Reciprocity Calibration Research Articles

Time-selective windowing technique in free-field microphone reciprocity calibration

Time-selective windowing techniques, which effectively remove multi-path noise, have been widely utilized for reciprocity calibration of microphone there are still limitations imposed by overlapping signals, particularly at low frequencies and for high Q microphones. Based on a fast Fourier transform analysis, the leakage due to a limited frequency range makes the overlap problem worse, not be perfectly separated. Instead of using conventional low-pass filters that are designed to have a flat response in the frequency range of interest, in this study, a filter with a Dolph-Chebyshev window shape was proposed because it has low sidelobe levels. After removing multi-path noise with a time-selective window, an inverse filter should be applied to compensate for distortion created by the applied filter. The method suggested in this paper extends the possible frequency range of free-field reciprocity calibration to frequencies below 2 kHz.

Phase sensitivity uncertainty in microphone pressure reciprocity calibration

The calibration of laboratory standard microphones by the pressure reciprocity method, as specified in IEC 61094-2, is used throughout the world as the basis for primary measurement standards for sound pressure. While the method has long been used to determine the magnitude of the pressure sensitivity of the microphone, the phase sensitivity has until recently been overlooked, and is notable by its absence in BIPM's database of CMCs. A new BIPM key comparison is therefore addressing this by including phase calibration within its scope, and is the incentive for a systematic evaluation of the associated measurement uncertainty. The analysis presented is based on the requirements of IEC 61094-2 and makes use of modelling and experimentation to determine uncertainty in phase pressure sensitivity for type LS1 and type LS2 microphones. Linearity of phase measurement and stray capacitance are the dominant electrical components, both acting independently of frequency. The most significant acoustic components are the uncertainty in thermal diffusivity at low frequencies and microphone parameter uncertainty at high frequencies. Measurement repeatability is below the level of the type B evaluation for most of the frequency range, but at low frequencies it dominates for both microphone types. For both types of microphone the overall measurement uncertainty is estimated to be below 0.5° over the central frequency range.

A Reference Infrasound Source with Low Distortion Based on Laser Pistonphone Technology

For safety protection from infrasound and its metrology, a reference infrasound source was developed on the basis of the laser pistonphone technique. The electromagnetic vibrator was made based on the technology of air bearings and a displacement feedback system. The air bearings reduce the damping of the vibrator, and the displacement feedback system could effectively control the distortion of the pistonphone. Through the displacement of the piston measured by a laser interferometer, the sound pressure could be calculated. In the meantime, the sound pressure was measured by a LS1P microphone with the reciprocity calibration results. The test results show that the difference between the measured pressure and the calculated one is no more than 0.01 dB from 5 to 20 Hz and the total distortion of the sound pressure at 124.0 dB is less than 0.7 % from 1 to 20 Hz.

Minimizing the Effects of Reflections by Using a Virtual Pulse Method, for Free-Field Reciprocity Calibration

The National Metrology Institute of Japan has developed a free-field reciprocity calibration system for type WS3 microphones as acoustic standards in the airborne ultrasonic range between 20 and 100 kHz, because numerous instruments radiate airborne ultrasound. Precise calibration of these microphones requires minimizing the influence of sound reflected from the objects such as absorbing wedges and supporting rods within the acoustic chamber. To minimize this influence, we applied the virtual pulse method, which is a signal processing technique used in the audible frequency to airborne ultrasonic range. Experimental and analytical results validated this method. Use of this method in the calibration of type WS3 microphones will decrease the calibration uncertainty in the free-field sensitivity level.

