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Reporton the CIPM key comparison CCAUV.U-K1

(ultrasonic power)

Final Report

October 2002

K. Beissner

Physikalisch-Technische Bundesanstalt

38116 Braunschweig, Germany

AbstractThis is the final report on the CIPM key comparison CCAUV.U-K1 (ultrasonic power). Ninenational metrology institutes world-wide participated, with the Physikalisch-TechnischeBundesanstalt, Germany, as the pilot institute. The transfer standard was an ultrasonic sourcetransducer based on a lithium niobate crystal. The task was to measure the electric input voltageto the transducer and the ultrasonic output power emitted by the transducer into an anechoicwater volume. The technical protocol specified three frequencies in the MHz range and fiveexcitation levels. The overall duration of the circulation of the transfer standard includingremeasurements was 30 months. The report describes the measurement methods applied by theparticipants, the results obtained and the associated uncertainties. The participants' relativeexpanded uncertainties for the ultrasonic power or equivalent quantities at the variousfrequencies and excitation levels range from 1.8 × 10−2 to 20.9 × 10−2. Reference values anddegrees of equivalence are given. The obtained agreement between the participants' results cangenerally be considered satisfactory, in some cases excellent.

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Contents

1 Introduction 3

2 Fundamentals 3

3 List of participants and time schedule 4

4 Ultrasonic transducer and measurements required 5

5 Measurement methods applied and results stated by the participants 7

6 Stability 15

7 Reference values and degrees of equivalence 19

References 56

Annex A. Formulae 57

Annex B. Technical protocol 62

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1 Introduction

During its meeting on 10 and 11 March 1998, the AVG Working Group (that later became theConsultative Committee for Acoustics, Ultrasound and Vibration, CCAUV) decided to recommendcarrying out a comparison of ultrasonic power in water. This comparison later became the CIPMkey comparison CCAUV.U-K1. Participating were nine national metrology institutes world-wide.The pilot laboratory was the Physikalisch-Technische Bundesanstalt (PTB), Germany. Thepresent text is the final report.

The comparison was undertaken on the basis of the Mutual Recognition Arrangement (MRA) of1999 and of its Appendix F, "Guidelines for CIPM key comparisons". According to these, the finalreport not only includes the results and uncertainties reported by the participants but also givesproposals for reference values and degrees of equivalence.

Draft A was circulated to the participants in March 2002. All participants agreed to the report.Draft B was finalized in August 2002 and approved by the CCAUV during its meeting on 1 and 2October 2002.

2 Fundamentals

The procedures to be followed were first discussed in letters exchanged between the pilotinstitute and the participants and then described in the technical protocol and circulated inSeptember 1999. They were again circulated in April 2000 as the second version of the protocolwith an enlarged list of participants. The protocol is included in annex B to this report.

The task was to measure the time-averaged ultrasonic output power emitted by an ultrasonicsource transducer into an anechoic water volume at room temperature and under specifiedexcitation conditions. The preferred type of measuring device used in this context is the radiationforce balance (according to IEC 61161 [1], see also [2]) which makes use of the physical effect ofthe acoustic radiation force, i.e. the time-averaged force exerted by the acoustic field on anobstacle, the so-called target. Devices of this kind most frequently are based on a commercial,gravimetric precision balance, but there are also set-ups measuring the radiation force in otherways, and these latter ones usually are also referred to as radiation force balances, although in abroader sense.

As the ultrasonic output power depends on the input voltage applied to the transducer, the latterquantity also had to be measured by the participants. Two different types of voltage measurement(see below) were defined in the technical protocol.

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The technical protocol specified the excitation voltage as regards frequency and amplitude. Threedifferent frequencies and five different excitation levels were given. The aim was to cover therange of frequencies and ultrasonic power values typical of medical applications such asultrasonic diagnosis and therapy. Ultrasonic power is one of the fundamental quantities relevantto safety and global trade which characterize the output of medical ultrasonic equipment, and itsmeasurement and declaration are required by international standards (for example [3, 4])

3 List of participants and time schedule

The list of participants in the order of participation is given in table 1.

Table 1. List of participants in the order of participation

i Code Participating institute Acronym1 A Physikalisch-Technische Bundesanstalt, Braunschweig, Germany PTB2 B National Institute of Standards and Technology, Gaithersburg MD, USA NIST3 C National Research Council / Institute for National Measurement

Standards, Ottawa, CanadaNRC

4 D National Physical Laboratory, Teddington, UK NPL5 E Netherlands Organization for Applied Scientific Research / Prevention and

Health / Division Technology in Health Care, Leiden, The Netherlands (onbehalf of the NMi)

TNO

6 F Commonwealth Scientific and Industrial Research Organization / NationalMeasurement Laboratory, Lindfield NSW, Australia

CSIRO

7 G National Physical Laboratory, New Delhi, India NPLI8 H All-Russian Scientific Research Institute for Physical-Technical and

Radiotechnical Measurements, Mendeleevo, Russia (on behalf of theVNIIM)

VNIIFTRI

9 I National Institute of Metrology, Beijing, China NIM

The transducer was circulated in four loops. Each loop consisted of two participants, and then thetransducer was returned to the pilot laboratory (A) for remeasurement. Four remeasurementswere carried out, viz. RM1, RM2, RM3 and RM4. The full circulation scheme includingremeasurement was: A, B, C, RM1, D, E, RM2, F, G, RM3, H, I, RM4. The first day ofmeasurement (i.e., the first day of series A) was 19 July 1999; the last day of measurement (i.e.,the last day of series RM4) was 16 January 2002.

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4 Ultrasonic transducer and measurements required

The transfer standard was an ultrasonic source transducer specifically designed and fabricated bythe pilot laboratory for the purposes of precision measurements of ultrasonic output quantities. Itsidentification number was "PTB 24 LN 2 MHz". The active part was a gold-plated, air-backed,narrow-band, half-wave resonant lithium niobate crystal. The transducer was to be operated in itsfundamental resonance and in the third and fifth harmonics by applying a suitable RF voltage toits input. As these resonances are rather narrow, precise frequency values were specified to up tofive or six digits in the technical protocol, and are repeated in table 2 below. The participants wererequired to keep to these frequency values, with a maximum tolerance of ± 0.0008 MHz.

Input voltage values for five power levels were specified in the technical protocol (and need notbe repeated here). At nominally 1.9 MHz, four power levels were compulsory and the highestlevel was optional. At nominally 6.3 MHz and 10.5 MHz, only the "very low" and "low" levels wererequired. The entire measurement scheme is shown in table 2. It should be noted that thespecified input voltage values were not intended to exactly yield the nominal output power values,so a power result deviating from the nominal ultrasonic power value should not necessarily beconsidered incorrect.

Table 2. Scheme of the measurements required

Nominal frequency / MHz → 1.9 6.3 10.5Specified frequency / MHz → 1.8732 6.2838 10.5475

Level Nominal powervery low 10 mW yes yes yes

low 100 mW yes yes yesmedium 1 W yes

high 10 W yesvery high 15 W optional

The participants had to provide the necessary excitation voltage using their own generator andamplifier. Two types of voltage measurement were defined in the technical protocol as follows. Intype 1 the participant had to measure the RMS value of the actual voltage at the transducer inputusing his own methods and instruments. He then had to divide the measured ultrasonic outputpower Pout by the square of the actual RMS input voltage Uin in order to obtain G, the transducer'selectroacoustic radiation conductance

G = Pout / (Uin)2 ,

which is generally given in siemens and in this report in millisiemens (mS). For measurements oftype 2, a rectifier module provided by one of the participants (NIST) was circulated along with the

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transducer. The rectifier module was to be directly connected to the transducer input and its DCoutput voltage was to be measured by the participant using an appropriate voltmeter with aparticular input resistance. The RF input voltage applied to transducer and rectifier module was tobe adjusted so that particular values prescribed for the rectifier module output voltage wereexactly obtained, and the transducer's ultrasonic output power under these conditions was to bereported as Pref, the ultrasonic output power (in watt, W, or milliwatt, mW) under referenceconditions.

Consequently, two different quantities, namely G and Pref, will appear in this report along with theiruncertainties. G follows from an ultrasonic power measurement and a type-1 voltagemeasurement. Pref follows from an ultrasonic power measurement and involves a type-2 voltagemeasurement. Measuring G was compulsory, measuring Pref was optional. Type-2 voltagemeasurements were offered to the participants as they were assumed to help to reduceuncertainties and to understand potential radiation conductance discrepancies or even outliers. Itcan be stated in retrospect that five out of nine participants carried out type-2 measurements andthat in these five cases, the Pref results more or less followed the tendencies of the G results.

It should be noted that the measured ultrasonic power generally depends on the distance of thetarget from the transducer and that, according to the technical protocol, the zero-distance valuehad to be derived in each case, either experimentally or by theoretical correction. All G and Pref

values given in this report are understood as the final, zero-distance values.

The water temperature during the measurements was to be measured and reported, and it was tobe as close as possible to 21.5 °C, with a maximum difference of ± 2.0 °C.

A number of nominally identical transducers had been fabricated and checked by the pilotlaboratory, and the transducer 24 LN 2 MHz had been selected from these for reasons of stabilityand for its field structure. The structure of the ultrasonic field was investigated applying acousto-optical tomography and was found to be collimated and piston-like. The nominal beam radius was9.5 mm, the radius of the active electrode. The resonance frequencies given in table 2 were foundfrom frequency sweep experiments as the frequencies of maximum radiation conductance G.

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5 Measurement methods applied and results stated by the participants

The measurement methods and instruments applied by the participants are briefly given in thefollowing. Stating the name of a manufacturer or an instrument type should not be understood asan endorsement. All participants used radiation force devices for the ultrasonic powermeasurement.

The final results of the participants are listed. Unless otherwise stated, the actual frequenciesreported were exactly equal to those specified in table 2. Uncertainties are generally understoodas relative uncertainties in 10−2. uG is the relative standard uncertainty of G. uPref is the relativestandard uncertainty of Pref. Standard uncertainties are rounded to 0.05 × 10−2, expandeduncertainties to 0.1 × 10−2. A level of confidence of 0.9545 is understood. νeff and k are theeffective degrees of freedom and the coverage factor, respectively. Values of νeff = ∞ and k = 2(meaning k = 2.00) are given whenever (a) this was reported by the participant or (b) effectivedegrees of freedom νeff > 200 were reported by the participant or calculated by the project leader.The uncertainties were to be derived in accordance with the Guide to the Expression ofUncertainty in Measurement [5].

A. PTB

Participant A measured with one of the PTB standard radiation force balances, namely that basedon a Mettler AT250 balance. The ultrasonic beam was directed vertically upwards. Five targetswere used alternatively, namely three absorbers and two convex-conical reflectors. The threeabsorbers were from different materials and had a diameter of 50 mm, 110 mm and 110 mm,respectively. The two reflectors 60 mm in diameter were of nominally equal material and designbut had been fabricated at different times. Each final value reported below was the result of 4 to 8(G) or of 3 to 8 (Pref) independent measurements. The use of the targets depended on frequencyand power level as follows.1.9 MHz, very low: 6 independent measurements with 2 absorbers and 2 reflectors.1.9 MHz, low: 8 independent measurements with 3 absorbers and 2 reflectors.1.9 MHz, medium: 6 independent measurements with 3 absorbers.1.9 MHz, high: 7 (G) or 3 (Pref) independent measurements with 1 absorber.1.9 MHz, very high: 4 independent measurements with 1 absorber.6.3 MHz, very low: 6 independent measurements with 2 absorbers and 2 reflectors.6.3 MHz, low: 6 independent measurements with 2 absorbers and 2 reflectors.10.5 MHz, very low: 6 independent measurements with 2 absorbers and 2 reflectors.10.5 MHz, low: 6 independent measurements with 2 absorbers and 2 reflectors.

