Final Report on Key Comparison CCAUV.U-K3.1

Report on Key Comparison CCAUV.U-K3.1 1

Final Report on Key Comparison CCAUV.U-K3.1

Authors:

Julian Haller, Christian Koch

Physikalisch-Technische Bundesanstalt

Bundesallee 100

38116 Braunschweig

[email protected]

Co-Authors:

Rodrigo P.B. Costa-Felix, INMETRO

Premshankar Kedarnath Dubey, NPLI

Giovanni Durando, INRIM

Yong Tae KIM, KRISS

Masahiro Yoshioka, NMIJ/AIST


1. Introduction

In October 2013, during the 9th meeting of the CCAUV in Sèvres, France, the results of the key comparison

CCAUV.U-K3 were presented and the Draft B report was agreed upon shortly thereafter by email. The

results have also been published in the meantime [1]. During the meeting it was decided to start a new

comparison CCAUV.U-K3.1 to give all participants of the preceding loop who delivered discrepant values

the opportunity to perform new measurements. In addition, NMIJ was included since the institute could

not take part in CCAUV.U-K3 because of the horrible earthquake in 2011. Furthermore, NMC A*STAR had

asked for the opportunity to take part, but resigned later from the comparison.

The goal of the key comparison was to show the capabilities of the participating laboratories to determine

the acoustic radiation conductance of an ultrasonic transducer by measuring the total time-averaged

ultrasonic power emitted for an applied rms voltage in the nominal frequency range from 2 MHz to 16 MHz

and for nominal output power values between 10 mW and 15 W. Although the ultrasound power is the

measurand of the key comparison, the participants were asked to report the radiation conductance which

is independent of the applied voltage and is therefore a characteristic property of the transducer at a

particular frequency. Nevertheless, the key comparison primarily represents the ultrasound power

measurement capabilities of the participating NMIs and is suitable for justifying CMC entries of this

variable.

This key comparison was planned and conducted according to the “Guidelines for CIPM Key Comparisons”

issued by the BIPM [2].

Participants and Schedule

The following list contains the participants who planned to take part in this comparison:

• INMETRO, Brazil

• INRIM, Italy

• KRISS, Korea

• NMC A*STAR, Singapore (withdrawn)

• NMIJ, Japan

• NPLI, India

• PTB, Germany, as pilot

The original schedule of the comparison is given in Table 1. During the key comparison, some slight delays

could not be avoided. Furthermore, NMC A*STAR decided to withdraw its participation request during the

key comparison and INRIM realized that their balance had been malfunctioning during their measurements.

In agreement with the other participants, INRIM performed a second set of measurements at the end of

the key comparison. Their first set of measurements was discarded and will neither be shown nor analysed

in the following sections. This led to a slightly modified time schedule, which is given in the last two

columns of Table 1.

Measurement Settings

The task was to measure the total time-averaged ultrasonic output power, Pout, emitted by the transducer

under specified conditions of electrical excitation (see below) into an anechoic (i.e., free-field) water load.

The water temperature had to be measured and reported. It should be as close as possible to 21.5 °C. The

difference should not exceed ± 2.0 °C. The use of degassed water was highly recommended and was

mandatory at the “high” level where the oxygen content was to be measured and reported.