Free-field reciprocity calibration of low-frequency ultrasonic transducers

Techniques developed for the calibration of electroacoustic transducers provide many practical applications of the principles studied in advanced undergraduate and introductory graduate courses. This communication describes an implementation of the standard method of reciprocity calibration as presented in the popular text, Fundamentals of Acoustics by Kinsler et al. The measurements were performed on inexpensive off-the-shelf transducers designed to operate near 25 kHz and 40 kHz. The anechoic environment consisted of a 2-m3 box lined with absorbing material whose absorption coefficient was measured by the pulse-echo technique. The air density and the speed of sound were calculated using formulas available in the literature. The resulting values of transducer sensitivity (calibration factor) compared well, within 5 -10 %, with the values specified by the vendor. No accuracy statement was available for the transducers under test, not only because of their price, but mainly because no primary calibration services are available in the low ultrasonic range of frequencies, in contrast to the higher, MHz, range. A recent dissertation by N. Bouaoua, discovered in the course of this research, could fill this void should its procedures be adopted by a standards laboratory.

High intensity air ultrasound source for determining ultrasound microphone sensitivity up to 400 kHz

A broadband air jet ultrasound source, RSS101U-H, for animal bioacoustics research produces broadband ultrasound to at least 400 kHz. Free field reciprocity calibration of ½” condenser microphones on-axis, grid caps removed, using sine wave excitation by the method of Rudnick and Stein [JASA 20, pp 818-825, (1948)] was made (previously used to 280 kHz [JASA 67, p 7, (1980)]). Measurement from 5 kHz to 100 kHz was made in 1 kHz bins via an FFT analyzer. A communications receiver was used from 40 kHz to 400 kHz. The sensitivity of a ¼” microphone was determined from the free field of the reciprocity ½” microphone source. Air jet ultrasound level at 80 mm distance was then determined with the ¼“ microphone. Communications receiver 2.5 kHz bandwidth data was reduced to 1 kHz bin values. Air humidity sound absorption was determined via ANSI 1.26. The ¼” microphone sensitivity and broadband source sound level results in 1 kHz bands to 400 kHz are presented. Air jet spectral level was 97 dB re 20 uPa @ 75 kHz to 57 dB @ 400 kHz. This can be used to rapidly determine the sensitivity of any air ultrasound microphone over this frequency range.

A first laboratory course for teaching advanced acoustics.

The overwhelming majority of “structured” instructional activity in graduate schools offering advanced degrees in acoustics is spent in classes that require solution of problems sets and exams and might also include some relevant literature searches and reports. Most potential employers of these advanced degree recipients assume that their education included exposure to some hands-on measurement of sounds and vibrations followed by analysis and presentation of those measurements in an appropriate (typically graphical) format. At the very least, measurements using sound level meters, hydrophones, and accelerometers should be included along with their calibration as well as experience with transducers that includes comparison of measurements with theory. Nine laboratory exercises will be described that are required for an MS degree. These currently include characterization of electrodynamic loudspeaker parameters, Helmholtz resonators, coupled acousto-mechanical systems, sound propagation in a water-filled waveguide, shock wave development and wave-wave interactions in one dimension, determination of elastic moduli by measurement of bar resonances, reciprocity calibration, and accelerometer calibration. Instrumentation utilized in the course includes multi-channel spectrum analysis (swept-sine and FFT), lock-in amplifiers (phase-sensitive detection), function generators, and waveform capture using a digital storage oscilloscope. The importance of completing a “preliminary exercise” prior to each laboratory will be stressed.

Reciprocity Measurements in Acoustical and Mechano-Acoustical Systems. Review of Theory and Applications

In 1873 Lord Rayleigh defined the General Reciprocity Theorem for stable, finite, lumped, passive, linear dynamical systems which only contain reversible (bilateral) elements. In spite of Rayleigh's authority, there have been a number of papers expressing doubts about the validity of the theorem for certain acoustical and mechano-acoustical systems. It can be shown however, that these papers are either based on too primitive experiments or on too simple theoretical models. On the other hand there are many publications showing the validity of the theorem. It can be concluded that Rayleigh's theorem is correct. Flow disturbs reciprocity because it introduces non-reversible elements. Nevertheless, in many systems with flow, the disturbing effect is limited and reciprocity can still be applied. The most straightforward application of reciprocity is the measurement of transfer functions. Second in order, because it requires two measurements instead of one, is the measurement of acoustical or mechanical source strength by reciprocal substitution. Third in order, because it needs three measurements, is the reciprocity calibration of microphones and hydrophones. Until 1970, only the latter application was known. In the period between 1970 and 1988 the author of this paper and his colleagues developed a number of methods for the reciprocal measurement of transfer functions and source strength in mechano-acoustical and acoustical systems. It was shown that the reciprocal measurement of transfer functions and of source strength has often great advantages over the direct alternatives. Since 1985, others joined the efforts. Particularly J. W. Verheij, F. J. Fahy and I. L. Ver have done very much for the further development and dissemination of the methods. Nowadays they are widely applied in the automotive industry and in the shipbuilding industry, where they are used for transfer path analysis, data gathering for prediction methods, source identification, source characterisation and for radiation measurements. The methods are also applied to aircraft, trains and buildings, but the dissemination of the methods for those systems is less than for cars, trucks and ships. Further applications concern the development of quiet gearboxes, the development of quiet fans, the prediction of the effects of sonic booms and the design of musical instruments.