The final results reported were each obtained by linear, unweighted averaging of the independentmeasurements. In case absorbers and reflectors were used alternatively, each absorber was

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used twice and each reflector once, so that the absorber influence dominates in all final results.Each independent measurement was in fact a series of measurements at various, usually 8 or 12,target distances, and the zero-distance value was obtained by empirical extrapolation. On thewhole, the distance from the transducer surface to the nearest target point was between 2.0 mmand 26.2 mm. The water temperature was between 20.0 °C and 22.9 °C, with an average of21.5 °C. The type-1 voltage measurement was carried out with Ballantine 1394A thermalconverters. The rectifier output voltage in type 2 was measured using a Prema 5017 digitalmultimeter.

Table 3. List of the PTB final results and uncertainties

fnom / MHz Level G / mS uG / 10−2 νeff k k uG / 10−2

1.9 very low 4.890 1.4 ∞ 2 2.8" low 4.917 1.4 ∞ 2 2.8" medium 4.919 1.4 ∞ 2 2.8" high 4.937 1.4 ∞ 2 2.8" very high 4.950 1.4 ∞ 2 2.8

6.3 very low 5.660 1.7 ∞ 2 3.4" low 5.666 1.65 ∞ 2 3.3

10.5 very low 5.796 2.35 ∞ 2 4.7" low 5.842 2.25 ∞ 2 4.5

fnom / MHz Level Pref uPref / 10−2 νeff k k uPref / 10−2

1.9 very low 10.22 mW 1.35 ∞ 2 2.7" low 97.4 mW 1.3 ∞ 2 2.6" medium 1.032 W 1.3 ∞ 2 2.6" high 9.71 W 1.55 ∞ 2 3.1" very high 14.88 W 2.05 ∞ 2 4.1

6.3 very low 10.32 mW 1.6 ∞ 2 3.2" low 98.8 mW 1.55 ∞ 2 3.1

10.5 very low 10.38 mW 2.25 ∞ 2 4.5" low 99.9 mW 2.15 ∞ 2 4.3

B. NIST

Participant B measured with the NIST pulsed radiation force balance [6]. The ultrasonic beamwas directed vertically upwards. The target was a conical absorber 50 mm in diameter. Thedistance from the transducer surface to the apex of the conical target was 1.5 mm. An empiricalattenuation correction factor was applied to the results. The water temperature was between20.4 °C and 22.7 °C, with an average of 21.4 °C. Each of the final results was obtained from 7independent measurements. The type-1 voltage measurement was based on a calibration of therectifier module against Fluke A55 thermal converters. The rectifier module output voltage in type2 was measured using a Keithley 197 digital voltmeter.

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Table 4. List of the NIST final results and uncertainties


1.9 very low 4.857 1.5 ∞ 2 3.0" low 4.998 1.4 ∞ 2 2.8" medium 4.999 1.4 ∞ 2 2.8" high 5.033 1.4 ∞ 2 2.8

6.3 very low 5.760 2.0 ∞ 2 4.0" low 5.801 1.6 ∞ 2 3.2

10.5 very low 5.914 1.6 ∞ 2 3.2" low 6.052 1.5 ∞ 2 3.0


1.9 very low 10.10 mW 1.1 ∞ 2 2.2" low 99.0 mW 0.9 ∞ 2 1.8" medium 1.053 W 0.9 ∞ 2 1.8" high 9.97 W 0.9 ∞ 2 1.8

6.3 very low 10.34 mW 1.6 ∞ 2 3.2" low 101.1 mW 1.2 ∞ 2 2.4

10.5 very low 10.41 mW 1.1 ∞ 2 2.2" low 103.2 mW 1.0 ∞ 2 2.0

C. NRC

Participant C measured with a radiation force balance based on a Mettler AT210 balance. Theultrasonic beam was directed vertically downwards. The target was a concave-conical reflector90 mm in diameter. Target distance correction was made using the acoustic attenuationcoefficient from the literature. Measurements were made at three different target distances,namely 78 mm, 98 mm and 118 mm, and averaged. The water temperature was between 21.4 °Cand 22.8 °C, with an average of 22.2 °C. Each of the final results was obtained from 3independent measurements. The input voltage was measured using a Fluke 8920A voltmeter.Type-2 measurements were not carried out.

Table 5. List of the NRC final results and uncertainties



6.3 very low 5.966 6.65 ∞ 2 13.3" low 5.828 6.25 ∞ 2 12.5

10.5 very low 6.379 10.45 ∞ 2 20.9" low 6.985 10.2 ∞ 2 20.4

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D. NPL

At the "very low", "low" and "medium" levels, participant D measured with the NPL PrimaryStandard Radiation Force Balance (PS) which is based on a Sartorius M25-D balance. Theultrasonic beam was directed vertically upwards. The target was a convex-conical reflector60 mm in diameter. At the "medium" and "high" levels, participant D used the NPL ReferenceTherapy Level Balance (TL) which is based on a Sartorius AC211S-00MS balance. The ultrasonicbeam was directed vertically downwards. The target was a convex-conical reflector 80 mm indiameter. The distance from the transducer surface to the reflector tip was between 3 mm and10 mm (PS) and between 5 mm and 10 mm (TL). Correction to zero distance was made takinginto account the acoustic attenuation coefficient and an empirical momentum conversion factorthat had been determined beforehand. Absorber measurements were also carried out forcomparison purposes, but these results were not included in the final values. The watertemperature was between 20.4 °C and 23.4 °C, with an average of 21.4 °C. Each of the finalresults was obtained from 4 independent measurements. The type-1 voltage measurement wascarried out with a Racal-Dana 9303 RF level meter (via a high-impedance 10x probe) calibratedagainst Fluke A55 thermal converters each day before and after measuring the radiation force.The rectifier output voltage in type 2 was measured using a Keithley 2000 digital voltmeter.

Table 6. List of the NPL final results and uncertainties



6.3 very low 5.822 1.95 ∞ 2 3.9" low 5.800 1.75 ∞ 2 3.5

10.5 very low 5.735 2.8 ∞ 2 5.6" low 5.741 2.8 ∞ 2 5.6


1.9 very low 10.38 mW 1.75 ∞ 2 3.5" low 97.6 mW 1.6 ∞ 2 3.2" medium 1.027 W 1.55 ∞ 2 3.1" high 9.55 W 1.65 ∞ 2 3.3

6.3 very low 10.58 mW 1.85 ∞ 2 3.7" low 100.8 mW 1.6 ∞ 2 3.2

10.5 very low 10.28 mW 2.7 ∞ 2 5.4" low 98.7 mW 2.75 ∞ 2 5.5

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E. TNO

At the "very low", "low" and "medium" levels, participant E measured with a radiation forcebalance based on a Mettler AE163 balance (AE). The target was an absorber 40 mm x 100 mm insize. At the "medium", "high" and "very high" levels, participant E measured with a radiation forcebalance based on a Mettler PR2004 balance (PR). The target was an absorber 110 mm x130 mm in size. The ultrasonic beam was in both cases directed vertically downwards.Measurements were made at three different target distances, namely at 10 mm, 13 mm and16 mm (AE) and at 10 mm, 15 mm and 20 mm (PR). The results were extrapolated back to zerodistance. The water temperature was between 20.2 °C and 23.6 °C, with an average of 22.2 °C.Each of the final results was obtained from 4 (at the "very low" level) or 3 independentmeasurements. The input voltage was measured using Ballantine 1394A thermal converters.Type-2 measurements were not carried out.

Table 7. List of the TNO final results and uncertainties


1.9 very low 5.037 2.0 16.1 2.17 4.3" low 5.068 1.8 13.0 2.21 4.0" medium 5.014 1.1 11.4 2.24 2.5" high 5.102 0.95 9.8 2.29 2.2" very high 5.122 1.1 6.0 2.52 2.8

6.3 very low 5.772 1.9 11.8 2.24 4.2" low 5.718 1.15 8.3 2.35 2.7

10.5 very low 5.746 1.3 11.8 2.24 2.9" low 5.805 0.95 15.5 2.17 2.1

F. CSIRO

Participant F measured with a radiation force balance based on an Ohmic Instruments ModelUPM-DT-1 ultrasound power meter. The ultrasonic beam was directed vertically downwards. Thetarget was a convex-conical reflector 80 mm in diameter of CSIRO manufacture. The distancefrom the transducer surface to the reflector tip was 1 mm. Target distance correction was madeusing the acoustic attenuation coefficient from the literature. The water temperature was between21.1 °C and 22.9 °C, with an average of 22.1 °C. Each of the final results was obtained from 5 (atthe "medium" and "high" levels) or 4 independent measurements. The type-1 voltagemeasurement was carried out with a Tektronix TDS540 digitising oscilloscope via a TektronixP6201 FET probe. The rectifier output voltage in type 2 was measured using a Hewlett-Packard34401A multimeter.

Participant F did not measure at the "very low" level. He stated that the balance used did not havesufficient resolution nor precision to make a worthwhile measurement at this power level.

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Table 8. List of the CSIRO final results and uncertainties


1.9 low 5.574 6.5 6.2 2.50 16.2" medium 5.100 3.7 4.2 2.82 10.4" high 5.144 2.6 5.7 2.55 6.7" very high 5.128 4.0 4.7 2.70 10.8

6.3 low 6.614 6.6 5.8 2.54 16.810.5 low 6.901 6.95 7.7 2.38 16.6


1.9 low 114.5 mW 6.0 6.2 2.50 15.0" medium 1.124 W 3.2 4.2 2.82 9.0

6.3 low 115.4 mW 6.4 5.8 2.54 16.310.5 low 117.6 mW 6.8 7.7 2.38 16.2

G. NPLI

At the "very low" and "low" levels, participant G measured with a radiation force balance based ona Mettler M3 balance. The ultrasonic beam was directed vertically upwards. The target was aconvex-conical reflector 25 mm in diameter. At the "medium" and "high" levels, participant Gmeasured with a fixed path vertical float device. The ultrasonic beam was directed verticallydownwards. The target was a concave-conical reflector 60 mm in diameter. Distance variationexperiments showed much scatter in the results (in both cases, i.e., with the balance and the floatdevice). Participant G decided not to apply any distance correction and to set the zero-distancepower equal to the power actually measured. The reported values stem from measurements at 23mm (radiation force balance, distance between transducer and target's apex) or 33 mm (floatdevice, distance between transducer and float's top), respectively. Water temperatures rangingfrom 23.0 °C to 24.0 °C were reported, with an average of 23.4 °C. Each of the final results wasobtained from 8 to 14 measurements distributed over 3 days. The input voltage was measuredusing a Tektronix TDS 210 digital storage oscilloscope. At the "high" level, a 10x probe wasemployed along with the oscilloscope. Type-2 measurements were not carried out.

The results at nominally 6.3 MHz and 10.5 MHz reported by participant G were found to beanomalous. When this was investigated it was noted that, due to an oversight, the experimentshad been conducted at frequencies significantly different from those specified in the technicalprotocol (and repeated in table 2 above). Consequently these results are not valid and have beenexcluded from the comparison. The lowest frequency value of participant G is correct(1.8732 MHz), therefore the results obtained at this frequency have been retained.