Table 1: Planned and actual time schedule of the comparison

Planned Actual

No. Calibration laboratory Starting

date

Dispatching

date

Starting

date

Dispatching

date

1 PTB, Germany 01-Mar-14 22-Mar-14 01-Mar-14 20-Mar-14

2 NMIJ, Japan 05-Apr-14 26-Apr-14 03-Apr-14 21-Apr-14

3 KRISS, Korea 10-May-14 31-May-14 24-Apr-14 28-May-14

4 Re-measurement PTB 14-Jun-14 05-Jul-14 28-May-14 03-Jul-14

5 INRIM, Italy 19-Jul-14 09-Aug-14 11-Jul-14 31-Jul-14

6 NPLI, India 23-Aug-14 13-Sep-14 02-Sep-14 19-Sep-14

7 Re-measurement PTB 27-Sep-14 18-Oct-14 15-Oct-14 21-Nov-14

8 NMC A*STAR,

Singapore 01-Nov-14 22-Nov-14 --- ---

9 INMETRO, Brazil 06-Dec-14 27-Dec-14 11-Dec-14 05-Jan-15

10 Re-measurement PTB 10-Jan-15 --- 10-Feb-15 13-Feb-15

11 INRIM, Italy --- --- 20-Feb-15 23-Mar-15

12 Re-measurement PTB --- --- 24-Mar-15 10-Apr-15

A continuous-wave, sinusoidal excitation voltage had to be applied to the transducer and measured by the

participant. There were four voltage levels, namely “very low”, “low”, “medium”, and “high”. The specified

rms voltage values, Us, and the specified frequency values, fs, are given in Table 2. The actual frequency, fa,

was to be reported, and it had to agree with the specified one to within ± 0.0010 MHz.

The term “frequency-power setting” (FPS) and the respective number given in the last column of Table 2

will be used in the following to define measurement parameters with respect to power and frequency.

Table 2: Specified frequency-power settings, the number of a relevant frequency-power setting (FPS) will

be used in the following for defining measurement parameters.

fs / MHz level Us / V FPS

2.0150 very low 1.25 1 medium 13.5 2

high 50.0 3

6.7513 very low 1.20 4

low 4.00 5

11.3318 very low 1.25 6

low 4.00 7

15.8942 low 3.70 8

The actual rms transducer input voltage Uin had to be measured and reported by the participant using his

own methods and instruments. It had to agree with the respective specified voltage Us of Table 1 within an

interval of ± 5 %.

In each case, at least four independent measurements had to be carried out and taken into account in the

final result. “Independent” is intended to mean that the measurement vessel and the target are


disassembled and reassembled and that the water is changed. Measurements using different targets are

also independent, of course.

If a participant used a measurement method where the temporal voltage waveform is not of the

continuous-wave and sinusoidal type, he had to transform the results obtained accordingly and report

them in a form which makes direct comparison with the continuous-wave results possible.

In each case, the electro-acoustic radiation conductance G had to be calculated according to

G = Pout /(Uin)2 . (1)

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

The input voltage Uin refers to the transducer input and had to be measured at a point as close as possible

to the transducer input connector. If the voltage was measured at a remote point, the participant was

responsible for correcting this.


2. Results

2.1 Stability of the circulated standard transducer

The stability of the circulated standard transducers was evaluated through the five re-measurements at PTB

(see Table 1). In addition, three sets of measurements had been performed prior to the key comparison.

The results of all these measurements are given in Table 3 and plotted in Fig. 1 (top). The stated expanded

uncertainties k∙uG are based on a coverage factor k = 2. The level of confidence is 95.45 %. “Re3” and “Re5”

are obtained from four independent measurements at each condition, all other measurements from two

independent measurements at each condition. “Re3” is considered to be PTB’s result of the key

comparison.

Table 3: Results of the five re-measurements at PTB and the three measurements before the start of the

key comparison; the frequency-power settings (FPS) correspond to the definition given in Table 2.

