation D ' = D − 2δ and ⎛ u ( D ' ) ⎞ ⎛ u ( D ) ⎞ ⎛ 2u (δ ) ⎞ ⎜ ⎟ ≈⎜ ⎟ +⎜ ⎟ ⎝ D' ⎠ ⎝ D ⎠ ⎝ D ⎠ 2 we find, D >> 2δ Using the approximation 2 2 20 lg(1 + x) ≈ 8.7 x ⎛ u ( D ) ⎞ ⎛ 2u (δ ) ⎞ ⎛ u ( D' ) ⎞ ⎛ D '+u ( D ' ) ⎞ u D = 20 lg⎜ ⎟ ⎟ +⎜ ⎟ ≈ 8 .7 ⎜ ⎟ ≈ 8 .7 ⎜ D' ⎝ D ⎠ ⎝ D ⎠ ⎝ D' ⎠ ⎝ ⎠ 2 2 dB Assuming that the maximum uncertainty of the acoustic center position is 1 mm, we have uD = 0,011 D dB Air absorbtion component u (αD ' ) = [ D ' u (α )]2 + [αu ( D ' )]2 ≈ u (α ) D Assuming that the air absorption coefficient α(f) is defined with a maximum relative uncertainty of 10 %, while 2 α ≈ 0,004 + 8,63.10 −4 FkHz u (α ) D = [ 0,1 D 2 αD = 10 −5 7 + 1,5 FkHz 0,3 3 ] dB Result processing component Rounding the results component : u proc1 Repeatability is estimated as : = 0,001 = 0,0056 3 u proc 2 = 0,005 + 0,001FkHz dB dB Transposition to the reference conditions. The correction is CCond = C P Δ P + CT Δ T with Δ P = P − Pref Δ T = T − Tref 2 u Cond = C P2 u 2 (P ) + u 2 (C P )u 2 (ΔP ) + CT2 u 2 (T ) + u 2 (CT )u 2 (ΔT ) Page 39 of 44 where u(ΔP), u(ΔT) are the standard deviations corresponding to the ranges of static pressure or temperature allowed for the calibration. Using the raw approximations : CP = 0,0006 + 0,000012 FkHz dB/hPa and CT = 0,005 + 0,00067 FkHz dB/K And assuming that u(CP)/CP = u(CT)/CT = 10 % Using the uncertainties listed in 1, we obtain : u proc3 = C P u (P ) = 0,0017 + 3,5.10 −5 FkHz u proc 4 = CT u (T ) = 0,006 + 7,7.10 −4 FkHz dB dB And considering the extreme variations allowed : u (ΔP) = 200 3 = 115 hPa u (ΔT ) = 3 = 1,7 °C 3 we obtain : u proc5 = u (C P ).u (ΔP ) = 0,004 + 8.10 −5 FkHz u proc6 = u (CT ).u (ΔT ) = 0,001 + 6,7.10 −5 FkHz dB dB Polarization component Assuming that u (VPol ) = 0,2 3 V ⎛ V + u (VPol ) ⎞ ⎛ 0,2 ⎞ ⎟⎟ ≈ 8,7⎜⎜ u Pol = 20 lg⎜⎜ Pol ⎟⎟ = 0,005 dB VPol ⎝ 200 3 ⎠ ⎝ ⎠ Angular deviation component Using a directivity law based on the cylindrical piston in a plane baffle, transposed on the size of the LS2 microphones, we obtain the approximation : 2 uϑ ≈ u (ϑ ).36.10 −6 FkHz Using u (ϑ ) = dB 2 2 deg , we obtain uϑ ≈ 42.10 −6 FkHz 3 with ϑ expressed in degree dB Acoustical disturbances component Page 40 of 44 Acoustical disturbances are not completely removed by the treatment and the treatment will cause a systematic error in the measured sensitivity product. Simulation with LS2 microphones give uecho = 0,01 dB Electrical disturbances component The estimation for the total harmonic distortion is uTHD = 0,01 3 = 0,0058 dB Crosstalk is partially removed by the acoustical treatment. The estimation for the residual component is : u cross = 0,005 + 0,005 FkHz dB Unknown component Free field calibration comparisons carried out in the past showed systematic deviations in the high frequency range (f ≥ 10 