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Table 9. List of the NPLI final results and uncertainties



H. VNIIFTRI

Participant H measured with a tethered float radiometer similar to that described in [7]. There aretwo versions with different sensitivities (depending on the silver chains used): EIMU-1 which is themore sensitive device, and EIMU-2. The ultrasonic beam was directed vertically downwards. Thetarget was in both cases a concave-conical reflector 100 mm in diameter. The (effective) targetdistance from the transducer was between 33 mm and 141 mm. Effective attenuation coefficientswere derived from the measurements (as percentage values of the full acoustic attenuationcoefficient known from the literature, the percentage values were found to depend on frequency)and were used to calculate the zero-distance results. At the "very low" level, the device EIMU-1and at the "high" level, the device EIMU-2 was used. At the "low" and "medium" levels, the twodevices were used alternately. The water temperature was between 20.0 °C and 22.9 °C, with anaverage of 21.9 °C. Each of the final results was obtained from 10 independent measurements.Actual frequency values of 1.8730 MHz, 6.2840 MHz and 10.5470 MHz were reported. They areslightly different from the specified values but within the permitted tolerance. The input voltagewas measured using a VK3-61A digital broadband voltmeter (Radiofactory, Minsk) and a V3-63digital RF voltmeter (Punnaret, Tallinn). Type-2 measurements were not carried out.

Table 10. List of the VNIIFTRI final results and uncertainties


1.9 very low 4.841 2.8 29 2.09 5.9" low 4.674 1.7 139 2.02 3.4" medium 4.755 1.85 54 2.05 3.8" high 4.817 2.05 33 2.08 4.3

6.3 very low 5.447 3.15 66 2.04 6.4" low 5.444 2.3 ∞ 2 4.6

10.5 very low 5.606 3.5 ∞ 2 7.0" low 5.882 3.3 ∞ 2 6.6

I. NIM

Participant I used two different balances. The target was a conical reflector 80 mm in diameterhaving two functions. One side can be used as a 135° concave-conical reflector, and the otherside as a 90° convex-conical reflector. The distance between target and transducer was between

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5 mm and 21 mm. Target distance correction was made using the acoustic attenuation coefficientfrom the literature. At the "very low" and "low" levels, participant I measured with a radiation forcebalance based on a Perkin-Elmer AD-2Z balance. The ultrasonic beam was directed verticallyupwards and towards the convex-conical side of the target. At the "medium", "high" and "veryhigh" levels, participant I measured with a radiation force balance based on a Perkin-Elmer AM-2balance. The ultrasonic beam was directed vertically downwards and towards the concave-conical side of the target. The water temperature was between 20.5 °C and 22.7 °C, with anaverage of 21.7 °C. Each of the final results was obtained from 6 independent measurements.Actual frequency values of 1.8733 MHz, 6.2840 MHz and 10.5478 MHz were reported. They areslightly different from the specified values but within the permitted tolerance. Both type-1 andtype-2 voltages were measured with a Hewlett-Packard 3403c RMS voltmeter.

Table 11. List of the NIM final results and uncertainties


1.9 very low 4.789 1.7 42 2.06 3.5" low 4.856 1.45 25 2.11 3.1" medium 4.948 1.45 19 2.14 3.1" high 5.047 1.4 20 2.13 3.0" very high 5.033 1.25 16 2.17 2.7

6.3 very low 5.674 2.0 28 2.09 4.2" low 5.739 2.0 16 2.17 4.4

10.5 very low 6.090 1.8 44 2.06 3.7" low 5.910 2.3 63 2.04 4.7


1.9 very low 10.08 mW 1.75 33 2.08 3.7" low 94.0 mW 1.55 32 2.08 3.3" medium 1.026 W 1.4 25 2.11 3.0" high 10.05 W 1.4 24 2.11 3.0" very high 15.23 W 1.35 23 2.11 2.9

6.3 very low 10.52 mW 1.55 33 2.08 3.3" low 103.3 mW 1.6 35 2.07 3.3

10.5 very low 10.71 mW 1.65 34 2.08 3.5" low 101.0 mW 1.6 34 2.08 3.4

RM. PTB remeasurements

Here almost the same applies as stated under "A" above. The only difference is that in eachremeasurement the number of independent measurements was smaller, namely about half thatunder "A". In those cases in which an absorber was used twice under "A", it was used once here,and only one reflector was used here. The average water temperatures were as follows: 21.4 °C(RM1), 21.6 °C (RM2), 21.8 °C (RM3), 21.4 °C (RM4).

The RM results will be reported and discussed in section 6.2 below.

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6 Stability

6.1 Temperature dependence

The temperature dependence of G and Pref was checked by the pilot laboratory at the "low" level,in the range of water temperatures from 18.8 °C to 23.4 °C. Both quantities decreased withincreasing temperature but at a very low rate. The effects observed were smaller than themeasurement uncertainty and the results to be given are, therefore, not fully significant, althoughthey could be roughly reproduced upon repeat. Table 12 presents the observed temperaturecoefficient of G and Pref.

Table 12. Observed temperature coefficient (in % / °C) of G and Pref

at 1.9 MHz at 6.3 MHz at 10.5 MHzTemp. coeff. of G in % / °C − 0.07 − 0.07 − 0.12

Temp. coeff. of Pref in % / °C − 0.20 − 0.18 − 0.24

The effect is obviously slightly different for G and Pref. This indicates that the voltagemeasurement also has some influence here. The entire measurement series with increasingwater temperature took one day, and during this time the room temperature also increased andthe electronic instruments warmed up. Thus the effect may also depend on the stability of thevoltmeters and of the rectifier module with respect to temperature and time.

The temperature values mentioned in section 5 above are the temperatures from all individualmeasurements. The temperatures to be associated with the (averaged) final results in tables 3 to11, on the other hand, range from 20.8 °C to 24.0 °C, which means a rectangular distribution of± 1.6 °C. In view of the rather low temperature coefficients of table 12, corrections for temperatureeffects are not considered necessary (the more so since the potential influence of roomtemperature changes on the participants' voltmeters cannot be taken into account here) but ageneral uncertainty contribution due to the temperature dependence will be given below.

6.2 Temporal stability

The full list of the remeasurement results obtained by the pilot laboratory is given in table 13.

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Table 13a. Remeasurement results of G in mS

A RM1 RM2 RM3 RM4 diff / 10−2 σ / 10−2

Jul-Aug 99 Feb-Mar 00 Aug-Sep 00 May-Jun 01 De01-Ja021.9 MHzvery low 4.890 4.890 4.907 4.907 4.920 0.62 0.26

low 4.917 4.917 4.916 4.922 4.930 0.28 0.11medium 4.919 4.927 4.926 4.930 4.936 0.35 0.13

high 4.937 4.929 4.946 4.937 4.948 0.39 0.16very high 4.950 4.940 4.947 4.942 4.957 0.35 0.14

av. 4.922 4.921 4.928 4.928 4.938 0.35 0.146.3 MHzvery low 5.660 5.655 5.655 5.666 5.665 0.21 0.10

low 5.666 5.674 5.679 5.680 5.681 0.26 0.11av. 5.663 5.664 5.667 5.673 5.673 0.18 0.08

10.5 MHzvery low 5.796 5.833 5.845 5.838 5.852 0.96 0.37

low 5.842 5.858 5.851 5.841 5.864 0.39 0.17av. 5.819 5.846 5.848 5.840 5.858 0.67 0.25

av. 5.286 5.291 5.297 5.296 5.306 0.37 0.14

Table 13b. Remeasurement results of Pref in mW ("very low", "low") or W ("medium", "high", "veryhigh"), respectively

A RM1 RM2 RM3 RM4 diff / 10−2 σ / 10−2

Jul-Aug 99 Feb-Mar 00 Aug-Sep 00 May-Jun 01 De01-Ja021.9 MHzvery low 10.223 10.271 10.302 10.261 10.314 0.89 0.35

low 97.41 97.37 97.23 97.36 97.57 0.35 0.13medium 1.0321 1.0336 1.0336 1.0338 1.0353 0.31 0.11

high 9.711 9.705 9.721 9.710 9.733 0.28 0.11very high 14.875 14.850 14.905 14.952 14.958 0.72 0.326.3 MHzvery low 10.323 10.329 10.235 10.272 10.273 0.91 0.38

low 98.76 99.10 98.92 99.02 98.93 0.34 0.1310.5 MHzvery low 10.382 10.481 10.435 10.427 10.394 0.95 0.37

low 99.90 100.29 99.96 99.94 99.94 0.39 0.16

av. γ 1.0054 1.0078 1.0064 1.0068 1.0076 0.24 0.10

Table 13a includes additional rows for "av." standing for "average". The average G values for1.9 MHz, 6.3 MHz and 10.5 MHz are shown in these rows. The last row gives the total average ofall nine G values, a quantity that is not significant in itself but may be used to study the averagechange of G from remeasurement to remeasurement.

17

The quantity γ appearing in the last row of table 13b is understood as the ratio of Pref to therespective nominal power value (as shown in table 2 above), and the last row of table 13b gives γas averaged over all nine results. Again, this quantity is not significant in itself but may be used tostudy the average change of Pref from remeasurement to remeasurement.

In order to quantify the differences between the values in each row, the quantities diff and σ havebeen calculated and appear in the tables. diff is the relative difference between the highest andlowest value in each row. σ is the relative experimental standard deviation of the five values ineach row. It can be seen that in all cases diff is below 1 × 10−2 and σ below 0.4 × 10−2, even at the"very low" level with its increased influence of random background noise in the balance readout.

When the "average" behaviour is considered (last row in both cases), σ turns out to be 0.14 × 10−2

for G and 0.10 × 10−2 for Pref. This means that the transducer is very stable and that the observedtemporal changes of the output are small in comparison with the measurement uncertainty andare, therefore, insignificant.

There appears to be, however, a small tendency in the results. The averaged G values in the lastrow of table 13a slightly increase with time, and the corresponding tendency is much less clear inthe last row of table 13b. The resulting average annual increase can be calculated to be0.13 %/year for G and 0.06 %/year for Pref. It might be possible to take this tendency into accountand to correct the results of this key comparison accordingly or to assume a time-dependentreference value. This is not done here, for the following reasons.I) The effect is small in comparison with the measurement uncertainty of all participants and,therefore, more or less uncertain.II) If the small apparent temporal increase is considered a true effect, the question arises as towhy it is different for G and Pref. It could then be assumed that the temporal stability of thevoltmeters used has an influence, and a general correction for the results of the participantswould be difficult under these circumstances.III) The main G results of this key comparison do not support the assumption of increasingradiation conductance. In Fig. 2 below, for example, the results and uncertainty bars ofparticipants G and H look "low" rather than "high". If radiation conductance increasing with timewas assumed, the situation would become more unfavourable for these participants.

In conclusion and considering the transducer stability with respect to both temperature and time,instead of applying individual corrections to the participants' results, an additional contribution tothe uncertainty of the reference value is taken into account, and this also has an influence on thedegrees of equivalence to be derived. The temperature span of ± 1.6 °C mentioned abovemultiplied by the temperature coefficients of table 12 and converted into a standard uncertaintyleads to standard uncertainties of about 0.1 × 10−2 for G and 0.2 × 10−2 for Pref. These valuescombined (in quadrature) with σ from the last row of tables 13a and 13b, respectively, yield astandard uncertainty of 0.2 × 10−2 and an expanded uncertainty of 0.4 × 10−2 for both G and Pref.

18

These uncertainty contributions are much smaller than the uncertainty of the reference valuestemming from the uncertainties of the participants' results.

19

7 Reference values and degrees of equivalence

Two different quantities were measured in this key comparison in nine frequency-powercombinations. The discussion of the results will therefore be subdivided into 18 subsections. Thesymbol x will generally be used for the measurand, standing for G or Pref, respectively.Uncertainties are again understood as relative uncertainties. Again a level of confidence of0.9545 is understood. The formulae used are explained in annex A.

First, the reference value xR and its relative standard uncertainty u(xR) and effective degrees offreedom ν(xR) are given in each subsection. As agreed with the participants, the reference valueis generally identified with the weighted mean, with the reciprocal square of the individualstandard uncertainties used as weights (see annex A). However, the compatibility of the weightedmean with the respective results is checked in each case using a criterion as described in annexA, and if this check fails, the median as a more robust location parameter is used as the referencevalue. This will occur in three out of 18 cases. It should be noted that the reference value is ineach case obtained from all results and that no cut-off uncertainty limits are applied.