FPS Measurements in advance Re-Measurements CCAUV.U-K3.1

Dec 12

Feb 13

Jun 13

Re1

Mar 14

Re2

Jun 14

Re3

Oct 14

Re4

Feb 15

Re5

Apr 15

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

G

mS

k∙uG

/%

1 5.83 3.9 5.84 3.1 5.83 3.3 5.81 3.0 5.83 3.1 5.80 3.2 5.81 3.5 5.82 3.4

2 5.84 2.8 5.83 2.7 5.85 2.8 5.82 3.0 5.84 3.0 5.83 3.0 5.82 3.0 5.81 3.0

3 5.88 2.7 5.85 2.7 5.89 2.7 5.90 3.0 5.90 3.0 5.90 3.0 5.86 3.0 5.87 3.0

4 6.57 3.7 6.55 4.0 6.53 4.0 6.57 3.7 6.56 3.8 6.55 4.4 6.56 4.0 6.58 3.8

5 6.56 3.3 6.56 3.3 6.56 3.3 6.55 4.0 6.56 4.0 6.54 3.6 6.57 3.4 6.57 4.0

6 6.78 5.3 6.81 5.1 6.79 5.2 6.76 4.9 6.76 5.7 6.77 5.5 6.81 5.5 6.79 5.0

7 6.78 4.6 6.77 4.7 6.80 4.6 6.78 4.7 6.77 6.3 6.78 4.7 6.79 4.6 6.80 5.1

8 7.11 8.6 7.08 8.6 7.09 8.4 7.09 8.6 7.12 8.8 7.09 8.6 7.10 8.5 7.10 8.8

For the results listed in Table 3, some basic analysis (arithmetic mean, standard deviation, minimum and

maximum values) has been performed for every frequency-power setting. The results are listed in Table 4.

The standard deviation for all frequency-power settings is smaller than 0.3 % (and at least one order of

magnitude smaller than the measurement uncertainty for the respective frequency-power setting). All

results deviate by less than 0.5 % from the respective mean value, as can be seen in Fig. 1 (bottom). Neither

a systematic drift nor a step in the results was found for any of the conditions. The circulated transducer is

thus considered to be stable throughout the key comparison.

Table 4: Basic analysis of the eight measurements at PTB listed in Table 3. “Mean”: Arithmetic mean; “STD”:

standard deviation; “Min”: lowest measurement result; “Max”: highest measurement result; “Max-Min”:

Difference between highest and lowest measurement result.

FPS

Analysis

Mean

STD

STD

Min

Max

Max-

Min

G

mS

mS

%

G

mS

G

mS

%

1 5.82 0.01 0.23 5.80 5.84 0.76

2 5.83 0.01 0.20 5.81 5.85 0.61

3 5.88 0.02 0.29 5.85 5.90 0.84

4 6.56 0.01 0.22 6.53 6.58 0.76

5 6.56 0.01 0.16 6.54 6.57 0.57

6 6.78 0.02 0.26 6.76 6.81 0.74

7 6.79 0.01 0.13 6.77 6.80 0.40

8 7.10 0.01 0.17 7.08 7.12 0.52


Figure 1: Results from the eight measurements at PTB listed in Table 3 (top) and deviation of the single

measurements from the respective mean (bottom).


2.2 Complete key comparison results

The complete key comparison results, i.e. the results reported by the participants, are listed in Table 5 and

plotted in Fig. 2. The stated expanded uncertainties k∙uG are based on a coverage factor k = 2. The level of

confidence is 95.45 %

Table 5: Results of the key comparison participants; all values are given with as many decimal places as

reported.

M1

PTB

M2

NMIJ

M3

KRISS

M4

INRIM

M5

NPLI

M6

INMETRO

FPS f

/ MHz

power

level

G

/mS

k∙uG

/%

G

/mS

k∙uG

/%

G

/mS

k∙uG

/%

G

/mS

k∙uG

/%

G

/mS

k∙uG

/%

G

/mS

k∙uG

/%

1

2.015

very low 5.80 3.2 6.357 6.0 5.86 6.0 5.87 8.66 5.827 4.88 6.04 10

2 med 5.83 3.0 6.172 6.0 5.86 4.9 5.71 3.10 5.892 4.30 6.19 6

3 high 5.90 3.0 6.072 6.2 5.94 5.7 5.86 6.30 5.901 4.76 6.29 5

4 6.7513

very low 6.55 4.4 6.371 5.2 6.54 6.0 6.53 7.50 6.355 5.26 6.03 10

5 low 6.54 3.6 6.693 4.4 6.51 5.3 6.60 4.00 6.414 4.66 6.60 5

6 11.3318

very low 6.77 5.5 6.344 6.4 6.70 6.0 6.88 8.42 6.886 5.58 6.21 10

7 low 6.78 4.7 6.405 5.8 6.73 5.3 6.78 4.30 6.918 5.12 6.74 5

8 15.8942 low 7.09 8.6 6.406 7.9 7.05 6.2 7.00 7.02 7.484 5.27 7.24 5

Figure 2: Results of the key comparison from all six participants. Error bars indicate the expanded

uncertainties k∙uG (k = 2), as given in Table 5.