Experimental measurement of the nonlinearities of electrodynamic microphones

This paper presents an experimental way of characterizing the nonlinearities of electrodynamic microphones used as acoustical sources. This functioning occurs for reciprocal calibration techniques. For this purpose, its electrical impedance is measured with a Wayne Kerr wedge which has an excellent precision. Moreover, it can be noted that the Thiele and Small model is used to characterize its electrical impedance. Furthermore, an experimental method based on Simplex algorithm allows us to construct polynomial laws which describe the dependence of the Thiele and Small parameters with the input voltage. The nonlinear variations obtained allow us to determine the nonlinear differential equation of the electrodynamic microphone. Then, this equation is solved numerically in order to confirm the accuracy of the polynomial laws obtained by the Simplex algorithm. The distortions are measured with a laser Doppler velocimeter and compared with the ones obtained by the numerical solving of the nonlinear differential equation. The experimental displacement spectrum is consistent with the theoretical one.

The determination of uncertainty in the calibration of acoustic emission sensors

The paper reviews the background and methodology of the primary calibration of Acoustic Emission (AE) sensors. Two practically realised basic calibration methods are described and explained. The method of reciprocity calibration is based on the reciprocity theorem. The input current and reception signal voltage for tone bursts of varying frequency are measured for each pair together with known reciprocity parameters. The step function calibration method is based on the generation of well-characterised displacements of capillary brakes on the surface of the block. The response of the sensor under test is then compared to the response of the reference transducer. The comparison of the results of both methods on a steel block is presented. The shapes of measured calibration characteristics are approximately the same, but there is a difference in amplitude between characteristics. The uncertainty of measurement by reciprocity calibration is determined and presented in the paper. The uncertainty in the range from 60 kHz to 285 kHz was ±3 dB and from 285 kHz to 1 MHz, up to ± 8dB.

Final report on key comparison COOMET.AUV.A-K1

A regional key comparison on primary standards for sound in air, COOMET.AUV.A-K1, based on pressure reciprocity calibration of laboratory standard microphones, was held in 2002. The results were submitted to and approved by the CCAUV in October 2008. Six national metrology institutes took part and the results of five of the laboratories have been linked to the corresponding CCAUV.A-K1 comparison. A generalized least squares approach was used to determine the degrees of equivalence for 14 acoustic frequencies and the results demonstrate agreement within the stated uncertainties.Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCAUV, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).

Microphone calibration.

Microphone calibration accurate acoustical measurements are desirable for legal reasons and for research and development. The uncertainty in acoustic measurements may cause uncertainty in determining improvement in design and development of products. International standards may still be improved for calibration of the measurement technique at low frequencies and at high frequencies especially. The absolute calibration of measurement microphones is dominated by reciprocity calibration. This has been dominating in acoustic metrology for many years and rightly so for the middle frequency range 100–1000 Hz. Other methods are very useful at low frequencies and at high frequencies with a good overlap to the reciprocity technique and may offer lower uncertainty especially for calibration in the field where the major part of acoustical measurements take place. Microphone comparison, piston phone calibration, scaling in microphone size at high frequencies, electrostatic actuator, and directionality are some of the techniques used in practical calibration work.