Once the reference value has been determined, the degree of equivalence of each laboratorywith respect to the reference value is given by the relative deviation dj = (xj – xR) / xR and by therelative expanded uncertainty of the deviation, k(dj) u(dj), which is simply referred to as ku in thetables. Explanations are given in annex A.

The degree of equivalence between two laboratories is given by the mutual relative deviationdij = di – dj and by the relative expanded uncertainty of the mutual deviation, k(dij) u(dij), which isalso simply referred to as ku in the tables.

No correlations between the participants have been identified and no covariances need to betaken into account.

20

7.1 Radiation conductance G, 1.9 MHz, "very low"

The weighted mean is used as the reference value here.

Table 14. The reference value and its (relative) uncertainty. G, 1.9 MHz, "very low"xR / mS u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

4.875 0.7 ∞ 2 1.4

Table 15. Final G results and relative deviations from the reference value. ku means k(dj) u(dj).The degree of equivalence of each participant with the reference value is given by dj and ku

Part. A B C D E G H Ixj / mS 4.890 4.857 5.367 4.950 5.037 4.636 4.841 4.789dj / 10−2 0.3 -0.4 10.1 1.5 3.3 -4.9 -0.7 -1.8u(dj)/10−2 1.25 1.35 4.45 1.75 1.95 2.15 2.7 1.55ν(dj) ∞ ∞ ∞ ∞ 20.6 ∞ 33.1 61.8k(dj) 2 2 2 2 2.13 2 2.08 2.04

ku / 10−2 2.5 2.7 8.9 3.5 4.2 4.3 5.6 3.2

A B C D E G H I-10

0

10

20

d j / 10

-2

Participant

Fig. 1. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.G, 1.9 MHz, "very low"

21

Table 16. Degrees of equivalence between two participants. G, 1.9 MHz, "very low". ku meansk(dij) u(dij).

Part. j A B C D EPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A 0.7 4.1 -9.8 9.5 -1.2 4.7 -3.0 5.2B -0.7 4.1 -10.5 9.5 -1.9 4.8 -3.7 5.3C 9.8 9.5 10.5 9.5 8.6 9.8 6.8 10.0D 1.2 4.7 1.9 4.8 -8.6 9.8 -1.8 5.7E 3.0 5.2 3.7 5.3 -6.8 10.0 1.8 5.7

G -5.2 5.3 -4.5 5.4 -15.0 10.1 -6.4 5.9 -8.2 6.2H -1.0 6.4 -0.3 6.5 -10.8 10.7 -2.2 6.9 -4.0 7.1I -2.1 4.4 -1.4 4.6 -11.9 9.6 -3.3 5.1 -5.1 5.5

Part. j G H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A 5.2 5.3 1.0 6.4 2.1 4.4B 4.5 5.4 0.3 6.5 1.4 4.6C 15.0 10.1 10.8 10.7 11.9 9.6D 6.4 5.9 2.2 6.9 3.3 5.1E 8.2 6.2 4.0 7.1 5.1 5.5

G -4.2 7.3 -3.1 5.6H 4.2 7.3 1.1 6.7I 3.1 5.6 -1.1 6.7

22

7.2 Radiation conductance G, 1.9 MHz, "low"

In this case the compatibility check of the weighted mean fails (because of result H). The medianis, therefore, used as the reference value here.

Table 17. The reference value and its (relative) uncertainty. G, 1.9 MHz, "low"xR / mS u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

4.935 1.55 8.3 2.35 3.6


Part. A B C D E F G H Ixj / mS 4.917 4.998 5.049 4.935 5.068 5.574 4.649 4.674 4.856dj / 10−2 -0.4 1.3 2.3 0.0 2.7 12.9 -5.8 -5.3 -1.6u(dj)/10−2 1.95 1.95 3.5 2.1 2.2 7.2 2.4 2.1 1.95ν(dj) 21.4 22.1 ∞ 29.9 20.3 6.8 49.3 28.4 19.6k(dj) 2.12 2.12 2 2.09 2.13 2.45 2.05 2.09 2.14

ku / 10−2 4.1 4.1 7.0 4.4 4.7 17.7 4.9 4.4 4.2

A B C D E F G H I-12

-8

-4

0

4

8

12

16

20

24

28

32

d j / 10

-2

Participant

Fig. 2. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.G, 1.9 MHz, "low"

23

Table 19. Degrees of equivalence between two participants. G, 1.9 MHz, "low". ku meansk(dij) u(dij).


A -1.6 4.0 -2.7 7.8 -0.4 4.4 -3.1 4.8B 1.6 4.0 -1.0 7.8 1.3 4.5 -1.4 4.9C 2.7 7.8 1.0 7.8 2.3 8.0 -0.4 8.2D 0.4 4.4 -1.3 4.5 -2.3 8.0 -2.7 5.2E 3.1 4.8 1.4 4.9 0.4 8.2 2.7 5.2F 13.3 18.4 11.7 18.4 10.6 18.8 12.9 18.4 10.3 18.4G -5.4 4.9 -7.1 5.0 -8.1 8.3 -5.8 5.3 -8.5 5.6H -4.9 4.3 -6.6 4.3 -7.6 8.0 -5.3 4.7 -8.0 5.1I -1.2 4.1 -2.9 4.1 -3.9 7.8 -1.6 4.5 -4.3 4.9

Part. j F G H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -13.3 18.4 5.4 4.9 4.9 4.3 1.2 4.1B -11.7 18.4 7.1 5.0 6.6 4.3 2.9 4.1C -10.6 18.8 8.1 8.3 7.6 8.0 3.9 7.8D -12.9 18.4 5.8 5.3 5.3 4.7 1.6 4.5E -10.3 18.4 8.5 5.6 8.0 5.1 4.3 4.9F 18.7 18.4 18.2 18.4 14.5 18.4G -18.7 18.4 -0.5 5.2 -4.2 5.0H -18.2 18.4 0.5 5.2 -3.7 4.4I -14.5 18.4 4.2 5.0 3.7 4.4

24

7.3 Radiation conductance G, 1.9 MHz, "medium"


Table 20. The reference value and its (relative) uncertainty. G, 1.9 MHz, "medium"xR / mS u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

4.953 0.55 ∞ 2 1.1


Part. A B C D E F G H Ixj / mS 4.919 4.999 5.062 4.919 5.014 5.100 4.960 4.755 4.948dj / 10−2 -0.7 0.9 2.2 -0.7 1.2 3.0 0.1 -4.0 -0.1u(dj)/10−2 1.3 1.35 3.5 1.6 1.0 3.8 1.4 1.7 1.35ν(dj) ∞ ∞ ∞ ∞ 20.6 4.4 ∞ 66.7 26.4k(dj) 2 2 2 2 2.13 2.77 2 2.04 2.10

ku / 10−2 2.6 2.7 7.0 3.2 2.1 10.5 2.8 3.5 2.9

A B C D E F G H I-8

-6

-4

-2

0

2

4

6

8

10

12

14

d j / 10

-2

Participant

Fig. 3. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.G, 1.9 MHz, "medium"

25

Table 22. Degrees of equivalence between two participants. G, 1.9 MHz, "medium". ku meansk(dij) u(dij).


A -1.6 4.0 -2.9 7.6 0.0 4.4 -1.9 3.7B 1.6 4.0 -1.3 7.6 1.6 4.4 -0.3 3.7C 2.9 7.6 1.3 7.6 2.9 7.8 1.0 7.4D 0.0 4.4 -1.6 4.4 -2.9 7.8 -1.9 4.1E 1.9 3.7 0.3 3.7 -1.0 7.4 1.9 4.1F 3.7 10.5 2.0 10.5 0.8 11.4 3.7 10.5 1.7 10.6G 0.8 4.1 -0.8 4.2 -2.1 7.7 0.8 4.6 -1.1 3.8H -3.3 4.6 -4.9 4.6 -6.2 7.9 -3.3 5.0 -5.2 4.3I 0.6 4.1 -1.0 4.2 -2.3 7.7 0.6 4.5 -1.3 3.8


A -3.7 10.5 -0.8 4.1 3.3 4.6 -0.6 4.1B -2.0 10.5 0.8 4.2 4.9 4.6 1.0 4.2C -0.8 11.4 2.1 7.7 6.2 7.9 2.3 7.7D -3.7 10.5 -0.8 4.6 3.3 5.0 -0.6 4.5E -1.7 10.6 1.1 3.8 5.2 4.3 1.3 3.8F 2.8 10.5 7.0 10.5 3.1 10.5G -2.8 10.5 4.1 4.7 0.2 4.3H -7.0 10.5 -4.1 4.7 -3.9 4.7I -3.1 10.5 -0.2 4.3 3.9 4.7

26

7.4 Radiation conductance G, 1.9 MHz, "high"

In this case the compatibility check of the weighted mean fails (because of result G). The medianis, therefore, used as the reference value here.

Table 23. The reference value and its (relative) uncertainty. G, 1.9 MHz, "high"xR / mS u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

5.033 1.35 8.4 2.35 3.1


Part. A B C D E F G H Ixj / mS 4.937 5.033 5.239 4.932 5.102 5.144 4.653 4.817 5.047dj / 10−2 -1.9 0.0 4.1 -2.0 1.4 2.2 -7.6 -4.3 0.3u(dj)/10−2 1.8 1.65 4.65 2.05 1.55 2.75 2.45 2.35 1.65ν(dj) 28.7 19.5 ∞ 46.1 14.0 9.0 96.0 37.6 17.3k(dj) 2.09 2.14 2 2.06 2.19 2.32 2.03 2.07 2.15

ku / 10−2 3.8 3.5 9.3 4.2 3.4 6.4 5.0 4.8 3.6

A B C D E F G H I-14

-7

0

7

14

d j / 10

-2

Participant

Fig. 4. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.G, 1.9 MHz, "high"

27

Table 25. Degrees of equivalence between two participants. G, 1.9 MHz, "high". ku meansk(dij) u(dij).


A -1.9 4.0 -6.0 9.6 0.1 4.4 -3.3 3.4B 1.9 4.0 -4.1 9.6 2.0 4.5 -1.4 3.5C 6.0 9.6 4.1 9.6 6.1 9.8 2.7 9.4D -0.1 4.4 -2.0 4.5 -6.1 9.8 -3.4 4.0E 3.3 3.4 1.4 3.5 -2.7 9.4 3.4 4.0F 4.1 6.9 2.2 6.9 -1.9 10.8 4.2 7.1 0.8 6.8G -5.6 5.0 -7.6 5.0 -11.6 10.1 -5.5 5.4 -8.9 4.6H -2.4 4.9 -4.3 4.9 -8.4 10.0 -2.3 5.3 -5.7 4.5I 2.2 4.0 0.3 4.1 -3.8 9.6 2.3 4.5 -1.1 3.6


A -4.1 6.9 5.6 5.0 2.4 4.9 -2.2 4.0B -2.2 6.9 7.6 5.0 4.3 4.9 -0.3 4.1C 1.9 10.8 11.6 10.1 8.4 10.0 3.8 9.6D -4.2 7.1 5.5 5.4 2.3 5.3 -2.3 4.5E -0.8 6.8 8.9 4.6 5.7 4.5 1.1 3.6F 9.8 7.4 6.5 7.3 1.9 7.0G -9.8 7.4 -3.3 5.8 -7.8 5.1H -6.5 7.3 3.3 5.8 -4.6 5.0I -1.9 7.0 7.8 5.1 4.6 5.0

28

7.5 Radiation conductance G, 1.9 MHz, "very high"


Table 26. The reference value and its (relative) uncertainty. G, 1.9 MHz, "very high"xR / mS u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

5.049 0.75 36.2 2.07 1.5


Part. A E F Ixj / mS 4.950 5.122 5.128 5.033dj / 10−2 -2.0 1.4 1.6 -0.3u(dj)/10−2 1.2 0.9 4.0 1.0ν(dj) ∞ 17.3 5.0 30.9k(dj) 2 2.15 2.65 2.08

ku / 10−2 2.4 1.9 10.6 2.2

A E F I-10

-5

0

5

10

d j / 10

-2

Participant

Fig. 5. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.G, 1.9 MHz, "very high"

29

Table 28. Degrees of equivalence between two participants. G, 1.9 MHz, "very high". ku meansk(dij) u(dij).