3. Analysis

3.1 Analysis of all results

First of all, a consistency check of the results was performed following the recommendations by the BIPM

Advisory Group on Uncertainties. A weighted mean was calculated for each frequency-power setting:

= ∑ , , ∑ ,

, (2)

where N = 6 is the number of participants, Gi,k is the radiation conductance value for frequency-power

setting i reported by participant k, and u2(Gi,k) is the respective standard uncertainty. Next, the standard

deviations of the weighted means were calculated as

= ∑ , . (3)

To check the consistency of the complete data set, the observed χ2-values

obs, = ∑ , , (4)

were calculated. The consistency check fails for one of the frequency-power settings if

Pr#$ > obs,& < 0.05, (5)

where ν is the degree of freedom (with ν = N-1) and Pr denotes 'the probability of'. This leads to an upper

limit on χobs,i2 (χmax

2 = 11.0705 for N = 6). Fig. 3 shows the values of χobs2 in relation to the calculated limit

from equation (4) using a χ2-probability distribution. Obviously, for all frequency-power settings except for

frequency-power setting 8, the criterion is fulfilled.

Figure 3: Consistency check for the different frequency-power settings when all results are considered. See

text for explanation.


In order to identify discrepant measurement results, the deviations from the weighted means, di,k=Gi,k- Ḡi,

were calculated, as well as their uncertainties, u2(di,k)=u2(Gi,k) - u2(Ḡi). With these two quantities, the

outlying criterion

(),( > 2 ∙ , ), ⇔ (/,(∙ /,> 1 (6)

was tested for all measurement results. All calculated values are given in Table 6, with “Outlier test” being

di,k/2∙u(di,k). This means that a particular result is considered as discrepant if “Outlier test” is > 1. Those

values are marked in red and bold. All results are plotted in Fig. 4.

In addition, an independent analysis of the results was performed following Nielsen [3]. Since the obtained

results agreed with the presented ones within many more digits after the decimal point than shown, they

are not additionally listed here.

Table 6: Basic analysis of the results when all results are considered.

PTB NMIJ KRISS INRIM NPLI INMETRO

FPS 1 (i=1) (2.015 MHz, very low)

Weighted mean Ḡ = 5.889 mS

Uncertainty of Ḡ. u(Ḡ) = 0.063 mS (=1.070 %)

Deviation from Ḡ, dk / mS -0.089 0.468 -0.029 -0.019 -0.062 0.151

uncertainty u of dk,

u2(d )

/ mS 0.068 0.180 0.164 0.246 0.127 0.295

Outlier test 0.650 1.301 0.087 0.038 0.241 0.256

FPS 2 (i=2) (2.015 MHz, med)



Deviation from Ḡ, dk / mS -0.024 0.318 0.006 -0.144 0.038 0.336


u2(d )

/ mS 0.073 0.179 0.135 0.074 0.117 0.179

Outlier test 0.167 0.889 0.021 0.974 0.161 0.936

FPS 3 (i=3) (2.015 MHz, high)



Deviation from Ḡ, dk / mS -0.067 0.105 -0.027 -0.107 -0.066 0.323


u2(d )

/ mS 0.068 0.179 0.160 0.176 0.128 0.147

Outlier test 0.494 0.292 0.085 0.305 0.257 1.101




Deviation from Ḡ, dk / mS 0.114 -0.065 0.104 0.094 -0.081 -0.406


u2(d )

/ mS 0.123 0.147 0.181 0.233 0.149 0.292

Outlier test 0.465 0.221 0.287 0.202 0.272 0.696

FPS 5 (i=5) (6.7513 MHz, low)



Deviation from Ḡ, dk / mS -0.021 0.132 -0.051 0.039 -0.147 0.039


u2(d )