Acoustical impedance measurement.

Many components of specialty transducers have extremely tight acoustic impedance tolerances and become difficult to measure in a production environment. Comparing the device to the acoustical impedance of a cavity is one method of determining its acoustical impedance. A precise method of determining the acoustical impedance is described. The technique applies methods normally found in defining cavities for pressure reciprocity calibration to obtain a precision acoustical reference. Pressure reciprocity standards also define how environmental factors influence acoustical properties and these are included into the system to maintain the precision regardless of the environmental conditions or the frequency of operation. Further improvements are obtained by employing differential measurements throughout the measurement and calibration process to eliminate many common errors common to field calibration of microphones. Ultimately the measured data are curve fitted to an equivalent circuit model to extract the desired components from the measurement artifacts. This talk will discuss the method of defining the acoustical components and extracting the desired value from the equivalent circuit model.

A note on determination of the diffuse-field sensitivity of microphones using the reciprocity technique

The diffuse-field response of a microphone is usually obtained by adding a random-incidence correction to the pressure response of the microphone. However, the random-incidence correction is determined from a relative measurement, and its accuracy depends not only on the relative response at all angles of incidence but also on the accuracy of the frequency response at normal incidence. By contrast, this paper is concerned with determining the absolute diffuse-field response of a microphone using the reciprocity technique. To examine this possibility, a reciprocity calibration setup is used for measuring the electrical transfer impedance between a pair of microphones placed in a miniature (2 m(3)) reverberation room. The transfer function between the microphones is measured using fast Fourier transform analysis and pseudorandom noise. The calculation of the diffuse-field sensitivity involves (a) separation of the reverberant response from the total response, (b) determination of the reverberation time, and (c) averaging over space and frequency. The resulting diffuse-field correction is compared with an estimate of the random-incidence correction determined in an anechoic room and with a numerical prediction.

Progress in Primary Calibration of Acoustic Emission Sensors

The paper reviews the background of the primary calibration of acoustic emission sensors and the determination of uncertainty by this calibration. There are discussed the aims and the purpose of the primary calibration and main sources of uncertainty in practical usage of calibration results. The comparison of the results of the both method is presented. The shape of calibration characteristics corresponds well up to 500 kHz. The calculation of the uncertainty in the reciprocity and step function calibration is closely described. The problem of propagation of uncertainty in the fast fourier algorithm was solved. Uncertainty of measurement by primary calibration is determined and presented in the paper. The uncertainty in reciprocity calibration of UT 1000 in range from 60 kHz to 285 kHz was ±3dB and from 285 kHz to 1 MHz up to ±8 dB and the same results in the calibration by step function. The calculation of the uncertainty includes all the presumable sources. Such as variation of input coefficient of reciprocity parameter, impact of thickness of glass capillary Also the main problems, that were solved and have to be solved, are presented.

Low frequency hydrophone calibration with using tensometric pressure sensor

Usually when calibrating a hydrophone in an acoustic coupler the piezoelectric hydrophones use an auxiliary transducer. Widely applicable reciprocity calibration is high‐ly accurate, but difficult in realization and laborious. The method of comparison with a reference transducer is more simple and quick, but less accurate. In the paper the method of low frequency hydrophone calibration using the auxiliary transducer with a flat frequency response up to 3 kHz is considered. The auxiliary transducer is calibrated accurately by changing the water column in the acoustic coupler. It finally allows us to calibrate measuring hydrophones more accurately too. The measuring equipment on the basis of tensometric pressure sensor type MPX 5010 is considered.