Part. j A EPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -3.4 3.7

E 3.4 3.7F 3.5 10.9 0.1 10.9

I 1.6 3.8 -1.8 3.6

Part. j F IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -3.5 10.9 -1.6 3.8

E -0.1 10.9 1.8 3.6F 1.9 10.9

I -1.9 10.9

30




5.715 0.85 ∞ 2 1.7


Part. A B C D E H Ixj / mS 5.660 5.760 5.966 5.822 5.772 5.447 5.674dj / 10−2 -1.0 0.8 4.4 1.9 1.0 -4.7 -0.7u(dj)/10−2 1.5 1.85 6.9 1.8 1.75 2.9 1.8ν(dj) ∞ ∞ ∞ ∞ 18.0 77.5 41.3k(dj) 2 2 2 2 2.15 2.03 2.06

ku / 10−2 3.0 3.7 13.8 3.6 3.8 5.9 3.8

A B C D E H I-12

-8

-4

0

4

8

12

16

20

d j / 10

-2

Participant


31



A -1.7 5.3 -5.4 14.3 -2.8 5.2 -2.0 5.3B 1.7 5.3 -3.6 14.5 -1.1 5.7 -0.2 5.7C 5.4 14.3 3.6 14.5 2.5 14.5 3.4 14.4D 2.8 5.2 1.1 5.7 -2.5 14.5 0.9 5.7E 2.0 5.3 0.2 5.7 -3.4 14.4 -0.9 5.7

H -3.7 7.0 -5.5 7.3 -9.1 15.1 -6.6 7.3 -5.7 7.3I 0.2 5.3 -1.5 5.7 -5.1 14.5 -2.6 5.7 -1.7 5.8

Part. j H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2

A 3.7 7.0 -0.2 5.3B 5.5 7.3 1.5 5.7C 9.1 15.1 5.1 14.5D 6.6 7.3 2.6 5.7E 5.7 7.3 1.7 5.8

H -4.0 7.3I 4.0 7.3

32




5.720 0.7 88.8 2.03 1.4


Part. A B C D E F H Ixj / mS 5.666 5.801 5.828 5.800 5.718 6.614 5.444 5.739dj / 10−2 -0.9 1.4 1.9 1.4 -0.0 15.6 -4.8 0.3u(dj)/10−2 1.5 1.5 6.35 1.65 0.95 7.6 2.1 1.9ν(dj) ∞ ∞ ∞ ∞ 19.8 5.9 ∞ 20.4k(dj) 2 2 2 2 2.13 2.53 2 2.13

ku / 10−2 3.0 3.0 12.7 3.3 2.1 19.2 4.2 4.1

A B C D E F H I-12

0

12

24

36

d j / 10

-2

Participant


33



A -2.4 4.6 -2.8 13.2 -2.3 4.9 -0.9 4.1B 2.4 4.6 -0.5 13.2 0.0 4.8 1.5 4.1C 2.8 13.2 0.5 13.2 0.5 13.2 1.9 13.0D 2.3 4.9 -0.0 4.8 -0.5 13.2 1.4 4.3E 0.9 4.1 -1.5 4.1 -1.9 13.0 -1.4 4.3F 16.6 19.4 14.2 19.4 13.7 21.5 14.2 19.4 15.7 19.4

H -3.9 5.5 -6.2 5.5 -6.7 13.5 -6.2 5.7 -4.8 5.0I 1.3 5.4 -1.1 5.3 -1.6 13.4 -1.1 5.5 0.4 4.9

Part. j F H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -16.6 19.4 3.9 5.5 -1.3 5.4B -14.2 19.4 6.2 5.5 1.1 5.3C -13.7 21.5 6.7 13.5 1.6 13.4D -14.2 19.4 6.2 5.7 1.1 5.5E -15.7 19.4 4.8 5.0 -0.4 4.9F 20.5 19.4 15.3 19.4

H -20.5 19.4 -5.2 6.1I -15.3 19.4 5.2 6.1

34




5.842 0.8 97.0 2.03 1.6


Part. A B C D E H Ixj / mS 5.796 5.914 6.379 5.735 5.746 5.606 6.090dj / 10−2 -0.8 1.2 9.2 -1.8 -1.6 -4.0 4.2u(dj)/10−2 2.2 1.45 11.4 2.65 1.05 3.25 1.7ν(dj) ∞ ∞ ∞ ∞ 31.1 ∞ 63.5k(dj) 2 2 2 2 2.08 2 2.04

ku / 10−2 4.4 2.9 22.8 5.3 2.2 6.6 3.5

A B C D E H I-15

-10

-5

0

5

10

15

20

25

30

35

d j / 10

-2

Participant


35



A -2.0 5.7 -10.0 23.3 1.0 7.2 0.9 5.4B 2.0 5.7 -8.0 23.1 3.1 6.4 2.9 4.2C 10.0 23.3 8.0 23.1 11.0 23.5 10.8 23.0D -1.0 7.2 -3.1 6.4 -11.0 23.5 -0.2 6.1E -0.9 5.4 -2.9 4.2 -10.8 23.0 0.2 6.1

H -3.3 8.2 -5.3 7.5 -13.2 23.8 -2.2 8.7 -2.4 7.2I 5.0 6.0 3.0 5.0 -5.0 23.1 6.1 6.7 5.9 4.7

Part. j H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2

A 3.3 8.2 -5.0 6.0B 5.3 7.5 -3.0 5.0C 13.2 23.8 5.0 23.1D 2.2 8.7 -6.1 6.7E 2.4 7.2 -5.9 4.7

H -8.3 7.7I 8.3 7.7

36




5.875 0.7 67.6 2.04 1.4


Part. A B C D E F H Ixj / mS 5.842 6.052 6.985 5.741 5.805 6.901 5.882 5.910dj / 10−2 -0.6 3.0 18.9 -2.3 -1.2 17.5 0.1 0.6u(dj)/10−2 2.15 1.4 12.1 2.65 0.7 8.15 3.25 2.2ν(dj) ∞ ∞ ∞ ∞ 79.4 7.8 ∞ 75.7k(dj) 2 2 2 2 2.03 2.38 2 2.03

ku / 10−2 4.3 2.8 24.2 5.3 1.4 19.3 6.5 4.5

A B C D E F H I-9

0

9

18

27

36

45

d j / 10

-2

Participant


37



A -3.6 5.5 -19.5 24.7 1.7 7.1 0.6 4.9B 3.6 5.5 -15.9 24.5 5.3 6.3 4.2 3.7C 19.5 24.7 15.9 24.5 21.2 24.9 20.1 24.3D -1.7 7.1 -5.3 6.3 -21.2 24.9 -1.1 5.8E -0.6 4.9 -4.2 3.7 -20.1 24.3 1.1 5.8F 18.0 19.7 14.5 19.6 -1.4 29.7 19.7 19.8 18.7 19.5

H 0.7 8.0 -2.9 7.3 -18.8 25.1 2.4 8.6 1.3 6.9I 1.2 6.5 -2.4 5.6 -18.3 24.7 2.9 7.2 1.8 5.1

Part. j F H IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -18.0 19.7 -0.7 8.0 -1.2 6.5B -14.5 19.6 2.9 7.3 2.4 5.6C 1.4 29.7 18.8 25.1 18.3 24.7D -19.7 19.8 -2.4 8.6 -2.9 7.2E -18.7 19.5 -1.3 6.9 -1.8 5.1F 17.3 20.0 16.9 19.7

H -17.3 20.0 -0.5 8.1I -16.9 19.7 0.5 8.1

38

7.10 Ultrasonic power Pref, 1.9 MHz, "very low"


Table 41. The reference value and its (relative) uncertainty. Pref, 1.9 MHz, "very low"xR / mW u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

10.17 0.75 ∞ 2 1.5

Table 42. Final Pref results and relative deviations from the reference value. ku means k(dj) u(dj).The degree of equivalence of each participant with the reference value is given by dj and ku

Part. A B D Ixj / mW 10.22 10.10 10.38 10.08dj / 10−2 0.5 -0.7 2.0 -0.9u(dj)/10−2 1.2 0.85 1.65 1.6ν(dj) ∞ ∞ ∞ 48.7k(dj) 2 2 2 2.05

ku / 10−2 2.4 1.7 3.3 3.3

A B D I

-4

-2

0

2

4

6

d j / 10

-2

Participant

Fig. 10. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.Pref, 1.9 MHz, "very low"

39

Table 43. Degrees of equivalence between two participants. Pref, 1.9 MHz, "very low". ku meansk(dij) u(dij).

Part. j A B D IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A 1.2 3.5 -1.6 4.5 1.4 4.5B -1.2 3.5 -2.8 4.2 0.2 4.2D 1.6 4.5 2.8 4.2 2.9 5.1

I -1.4 4.5 -0.2 4.2 -2.9 5.1

40

7.11 Ultrasonic power Pref, 1.9 MHz, "low"

In this case the compatibility check of the weighted mean fails (because of result I). The medianis, therefore, used as the reference value here.

Table 44. The reference value and its (relative) uncertainty. Pref, 1.9 MHz, "low"xR / mW u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

97.6 1.35 4.2 2.82 3.8


Part. A B D F Ixj / mW 97.4 99.0 97.6 114.5 94.0dj / 10−2 -0.2 1.4 0.0 17.3 -3.7u(dj)/10−2 1.6 1.5 1.7 7.05 1.8ν(dj) 8.3 6.3 11.0 6.7 12.5k(dj) 2.35 2.49 2.25 2.46 2.22

ku / 10−2 3.8 3.7 3.9 17.3 4.0

A B D F I-9

0

9

18

27

36

d j / 10

-2

Participant

Fig. 11. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.Pref, 1.9 MHz, "low"

41

Table 46. Degrees of equivalence between two participants. Pref, 1.9 MHz, "low". ku meansk(dij) u(dij).

Part. j A B D F IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -1.6 3.2 -0.2 4.2 -17.5 17.6 3.5 4.0B 1.6 3.2 1.4 3.7 -15.9 17.6 5.1 3.6D 0.2 4.2 -1.4 3.7 -17.3 17.6 3.7 4.4F 17.5 17.6 15.9 17.6 17.3 17.6 21.0 17.6I -3.5 4.0 -5.1 3.6 -3.7 4.4 -21.0 17.6

42

7.12 Ultrasonic power Pref, 1.9 MHz, "medium"


Table 47. The reference value and its (relative) uncertainty. Pref, 1.9 MHz, "medium"xR / W u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

1.042 0.65 ∞ 2 1.3


Part. A B D F Ixj / W 1.032 1.053 1.027 1.124 1.026

dj / 10−2 -0.9 1.1 -1.4 7.9 -1.5u(dj)/10−2 1.15 0.7 1.4 3.4 1.25ν(dj) ∞ ∞ ∞ 4.5 39.6k(dj) 2 2 2 2.75 2.06

ku / 10−2 2.3 1.4 2.8 9.4 2.6

A B D F I-5

0

5

10

15

d j / 10

-2

Participant

Fig. 12. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.Pref, 1.9 MHz, "medium"

43

Table 49. Degrees of equivalence between two participants. Pref, 1.9 MHz, "medium". ku meansk(dij) u(dij).