/ mS 0.102 0.135 0.162 0.118 0.137 0.154

Outlier test 0.102 0.489 0.157 0.166 0.534 0.127




Deviation from Ḡ, dk / mS 0.105 -0.321 0.035 0.215 0.221 -0.455


u2(d )

/ mS 0.164 0.183 0.180 0.276 0.170 0.298

Outlier test 0.322 0.877 0.098 0.391 0.650 0.764

FPS 7 (i=7) (11.3318 MHz, low)



Deviation from Ḡ, dk / mS 0.044 -0.331 -0.006 0.044 0.182 0.004


u2(d )

/ mS 0.144 0.173 0.165 0.129 0.163 0.154

Outlier test 0.153 0.958 0.018 0.172 0.558 0.014




Deviation from Ḡ, dk / mS -0.014 -0.698 -0.054 -0.104 0.380 0.136


u2(d )

/ mS 0.291 0.236 0.199 0.228 0.175 0.156

Outlier test 0.024 1.479 0.136 0.228 1.086 0.435


Figure 4: Results and weighted means (full lines) for all FPSs when all reported results are considered. Error

bars and the dashed lines denote expanded standard uncertainties (k=2) of the results and the weighted

means, respectively.


3.2 Analysis of frequency-power settings with outlying results

The results from the previous section clearly show that for frequency-power settings 2, 4, 5, 6, and 7 the

reported results were found to be consistent and that there were no outliers. Therefore, the respective

values of the weighted means for these frequency-power settings are considered to be the final values of

CCAUV.U-K3.1.

For the other three frequency-power settings, namely 1, 3 and 8, for which outlying results were found

and/or the consistency check failed, further analysis was needed. The method described by Cox [4] is

applied here to find the largest subset of data which is consistent with the consistency check and the

outlying criterion:

According to this method, the largest subset is found by calculating the χ2-value and testing the outlying

criterion for a permutation of (N-1) participants (i.e. one participant is successively excluded). If both checks

are passed (i.e. the χ2-value is below the limit and no outlying results are found) for exactly one

permutation, this permutation (i.e. without the excluded participant) is considered the largest subset. If

both checks are passed for more than one permutation, the permutation yielding the smallest χ2-value is

considered the largest subset. If for none of the permutations both checks are passed, the procedure is

repeated with permutations of (N-2) participants, and so on, until the largest consistent subset that passes

both checks is found.

3.2.1 Largest subset for FPS 1

Applying the above procedure for FPS 1 clearly shows (see Table 7) that the largest subset is found by

excluding the data from NMIJ for this FPS. The corresponding results are listed in Table 8 and are

considered to be the final values of CCAUV.U-K3.1 for FPS1. Note that in Table 8 the uncertainty of the

deviations for the excluded result is calculated by u2(di,k)=u2(Gi,k) + u2(Ḡi), since Gi,k and Ḡi are not correlated

in this case, and following equation u2(di,k)=u2(Gi,k) - u2(Ḡi) in all other cases [4].

Table 7: Results for all permutations of (N-1) participants for FPS 1. “Outliers” denotes the number of

laboratories that fulfil the outlying criterion, when the result from “Excluded lab” is excluded from the

analysis.

Excluded lab Outliers χ2 (limit: 9.4877)

PTB 1 5.7251

NMIJ 0 0.6421

KRISS 1 7.3845

INRIM 1 7.4091

NPLI 1 7.1815

INMETRO 1 7.1518

Table 8: Basic analysis of the results for FPS 1 when the results from NMIJ are excluded (their values are

given nevertheless (grey background) for completeness).