A method to measure and interpret input impedance of small acoustic components

Many applications would require to characterize the input behaviour of small acoustic components such as small tubes, small rectangular or circular slits, small cavities (or their associations in the form of one-port passive linear acoustic systems). These applications relate to artificial ears, loudspeakers, microphones miniaturized or not (among other electroacoustic devices), and acoustic tools used in precise measurements. Today, these small components are characterized analytically using modelling wherein viscosity, heat conduction, inertia, and compressibility of the fluid are considered, beyond realistic boundary conditions (no slip conditions and no temperature variations near the walls). But the results are usually obtained with a relative uncertainty greater than 50% (due to the geometrical uncertainties of the components). Therefore, it is of importance to characterize experimentally the input properties of these kind of components with a good accuracy, that is to say to measure their input impedance with a relative uncertainty of the order of magnitude of 10 - 2 . These measurements were quite impossible until now because the input impedances of such components are usually much greater than those involved in the measuring set-up. Here a measurement procedure is presented which uses the very precise reciprocity calibration method and the corresponding set-up available on the market. The results obtained on classical elements are discussed by comparison between experimental and theoretical results, showing the precision that would be achieved.

Calibration of sensors for acoustic detection of neutrinos

Calibration of sensors is an important task for the acoustic detection of neutrinos. Different approaches have been tried and used (calibrated hydrophones, resistors, powerful lasers, light bulbs explosion, etc.) We propose some methods for calibration that can be used in both the lab and the telescope ("in situ"). In this paper, different studies following these methods and their results are reported. First, we describe the reciprocity calibration method for acoustic sensors. Since it is a simple method and calibrated hydrophones are not needed, this technique is accessible for any lab. Moreover, the technique could be used to calibrate the sensors of a neutrino telescope just by using themselves (reciprocally). A comparison of this technique using different kind of signals (MLS, TSP, tone bursts, white noise), and in different propagation conditions is presented. The limitations of the technique are shown, as well as some possibilities to overcome them. The second aspect treated is the obtaining of neutrinolike signals for calibration. Probably, the most convenient way to do it would be to generate these signals from transducers directly. Since transducers do not usually have a flat frequency response, distortion is produced, and neutrino-like signals could be difficult to achieve. We present some equalization techniques to offset this effect. In this sense, the use of inverse filter based in Mourjopoulos theory seems to be quite convenient.

Effect of Power Line Interference on Microphone Calibration Measurements Made at or Near Harmonics of the Power Line Frequency.

The electrical measurements required during the primary calibrations of laboratory standard microphones by the reciprocity method can be influenced by power line interference. Because of this influence, the protocols of international inter-laboratory key comparisons of microphone calibrations usually have not included measurements at power line frequencies. Such interference has been observed in microphone output voltage measurements made with a microphone pressure reciprocity calibration system under development at NIST. This system was configured for a particular type of standard microphone in such a way that measurements of relatively small signal levels, which are more susceptible to the effect of power line interference, were required. This effect was investigated by acquiring microphone output voltage measurement data with the power line frequency adjusted to move the frequency of the interference relative to the center frequency of the measurement system passband. These data showed that the effect of power line interference for this system configuration can be more than one percent at test frequencies harmonically related to the power line frequency. These data also showed that adjusting the power line frequency to separate the interference and test frequencies by as little as 1.0 Hz can reduce the effect of the interference by at least an order of magnitude. Adjustment of the power line frequency could enable accurate measurements at test frequencies that otherwise might be avoided.

Free-field reciprocity calibration of laboratory standard (LS) microphones using a time selective technique

Although the basic principle of reciprocity calibration of microphones in a free field is simple, the practical problems are complicated due to the low signal-to-noise ratio and the influence of cross talk and reflections from the surroundings. The influence of uncorrelated noise can be reduced by conventional narrow-band filtering and time averaging, while correlated signals like cross talk and reflections can be eliminated by using time-selective postprocessing techniques. The technique used at DPLA overcomes both these problems using a B&K Pulse analyzer in the SSR mode (steady state response) and an FFT-based time-selective technique. The complex electrical transfer impedance is measured in linear frequency steps from a few kHz to about three times the resonance frequency of the microphones. The missing values at low frequencies are estimated from a detailed knowledge of the pressure sensitivities. Next an inverse FFT is applied and a time window around the main signal is used to eliminate cross talk and reflections. Finally, the signal is transformed back to the frequency domain and the free field sensitivities calculated. The standard procedure at DPLA involves measurements at four distances and the repeatability of the calibrations over time is within ±0.03 dB up to about 1.5 times the resonance frequency of the microphones.