A -2.0 3.2 0.5 4.0 -8.8 9.5 0.6 3.9B 2.0 3.2 2.5 3.6 -6.8 9.6 2.6 3.4D -0.5 4.0 -2.5 3.6 -9.3 9.5 0.1 4.2F 8.8 9.5 6.8 9.6 9.3 9.5 9.4 9.5I -0.6 3.9 -2.6 3.4 -0.1 4.2 -9.4 9.5

44

7.13 Ultrasonic power Pref, 1.9 MHz, "high"


Table 50. The reference value and its (relative) uncertainty. Pref, 1.9 MHz, "high"xR / W u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

9.88 0.65 ∞ 2 1.3


Part. A B D Ixj / W 9.71 9.97 9.55 10.05

dj / 10−2 -1.7 1.0 -3.3 1.8u(dj)/10−2 1.4 0.7 1.5 1.3ν(dj) ∞ ∞ ∞ 38.9k(dj) 2 2 2 2.07

ku / 10−2 2.8 1.4 3.0 2.7

A B D I-7-6-5-4-3-2-1012345

d j / 10

-2

Participant

Fig. 13. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.Pref, 1.9 MHz, "high"

45

Table 52. Degrees of equivalence between two participants. Pref, 1.9 MHz, "high". ku meansk(dij) u(dij).


A -2.6 3.6 1.6 4.4 -3.4 4.3B 2.6 3.6 4.3 3.7 -0.8 3.5D -1.6 4.4 -4.3 3.7 -5.1 4.4

I 3.4 4.3 0.8 3.5 5.1 4.4

46

7.14 Ultrasonic power Pref, 1.9 MHz, "very high"


Table 53. The reference value and its (relative) uncertainty. Pref, 1.9 MHz, "very high"xR / W u(xR) / 10−2 ν(xR) k(xR) k(xR) u(xR) / 10−2

15.12 1.15 51.8 2.05 2.3


Part. A Ixj / W 14.88 15.23

dj / 10−2 -1.6 0.7u(dj)/10−2 1.7 0.8ν(dj) ∞ ∞k(dj) 2 2

ku / 10−2 3.4 1.6

A I-6

-3

0

3

d j / 10

-2

Participant

Fig. 14. Degrees of equivalence (dj and k(dj) u(dj)) with respect to the reference value.Pref, 1.9 MHz, "very high"

47

Table 55. Degrees of equivalence between two participants. Pref, 1.9 MHz, "very high". ku meansk(dij) u(dij).

Part. j A IPart. i dij /10−2 ku/10−2 dij /10−2 ku/10−2

A -2.3 4.9

I 2.3 4.9

48




10.43 0.85 ∞ 2 1.7


Part. A B D Ixj / mW 10.32 10.34 10.58 10.52dj / 10−2 -1.1 -0.9 1.4 0.9u(dj)/10−2 1.35 1.35 1.7 1.35ν(dj) ∞ ∞ ∞ 65.6k(dj) 2 2 2 2.04

ku / 10−2 2.7 2.7 3.4 2.7

A B D I-4

-3

-2

-1

0

1

2

3

4

5

d j / 10

-2

Participant


49



A -0.2 4.5 -2.5 4.9 -1.9 4.5B 0.2 4.5 -2.3 4.9 -1.7 4.5D 2.5 4.9 2.3 4.9 0.6 4.9

I 1.9 4.5 1.7 4.5 -0.6 4.9

50




101.1 0.75 ∞ 2 1.5


Part. A B D F Ixj / mW 98.8 101.1 100.8 115.4 103.3dj / 10−2 -2.3 0.0 -0.3 14.2 2.2u(dj)/10−2 1.35 1.0 1.45 7.25 1.5ν(dj) ∞ ∞ ∞ 5.9 56.1k(dj) 2 2 2 2.53 2.05

ku / 10−2 2.7 2.0 2.9 18.4 3.0

A B D F I-7

0

7

14

21

28

35

d j / 10

-2

Participant


51



A -2.3 3.9 -2.0 4.4 -16.4 18.6 -4.5 4.5B 2.3 3.9 0.3 4.0 -14.1 18.6 -2.2 4.2D 2.0 4.4 -0.3 4.0 -14.4 18.6 -2.5 4.6F 16.4 18.6 14.1 18.6 14.4 18.6 12.0 18.6I 4.5 4.5 2.2 4.2 2.5 4.6 -12.0 18.6

52




10.46 0.85 ∞ 2 1.7


Part. A B D Ixj / mW 10.38 10.41 10.28 10.71dj / 10−2 -0.8 -0.5 -1.7 2.4u(dj)/10−2 2.1 0.75 2.55 1.5ν(dj) ∞ ∞ ∞ 59.3k(dj) 2 2 2 2.04

ku / 10−2 4.2 1.5 5.1 3.1

A B D I-8

-6

-4

-2

0

2

4

6

d j / 10

-2

Participant


53



A -0.3 5.0 1.0 7.0 -3.2 5.7B 0.3 5.0 1.2 5.8 -2.9 4.1D -1.0 7.0 -1.2 5.8 -4.1 6.3

I 3.2 5.7 2.9 4.1 4.1 6.3

54




102.1 0.8 ∞ 2 1.6


Part. A B D F Ixj / mW 99.9 103.2 98.7 117.6 101.0dj / 10−2 -2.1 1.1 -3.3 15.2 -1.0u(dj)/10−2 2.0 0.7 2.55 7.8 1.4ν(dj) ∞ ∞ ∞ 7.9 59.2k(dj) 2 2 2 2.37 2.04

ku / 10−2 4.0 1.4 5.1 18.5 2.9

A B D F I-10

-5

0

5

10

15

20

25

30

35

d j / 10

-2

Participant


55



A -3.2 4.7 1.2 6.8 -17.3 18.9 -1.1 5.3B 3.2 4.7 4.4 5.7 -14.1 18.7 2.2 3.9D -1.2 6.8 -4.4 5.7 -18.5 19.0 -2.3 6.2F 17.3 18.9 14.1 18.7 18.5 19.0 16.3 18.8I 1.1 5.3 -2.2 3.9 2.3 6.2 -16.3 18.8

56

Acknowledgement

The author would like to thank Dipl.-Ing. W. Molkenstruck for valuable contributions.

References

[1] IEC 61161, Ultrasonic power measurement in liquids in the frequency range 0.5 MHz to 25MHz. Geneva, International Electrotechnical Commission, 1992, and Amendment 1, 1998.

[2] K. Beissner, Primary measurement of ultrasonic power and dissemination of ultrasonic powerreference values by means of standard transducers. Metrologia 36, 313-320 (1999).

[3] IEC 61157, Requirements for the declaration of the acoustic output of medical diagnosticultrasonic equipment. Geneva, International Electrotechnical Commission, 1992.

[4] IEC 61689, Ultrasonics − Physiotherapy systems − Performance requirements and methods ofmeasurement in the frequency range 0.5 MHz to 5 MHz. Geneva, International ElectrotechnicalCommission, 1996.

[5] Guide to the expression of uncertainty in measurement. ISO, IEC, BIPM et al., 1993.

[6] S. E. Fick, Ultrasound power measurement by pulsed radiation pressure. Metrologia 36, 351-356 (1999).

[7] K. C. Shotton, A tethered float radiometer for measuring the output power from ultrasonictherapy equipment. Ultrasound Med. Biol. 6, 131-133 (1980).

[8] K. Beissner, On a measure of consistency in comparison measurements. Metrologia 39, 59-63(2002).

[9] K. Beissner, On a measure of consistency in comparison measurements. II. Using effectivedegrees of freedom. Submitted to Metrologia.

[10] J. W. Mueller, Possible advantages of a robust evaluation of comparisons. J. Res. Natl. Inst.Stand. Technol. 105, 551-555 (2000).

57

Annex A. Formulae

This annex is a compilation of the methods and formulae used to calculate the reference values anddegrees of equivalence in the text. Contrary to the text body, uncertainties u and deviations d areunderstood in this annex in absolute and not in relative terms. They must be divided by theappropriate value, as for example by the reference value, in order to obtain the values in the text.

A.1. The weighted mean

It is assumed that N participating laboratories measured the relevant quantity of a travellingstandard and each stated a measurement result xi, a standard uncertainty u(xi) and a value ν(xi) forthe effective degrees of freedom. It is further assumed that the results xi are not correlated with oneanother.

The weighted mean µ is given by

w

xwN

iii

Σ=∑=1 µ (A1)

where the wi are the weights applied to the results and ∑w is an abbreviation for

∑=

=ΣN

iiww

1 . (A2)

As usual, the weights are set to

( )ii xuw 2 −= . (A3)

The (internal) standard uncertainty of the weighted mean of (A1) together with (A3) is known tobe given according to

( )( )

( )( )

1

1

22

1

22

2 −

=

−=

=

Σ= ∑∑ N

ii

N

iii

xuw

xuwu µ . (A4)

58

The effective degrees of freedom of the weighted mean can be calculated according to (G.2b) in[5] to be

( ) ( ) ( )( )

( )∑=

Σ=

N

i i

iix

xuwuw

1

44

44

ν

µµν . (A5)

In order to take into account the additional stability contribution to the uncertainty of the referencevalue mentioned at the end of section 6, a correction a with a standard uncertainty u(a) andeffective degrees of freedom ν(a) is formally applied to the weighted mean to obtain the referencevalue xR with its standard uncertainty u(xR) and effective degrees of freedom ν(xR) according to

ax R += µ , (A6)

( ) ( ) ( )auuxu 22R

2 += µ , (A7)

( ) ( )( )( )

( )( )a

auuxux

νµνµ

ν 44R

4

R

+

= . (A8)

The expectation value a is set to zero so that xR = µ (it is only the uncertainty of a that counts). Theeffective degrees of freedom ν(a) is set to ∞ for simplicity.

The coverage factor k(xR) for the expanded uncertainty of the reference value follows from ν(xR)and table G.2 in [5] or equivalent tables (interpolated).

The deviation dj of the result j from the reference value is

R xxd jj −= . (A9)

Its standard uncertainty u(dj) and effective degrees of freedom ν(dj) can be calculated ([8,9])according to

( ) ( ) ( )R222 2 1 xuxu

ww

du jj

j +

Σ

−= (A10)

and

59

( ) ( )( )( )

( )( )R

R4444

4

1

xxu

xxu

ww

ww

dud

j

jjj

jj

νν

ν

+

Σ

−

Σ

−

= . (A11)

The coverage factor k(dj) for the expanded uncertainty of dj follows from ν(dj) and table G.2 in [5]or equivalent tables (interpolated).

Note that (a) the terms with wj / ∑w in (A10) and (A11) reflect the dependence of xR on xj asdiscussed in detail in [8] and (b) that (A10) and (A11) look like the relevant formulae in [8] and[9] but in fact also take into account the influence of the correction a here, unlike the treatment in[8] and [9].

A.2. Compatibility check

The degree of equivalence of a result j with the reference value expresses the compatibility of thatresult with the reference value. Another problem is to ask whether or not the entire group of Nmeasurement results is compatible with the reference value or, vice versa, whether or not thereference value model chosen is compatible with the particular group of measurement results. Thisproblem has been discussed in [9] in the light of the recent literature. The general tendency is torecommend not using the weighted mean if there are indications that outliers or unrealisticuncertainty statements may be present as the weighted mean is sensitive to these, and to use amore robust location parameter instead.

After having obtained the weighted mean and the relevant degrees of equivalence the compatibilityof the weighted mean with the entire group of measurement results is, therefore, checked here. Thedeviations dj and their standard uncertainties u(dj) are used as before, but new coverage factorskg(dj) are introduced ("g" stands for "group"). The expressions |dj|/(kg(dj)u(dj)) are calculated for allparticipants and their maximum value is identified. If this maximum value is < 1, the weightedmean is considered compatible with the entire group of measurement results but if not, it is notconsidered compatible and a more robust location parameter (the median, see below) is usedinstead. Note that this often leads to an increased uncertainty of the reference value (seesubsections 7.2, 7.4 and 7.11).