Deviation from Ḡ, dk / mS -0.031 0.526 0.029 0.039 -0.004 0.209


u2(d )

/ mS 0.064 0.202 0.163 0.245 0.126 0.295

Outlier test 0.242 1.301 0.089 0.079 0.017 0.355


Applying the procedure for FPS 3 yields two cases, for which excluding the results from one lab makes all

other labs pass the outlying test (see Table 9). From these two cases, the smallest χ2-value is obtained when

the data from INMETRO are excluded. This permutation is thus the largest subset and the corresponding

results are listed in Table 10 and are considered to be the final values of CCAUV.U-K3.1. Note that as in


Table 8, in Table 10 the uncertainty of the deviations for the excluded result is calculated by u2(di,k)=u2(Gi,k)

+ u2(Ḡi), since Gi,k and Ḡi are not correlated in this case, and following equation u2(di,k)=u2(Gi,k) - u2(Ḡi) in all

other cases.



analysis.


PTB 0 4.7100

NMIJ 1 5.3444

KRISS 1 5.6568

INRIM 1 5.3138

NPLI 1 5.4208

INMETRO 0 0.8408

Table 10: Basic analysis of the results for FPS 3 when the results from INMETRO are excluded (their values

are given nevertheless (grey background) for completeness).


FPS 3 (i=3) (2.015 MHz, high)



Deviation from Ḡ, dk / mS -0.019 0.153 0.021 -0.059 -0.018 0.371


u2(d )

/ mS 0.064 0.178 0.158 0.174 0.127 0.169

Outlier test 0.147 0.430 0.067 0.169 0.071 1.101


Applying the procedure for FPS 8 yields only one case, for which excluding the results from one lab makes

all other labs pass the outlying test (see Table 11). This permutation (i.e. excluding the results from NMIJ) is

thus the largest subset and the corresponding results are listed in Table 12 and are considered to be the

final values of CCAUV.U-K3.1 for FPS 8. Note that in Table 12, again the uncertainty of the deviations for the

excluded result is calculated by u2(di,k)=u2(Gi,k) + u2(Ḡi), since Gi,k and Ḡi are not correlated in this case, and

following equation u2(di,k)=u2(Gi,k) - u2(Ḡi) in all other cases.



analysis.


PTB 2 12.1269

NMIJ 0 3.3792

KRISS 2 12.0549

INRIM 2 11.9209

NPLI 1 7.4083

INMETRO 2 11.3739

Table 12: Basic analysis of the results for FPS 8 when the results from NMIJ are excluded (their values are

given nevertheless (grey background) for completeness).







u2(d )

/ mS 0.289 0.271 0.195 0.225 0.171 0.152

Outlier test 0.205 1.479 0.405 0.463 0.805 0.103


4 Final results

With the findings from the previous section, the following results are considered as outliers and thus

omitted from the analysis of the data:

- FPS 1: NMIJ

- FPS 3: INMETRO

- FPS 8: NMIJ

The final results obtained accordingly are given in Table 13 and Figure 5. Figure 6 additionally shows that

the consistency check is fulfilled for all frequency-power settings when the outliers listed above are omitted

from the analysis.

Table 13: Basic analysis of the results when outliers are not considered (their values are given nevertheless

(grey background) for completeness). Note that the uncertainties of the deviations for the excluded results

are calculated by u2(di,k)=u2(Gi,k) + u2(Ḡi), since Gi,k and Ḡi are not correlated in these cases, and using

u2(di,k)=u2(Gi,k) - u2(Ḡi) in all other cases.





Deviation from Ḡ, dk / mS -0.031 0.526 0.029 0.039 -0.004 0.209


u2(d )

/ mS 0.064 0.202 0.163 0.245 0.126 0.295

Outlier test 0.242 1.301 0.089 0.079 0.017 0.355

FPS 2 (i=2) (2.015 MHz, med)



Deviation from Ḡ, dk / mS -0.024 0.318 0.006 -0.144 0.038 0.336


u2(d )

/ mS 0.073 0.179 0.135 0.074 0.117 0.179

Outlier test 0.167 0.889 0.021 0.974 0.161 0.936

FPS 3 (i=3) (2.015 MHz, high)



Deviation from Ḡ, dk / mS -0.019 0.153 0.021 -0.059 -0.018 0.371


u2(d )

/ mS 0.064 0.178 0.158 0.174 0.127 0.169

Outlier test 0.147 0.430 0.067 0.169 0.071 1.101




Deviation from Ḡ, dk / mS 0.114 -0.065 0.104 0.094 -0.081 -0.406


u2(d )