kHz). Causes are not well known but may be one of the following : Air composition in anechoic rooms Temperature increase near to the receiver microphone Crosstalk in the emitter microphone circuit In the absence of further explanations, deviations observed are take into account. The deviation follow approximately : ( u unk = 0,3.Lg FkHz / 8 ) dB for frequencies > 8 kHz Page 41 of 44 Uncertainties calculation Frequency Microphone sensitivity uncertainties (dB) [k=2] kHz D = 25 cm D = 30 cm D = 35 cm 1,00 0,17 0,24 0,32 1,25 0,14 0,19 0,25 1,6 0,12 0,16 0,20 2,0 0,11 0,13 0,17 2,5 0,09 0,11 0,14 3,15 0,09 0,10 0,11 4,0 0,08 0,09 0,10 5,0 0,08 0,08 0,09 6,3 0,08 0,08 0,08 8,0 0,09 0,08 0,08 10 0,10 0,10 0,10 12,5 0,13 0,13 0,13 16 0,17 0,16 0,16 20 0,21 0,21 0,21 25 0,26 0,26 0,26 31,5 0,31 0,31 0,31 40 0,38 0,38 0,38 Page 42 of 44 PTB Page 43 of 44 INMETRO Inmetro's estimated uncertainty - Reciprocity in Free Field - LS2P Microphone Uncertainty estimate Standard Uncertainty u linearity-analyzer (dB) u capacitance (dB) u temperature,humidity, pressure (dB) u acoustic center (dB) u polararization voltage (dB) u window-backscattering (dB) u subtraction-crosstalk (dB) u rounding (dB) u environmental corrections (dB) u environmental equations (dB) u repeatability (dB) u combined (dB) U95% (k=2) (dB) Declared uncertainty (dB) 1000 1250 1600 2000 2500 3150 4000 Frequency (Hz) 5000 6300 8000 10000 12500 16000 20000 25000 31500 40000 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0200 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0013 0,0034 0,0034 0,0034 0,0034 0,0034 0,0034 0,0033 0,0033 0,0033 0,0032 0,0032 0,0031 0,0031 0,0032 0,0032 0,0033 0,0040 0,0490 0,0489 0,0489 0,0488 0,0487 0,0486 0,0484 0,0483 0,0481 0,0480 0,0478 0,0476 0,0475 0,0474 0,0139 0,0142 0,0177 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0025 0,0289 0,0289 0,0289 0,0289 0,0289 0,0189 0,0089 0,0039 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0010 0,0020 0,0030 0,0040 0,0050 0,0060 0,0070 0,0080 0,0324 0,0398 0,0441 0,0452 0,0646 0,0669 0,0787 0,0826 0,0901 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0029 0,0000 0,0000 0,0000 0,0000 0,0000 0,0001 0,0001 0,0001 0,0002 0,0004 0,0005 0,0005 0,0003 0,0014 0,0015 0,0003 0,0008 0,0002 0,0002 0,0002 0,0002 0,0002 0,0003 0,0003 0,0004 0,0006 0,0009 0,0014 0,0020 0,0032 0,0046 0,0064 0,0089 0,0118 0,0103 0,0058 0,0063 0,0045 0,0028 0,0063 0,0029 0,0033 0,0032 0,0043 0,0068 0,0076 0,0110 0,0138 0,0192 0,0219 0,0232 0,061 0,061 0,061 0,061 0,061 0,057 0,054 0,053 0,062 0,066 0,069 0,069 0,084 0,086 0,085 0,090 0,098 0,12 0,12 0,12 0,12 0,12 0,11 0,11 0,11 0,12 0,13 0,14 0,14 0,17 0,17 0,17 0,18 0,20 0,13 0,12 0,12 0,12 0,12 0,11 0,11 0,11 0,12 0,13 0,15 0,18 0,18 0,18 0,20 0,22 0,24 Page 44 of 44