The procedure has been described in [9]. Basically, the coverage factors kg represent quantiles ofthe normal distribution or of Student's distribution, respectively, for a probability of 0.95451/N

instead of 0.9545, but there are also a number of additional details that require closer considerationand cannot be discussed here. The findings have been confirmed by empirical computersimulations in [9].

60

A.3. The median

The (unweighted) median which will be referred to here as m has been dealt with, for example, in[10]. Its standard uncertainty has been given in [10] to be

( ) MADN

mu1

858.1 −

= , (A12)

where MAD is the median of the absolute deviations (from the median).

The procedures of subsection A.1 are again followed, with the median m replacing the weightedmean µ and the standard uncertainty of (A12) replacing that of (A4). While the equations ofsubsection A.1 have been derived in an exact manner, their application to the median involves anumber of approximations that will be briefly mentioned as follows.

(1) The expression (A12) applies asymptotically to large N. Using it for lower N values means anapproximation of generally unknown accuracy.

(2) When searching for ν(m) leading to ν(xR) and k(xR) for the expanded uncertainty, thebehaviour of the median in this respect obviously is generally unknown, but there may be threeapproaches as follows. (a) Simply use ν(m) = ∞ and the corresponding k = 2. (b) Simply adopt(A5) with µ being replaced by m. (c) Assume ν(m) = N−1 and the corresponding k value. Thelast solution is chosen here, for two reasons. First, the uncertainty (A12) of the medianobviously is of the type of an external uncertainty. Second, computer simulations have shownthat solution (c) although not really being a good approximation to the real behaviour of themedian, is the best of the three solutions mentioned above.

(3) While u(xR) in (A10) and (A11) is associated with the (internal) standard uncertainty of theweighted mean, these equations are used here with u(xR) being the (external) uncertainty of themedian.

(4) (A10) and (A11) have been derived for the weighted mean and their exact counterparts for themedian are unknown. If (A10) and (A11) are also to be used for the median, values for theterms with wj / ∑w have to be inserted. The underlying fact that xj influences xR ([8]) certainlyalso occurs with the median, so these terms should not simply be omitted. Approximatewj / ∑w values for the median (to be used in (A10) and (A11)) are calculated here as follows.Using a numerical iteration approach, the median is represented as a weighted mean, with theweights assumed according to (1 + const × (xj – m)2)−1 and with the free constant const to befitted numerically. The algorithm yields values of wj / ∑w which are then used in (A10) and(A11). This model leads to the influence of the central values being much greater than that ofthe highest and lowest values, exactly as it should be to mimick the behaviour of the median.

61

A.4. Mutual degrees of equivalence

The deviation dij is given by

jiij ddd −= (A13)

which in the present case is equal to xi – xj. Its standard uncertainty u(dij) and effective degrees offreedom ν(dij) are given according to

( ) ( ) ( ) ( )auxuxudu jiij2222 2 ++= (A14)

and

( ) ( )( )( )

( )( )

( )( )a

auxxu

xxu

dud

j

j

i

i

ijij

ννν

ν444

4

2

++

= . (A15)

The factor 2 occurring in both formulae is due to the fact that the additional stability contributionto the uncertainty of the reference value mentioned at the end of section 6 is to be taken intoaccount twice, i.e., once in connection with result i and once with result j.

The coverage factor k(dij) for the expanded uncertainty of dij follows from ν(dij) and table G.2 in[5] or equivalent tables (interpolated).

BIPM/CIPM key comparison CCAUV.U-K1, ultrasonic power

Technical protocol

(second version with enlarged list of participants)

by K. Beissner

PTB, Braunschweig, Germany, April 2000

1. Introduction

This protocol describes the procedures to be used during the BIPM/CIPM key comparisonCCAUV.U-K1 (ultrasonic power). This comparison covers the measurement of the time-averaged, ultrasonic output power of an ultrasonic standard transducer in the nominal frequencyrange from 2 MHz to 10 MHz. In addition to this protocol, sections 7 and 8 of the "Guidelines forCIPM key comparisons" (1 March 1999) issued by the BIPM as Appendix F to the "Mutualrecognition" document should be observed.

2. Devices

An ultrasonic standard transducer is circulated. Its identification number is PTB 24 LN 2 MHz.The circular front face contains the active element which is a gold-plated, air-backed, narrow-band, half-wave resonant lithium niobate crystal of coaxial electrode design. The transducerrear is provided with a (female) BNC connector. This is the transducer's electric input for theinput voltage. The central lead of the connector is directly connected with the rear, "hot"electrode of the crystal. This means that the transducer does not contain any electroniccomponents and is not matched to 50 Ω. The transducer is of cylindrical shape, 30 mm indiameter, about 85 mm in length, and with a mass of about 120 g. The transducer front iscovered by a red plastic cap.

The transducer is intended for operation at its fundamental resonance and in the third and fifthharmonics.

A rectifier module is circulated along with the transducer. The module is provided with fivefemale BNC connectors and one male BNC connector. The module contains electroniccomponents. Its dimensions are about 85 mm x 61 mm x 44 mm. The mass is also about 120 g.The rectifier module can be used together with the transducer in measurements of a certaintype as described in section 7 below.

63

3. Time schedule

The time schedule of the comparison is as follows:

(1) PTB (pilot): July + August 1999(2) Transport to Washington: first half of September(3) NIST: mid-September to mid-November 1999(4) Transport to Ottawa: second half of November(5) NRC-INMS: December 1999 + January 2000(6) Transport to Braunschweig: first half of February(7) PTB remeasurement: mid-February to end of March 2000(8) Transport to Teddington: first half of April(9) NPL (UK): mid-April to mid-June 2000(10) Transport to Leiden: second half of June(11) NMi-TNO: July + August 2000(12) Transport to Braunschweig: first half of September(13) PTB remeasurement: mid-September to end of October 2000(14) Transport to Sydney: first half of November(15) CSIRO-NML: mid-November 2000 to mid-January 2001(16) Transport to New Delhi: second half of January(17) NPL (India): February + March 2001(18) Transport to Braunschweig: first half of April(19) PTB remeasurement: mid-April to end of May 2001(20) Transport to Moscow: first half of June(21) VNIIM-VNIIFTRI: mid-June to mid-August 2001(22) Transport to Beijing: second half of August(23) NIM: September + October 2001(24) Transport to Braunschweig: first half of November(25) PTB remeasurement: upon receipt of the transducer

4. Transport

Responsibility for "transport" rests with the preceding laboratory. The primary option should beto carry the devices by hand, by qualified metrology personnel. In this case and when an aircraftis used, the devices must be transported in the passenger cabin, not in the luggage hold. Ifhand-carrying is not possible because of financial or other restrictions, air freight shipping maybe considered, but the participant is responsible for the necessary precautions. It must beensured that the devices are transported in a pressurized and temperature-controlled hold, i.e.under conditions equal to those in the cabin of a passenger-carrying airplane.

64

The devices are accompanied by an ATA carnet (this does not apply to EC countries).Responsibility for compliance with the customs regulations rests with the participants. The valueof the devices is 10000 DM (transducer) and 100 DM (module).

The devices are accomodated in a black box (about 330 mm x 300 mm x 105 mm in size). Thebox as such is not a transport container of sufficient stability and it must be protected duringtransport. If carried by hand, the box is to be placed in a bag (taking, however, the maximumdimensions for hand baggage into account). If shipped, the box must be packed in a stablecontainer, protected by additional shock-damping material, and warning notes must be attachedto the package.

According to section 6 of the Guidelines for CIPM key comparisons, each participating instituteis responsible for its own costs for the measurements, transportation and any customs chargesas well as any damage that may occur within its country.

5. Receipt of the devices

After arrival of the devices, the participating institute shall inform the pilot institute of this by anymeans (see first address in section 10 below), unless the pilot institute is directly involved in thetransport. Immediately after receipt, the participating institute shall check the devices for anydamage. The crucial part is the radiating crystal of the transducer. The front electrode of thecrystal can be seen and inspected after removal of the front cap.

6. Conditions of use

The devices must be handled with care, i.e., only by qualified metrology personnel. Avoid anymechanical shock. Avoid any pressure (or negative pressure) on the front face of thetransducer.

"Water" is to be understood as distilled or deionized water throughout this protocol. Of course,the front cap added to the transducer is not intended for use in water.

One of the gold electrodes of the lithium niobate crystal forms the front face of the transducer.There are no shielding or matching layers. The front face of the transducer is subject to damageby contact with any material other than water, lens cleaning tissue, or the front cap providedwith the transducer. For the measurements of this key comparison, the transducer must becoupled directly to water, to nothing else. The use of a coupling membrane or coupling gel isprohibited. If it appears necessary to clean the front face, soft rinsing with water is the primaryoption, but organic solvents and lens cleaning tissues may be used as well, though with

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extreme care. If organic solvents are applied, their use must be restricted to short periods,otherwise the sealing material at the crystal rim might be damaged. Water drops left on the frontface should be removed by softly touching the surface with a soft tissue. The transducer faceshould not be wiped mechanically. Any movement tangential to the transducer surface involvesthe risk of producing scratches or of removing gold particles (unfortunately, gold is a rather softmaterial). No temporal limits to the duration of water contact have so far been found necessary,but unnecessarily long water contact should, however, be avoided, if possible.

Lithium niobate is sensitive to temperature gradients. Temperature shocks of any kind shouldbe avoided.

The front face and the lateral parts of the transducer housing are waterproof under normalconditions. The electric connector on the rear is equipped with a small vent, and is notwaterproof. If the entire transducer is to be submerged, this connector must be protected by amethod which prevents water from reaching its exterior surfaces. One method that has beenfound to work well involves the use of surgical rubber tubing, longer than the distance from thetransducer to the water line. The use of any sealing device or material inside the cable ortransducer connector is strictly prohibited.

The voltage at the transducer input shall not exceed 60 V (rms, AC or DC) when the transduceris in water. At and below the "medium" power level (see below), no temporal limits to theduration of transducer operation have so far been found necessary, but unnecessary transduceroperation at the "high" and "very high" levels (see below) should be avoided. At the "high" and"very high" levels (see below), transducer operation must be intermittent. Power-on intervalsmust not exceed 22 seconds each, and must be followed by power-off intervals at least fivetimes longer in duration. For example, a 10 second power-on interval must be followed by a 50second power-off interval.

No voltage should be applied when the transducer is in air. If really necessary, the voltage mustnot, however, exceed 3 V (rms).

Needless to say, the rectifier module is not waterproof. Its connectors are numbered from 1 to 6.Connectors 2 to 6 are connected to a common point: this is the module input. If the module isused, the male connector No. 3 must be connected directly (i.e., not via a cable and/oradapters) to the transducer input. The other four of these connectors can be used as follows:one for the rf input voltage to the transducer and the module, and up to three connectors formeasuring or monitoring the rf input voltage. The maximum voltage for these connectors is thesame as for the transducer, namely 60 V (rms, AC or DC).

Connector No. 1 is the module output. This connector which is identified by a thin white band isintended for measuring the DC output voltage of the module using a digital voltmeter. No

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external voltage should be applied here; however, the module will not be damaged if a voltageof up to 60 V (as above) is applied.

7. Measurements

7.1 General

The task is to measure the total, time-averaged ultrasonic output power, Pout, emitted by thetransducer under specified conditions of electrical excitation (see below) into an anechoic (i.e.,free-field) water load. The water temperature must be measured and reported. It should be asclose as possible to 21.5 °C. The difference should not exceed ± 2.0 °C. The use of degassedwater is highly recommended and is mandatory at the "high" and "very high" levels where theoxygen content is to be measured and reported.

The participants are free to apply their own ultrasonic power measurement method, and in mostcases this will be the radiation force balance method according to IEC 61161. The output powerrelates to the transducer surface (zero distance), and if the measurements are carried out atfinite distances, the participant must derive the zero-distance result from his measurements. Inconnection with this derivation or with other corrections, participants may wish to know thestructure of the ultrasonic field of the transducer. They are free to perform field scans but theseare not necessary. It is sufficient to know that the field is unfocussed and piston-like in sufficientapproximation. The nominal beam radius which is the radius of the rear, "hot" electrode is 9.5mm.

A continuous-wave, sinusoidal excitation voltage must be applied to the transducer andmeasured by the participant. There are five voltage levels, namely "very low", "low", "medium","high" and "very high". Details are given below. While measurements at all other voltage levelsare compulsory, those at the "very high" level are optional. The specified frequency values, fs,are given in Table 1. The actual frequency, fa, is to be reported, and it must agree with thespecified one to within ± 0.0008 MHz.

In each case, at least three independent measurements are to be carried out and taken intoaccount in the final result. "Independent" is intended to mean that measurement vessel andtarget are disassembled and reassembled and that the water is changed. Measurements usingdifferent targets are also independent, of course.

If a participant uses a measurement method where the temporal voltage waveform is not of thecontinuous-wave and sinusoidal type, he must transform the results obtained accordingly andreport them in a form which makes direct comparison with the continuous-wave results possible.

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7.2 Type 1 voltage measurement

These measurements are compulsory.

The rms value of the rf voltage Uin at the transducer input must be measured and reported bythe participant using his own methods and instruments. The electroacoustic radiationconductance G must be calculated according to

G = Pout /(Uin)2 (1)

It is given in siemens or decimal submultiples of this unit, for example in millisiemens (mS).

Table 1 states the specified voltages Us (rms value) for the various frequencies and levels. Theactual voltage Uin is to agree with the respective specified voltage to within ± 5 %.

The rf voltage is to be measured at a point as near as possible to the transducer inputconnector. If the rectifier module is not used, it will be necessary to use tee connectors orequivalent parts for the excitation voltage cable and the rf voltmeter(s). On the other hand, it isalso possible to use the rectifier module here, even if the participant does not wish to carry outmeasurements of type 2, and the excitation voltage cable and the rf voltmeter(s) can beconnected to the module. Measurements of type 1 may thus be carried out using, or not using,the rectifier module, and the results can be considered equivalent.

7.3 Type 2 voltage measurement

These measurements are optional.

The rectifier module is used in measurements of this type. The DC output voltage of the moduleis measured with a DC voltmeter. The transducer input voltage is adjusted so that a certainspecified value Urec of the DC voltage as measured by the DC voltmeter is obtained, and theultrasonic output power is measured under this reference condition and is referred to as Pref andreported.

The DC output voltage of the rectifier module depends on the input resistance of the DCvoltmeter. With reference to voltmeters available on the market, two main cases are consideredas follows: The specified DC voltage for the case where the voltmeter input resistance is (10.0 ±0.5) MΩ is referred to as Urec1 and is given in column 4 of Table 1. The specified DC voltage forthe case where the voltmeter input resistance is ≥ 1 GΩ is referred to as Urec2 and is given incolumn 5 of Table 1. If the input resistance of the voltmeter of a participant is not covered by

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one of these two cases, the participant should contact the project leader who will makeavailable Urec values for this particular case.

Note - The rectifier module does not operate on root-mean-square principles and its DC outputvoltage is more sensitive to the harmonic content of the rf voltage applied than it would be thecase if a true rms-measuring device was used. The maximum possible error of the DC outputvoltage can be assumed to be given roughly by the amount of the harmonic content of the rfvoltage. The harmonic content of the applied rf voltage should, therefore, be checked andshould be less than −50 dB (ideally: −60 dB).

Table 1. Specified values.

1 2 3 4 5

fs/MHz level Us/V Urec1

(voltm. res. = 10 MΩ)

Urec2

(voltm. res. ≥ 1

GΩ)

1.8732 very low 1.45 46.50 mV 47.04 mV

low 4.4 209.0 mV 211.0 mV

medium 14.3 774.0 mV 781.0 mV

high 44.5 2.470 V 2.491 V

very high 55 3.050 V 3.077 V

6.2838 very low 1.36 41.30 mV 41.62 mV

low 4.25 195.0 mV 196.7 mV

10.5475 very low 1.33 40.50 mV 40.83 mV

low 4.1 193.0 mV 194.8 mV

7.4 Measurements of type 1 and type 2 carried out at the same time

When the rectifier module is used, voltage measurements of type 1 and type 2 can be carriedout at the same time if the rf voltmeter used is connected to one of connectors 2, 4, 5 or 6

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(preferably to 2, 4 or 6 in order to be as close as possible to the transducer input) and if the DCvoltmeter is connected to connector 1.

Note - The Us values in column 3 of Table 1 do not necessarily correspond exactly to the Urec

values in columns 4/5. If the rf input voltage is adjusted so that one of the Urec values applies,the rf input voltage does not necessarily agree exactly with the corresponding Us, but agreementwill be within the required ± 5 %.

8. Reporting

The results are to be reported to the pilot institute at the latest six weeks after themeasurements of the respective participant were completed.

The report shall contain a description of the measurement method applied and of the equipmentused. The following details, among other things, are important:- the equipment used for the generation of the excitation voltage;- the rf voltmeter(s) used in measurements of type 1, and their calibration;- the DC voltmeter used in measurements of type 2 (if applicable), and its input resistance;- water properties, water volume;- how the measurements were performed, power-on-power-off intervals etc.;- how the zero-distance results were derived from results obtained at finite distances;- formulas used and calculation methods; possibly, considerations relating to non-plane fieldstructure;- full uncertainty budgets with an explanation of the details;- method applied to measure the ultrasonic power and all relevant practical details;In the case of a radiation force balance these would be:- arrangement of the balance set-up;- type of the balance;- all relevant details of the target(s) used.

All observations which might be important for the interpretation of the results should bereported.

The values of the following quantities shall be reported (see also Table 2 below; the number insquare brackets indicates the column in Table 2):- actual frequency, fa, in MHz [4];- water temperature, t, in °C [5];- oxygen content of the water in mg/litre (in measurements at the "high" and "very high" levels)[6];- rms value of the input voltage to the transducer, Uin, in V [7];

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- time-averaged ultrasonic power, Pmeas, in mW or W [8], measured at a distance d.- distance, d, of the measurement plane from the transducer surface, in mm [9];- output power, Pout, in mW or W [10], derived from Pmeas;- electroacoustic radiation conductance, G = Pout /(Uin)2, in mS [11];- relative uncertainty of G, uG, in % [12];- DC output voltage of the rectifier module, Urec, in mV or V (if applicable) [13];- reference output power, Pref, in mW or W (if applicable) [14];Note - As type 2 measurements are to be performed with the DC output voltage of the rectifiermodule adjusted to the specified value, Pref is identical with Pout.- relative uncertainty of Pref, uPref, in % (if applicable) [15].

The results should be reported in the format of Table 2 (which can be copied), or in a slightlymodified form if Table 2 is not completely appropriate for the particular measurementprocedures followed by the participant concerned. The individual measurements should bereported in the table. In this case, column 1 ("identification number") should be numberedconsecutively, according to the time sequence of the measurements. In addition, the final,average results shall be reported in a table of the same type. In this case, column 1 may containan identifier such as "av." or equivalent. Column 2 ("characterization") may be used to indicateparticular characteristics of a measurement, for example the target type if different targets areused. Column 3 covers the measurement type. Please enter "1" for type 1, "2" for type 2 and"1+2" for the case that measurements of type 1 and 2 are performed at the same time. If "1" or"2" is entered here, some of the spaces will, of course, remain empty in that line. All entries tocolumns 8, 10, 13 and 14 must also state the relevant unit.

9. Uncertainties

The final measurement results are G and Pref (the latter only in the case where the participantdecided to carry out measurements of type 2). In all cases where such final results are given,the associated measurement uncertainty shall be stated. For the evaluation of the measurementuncertainty, reference should be made to the BIPM/IEC/ISO "Guide to the expression ofuncertainty in measurement". According to section 6 of the Guidelines for CIPM keycomparisons, uncertainties are to be evaluated at a level of one standard uncertainty andinformation must be given on the number of effective degrees of freedom.

The participants are free to apply their own measurement methods. No general advice on theuncertainty budget can, therefore, be given. If the measurements are performed with a radiationforce balance according to IEC 61161, the main components of the uncertainty budget mayfollow from the points specified below:- calibration factor and linearity of the balance;- target imperfections and other acoustic imperfections of the measurement vessel;

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- target alignment;- definition of the effective measurement plane and derivation of Pout from Pmeas;- influence of the (non-plane) field structure;- uncertainty with which the speed of sound in water is known;- uncertainty of voltage measurements.A possible source of information is IEC 61161, Amendment 1.

10. List of addresses

Dr. Klaus BeissnerPhysikalisch-Technische BundesanstaltBundesallee 100D-38116 BraunschweigGermanyTel: +49 531 592 1431Fax: +49 531 592 9292E-mail: [email protected]

Prof. Dr. Rainer ReiboldPhysikalisch-Technische BundesanstaltBundesallee 100D-38116 BraunschweigGermanyTel: +49 531 592 1400Fax: +49 531 592 1015E-mail: [email protected]

Dr. Steven E. FickNISTSound Building100 Bureau Drive STOP 8221Gaithersburg, MD 20899-8221USATel: +1 301 975 6629Fax: +1 301 417 0514E-mail: [email protected]

Dr. George S. K. WongInstitute for National Meas. StandardsMontreal Road, Building M 36Ottawa, Ontario K1A 0R6CanadaTel: +1 613 993 6159Fax: +1 613 990 8765E-mail: [email protected]

Dr. Roy C. PrestonCentre for Mech. and Acoust. MetrologyNational Physical LaboratoryTeddington, Middlesex TW11 0LWUnited Kingdom

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Tel: +44 181 943 6154Fax: +44 181 943 6161E-mail: [email protected]

Rob T. HekkenbergDivision Technology in Health CareTNO Prevention and HealthP. O. Box 2215NL-2301 CE LeidenThe NetherlandsTel: +31 71 518 1242Fax: +31 71 518 1902E-mail: [email protected]

Dr. Adrian RichardsNatl. Measurem. Lab./Stand. and Appl. UltrasonicsCSIRO/Telecom. and Industrial PhysicsP. O. Box 218, Bradfield RoadLindfield, NSW 2070AustraliaTel: +61 2 9413 7418Fax: +61 2 9413 7202E-mail: [email protected]

Dr. V. MohananHead, Acoustics SectionNational Physical LaboratoryDr. K. S. Krishnan RoadNew Delhi - 110012IndiaTel: +91 11 5786592Fax: +91 11 5752678E-mail: [email protected]

Dr. Alexander M. EnyakovAll-Russian Sci. Res. Inst. for Phys.-Tech.and Radiotech. Measurements (VNIIFTRI)Mendeleevo, Moscow Region141570 RussiaTel: +7 095 535 9397Fax: +7 095 535 0880E- mail: [email protected]

Dr. Chen JianlinAcoustics LaboratoryNational Institute of Metrology18, Bei San Huan Dong LuBeijing 100013P. R. ChinaFax: +86 10 6421 8628E-mail: [email protected]

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Table 2. Reporting form

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

id. No. charact. m. type fa t ox. cont. Uin Pmeas d Pout G uG Urec Pref uPref

MHz °C mg/litre V mW or W mm mW or W mS % mV or V mW or W %

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