/ mS 0.123 0.147 0.181 0.233 0.149 0.292

Outlier test 0.465 0.221 0.287 0.202 0.272 0.696

FPS 5 (i=5) (6.7513 MHz, low)



Deviation from Ḡ, dk / mS -0.021 0.132 -0.051 0.039 -0.147 0.039


u2(d )

/ mS 0.102 0.135 0.162 0.118 0.137 0.154

Outlier test 0.102 0.489 0.157 0.166 0.534 0.127




Deviation from Ḡ, dk / mS 0.105 -0.321 0.035 0.215 0.221 -0.455


u2(d )

/ mS 0.164 0.183 0.180 0.276 0.170 0.298

Outlier test 0.322 0.877 0.098 0.391 0.650 0.764

FPS 7 (i=7) (11.3318 MHz, low)



Deviation from Ḡ, dk / mS 0.044 -0.331 -0.006 0.044 0.182 0.004


u2(d )

/ mS 0.144 0.173 0.165 0.129 0.163 0.154

Outlier test 0.153 0.958 0.018 0.172 0.558 0.014






u2(d )

/ mS 0.289 0.271 0.195 0.225 0.171 0.152

Outlier test 0.205 1.479 0.405 0.463 0.805 0.103


Figure 5: Results and weighted means (full lines) when outlying results are not considered (their values are

plotted nevertheless (grey background) for completeness). Error bars and dashed lines denote expanded

standard uncertainties (k=2) of the results and the weighted means, respectively.


Figure 6: Consistency check for all frequency-power settings when outlying results are not considered. Note

the different limits for frequency-power settings 1, 3, and 8 which reflect the respectively reduced number

of participants of the considered results.


5 Inter-laboratory degrees of equivalence

For the sake of readability, inter-laboratory degrees of equivalence will neither be listed in this report nor in

later reports. The inter-laboratory degree of equivalence between two laboratories “m” and “n” for a

particular frequency-power setting can, however, be calculated as

)1,2 = 1 − 2, (7)

and the expanded uncertainty of dm,n as

, )1,2 = ,1 + ,2. (8)


6 Linking with CCAUV.U-K3

In order to make the results from key comparison CCAUV.U-K3 and this key comparison directly

comparable, the obtained values from this key comparison will be linked to those from CCAUV.U-K3 in the

following. The procedure for linking follows the recommendations and considerations in [5], but some

general things that apply for the present case should be noted:

1) The procedure in [5] is formulated as a way for “linking the results of CIPM and RMO key comparisons”,

but can of course be applied to the present case for the linking of two CIPM key comparisons as well.

2) The procedure in [5] allows linking of two key comparisons in which the results are of different physical

dimensions, which is not the case here. The specified settings of frequency and voltage/power are

comparable for the two key comparisons (see Table 14).

3) All results are used for the analysis as given in Table 15 (final results of CCAUV.U-K3, taken from Table 6

in [1]) and Table 16 (CCAUV.U-K3.1).

4) For completeness, the outlying results from CCAUV.U-K3.1 will not be excluded from the linking

procedure, i.e. respective transformed results will be calculated. Note that this does not have any influence

on any of the other results.

Table 14: Comparison of the frequency-power settings (FPS) in CCAUV.U-K3 and CCAUV.U-K3.1.

FPS 1 2 3 4 5 6 7 8

Frequency f /MHz

CCAUV.U-K3 2.0130 6.7444 11.3204 15.8785

CCAUV.U-K3.1 2.0150 6.7513 11.3318 15.8942

Input rms voltage Uin /V

CCAUV.U-K3 1.30 13.0 50.9 1.21 3.90 1.17 3.78 3.60

CCAUV.U-K3.1 1.25 13.5 50.0 1.20 4.00 1.25 4.00 3.70

Nominal (according to the pilot lab) acoustic power /mW

CCAUV.U-K3 9.8 985 15168 9.7 101 9. 6 100 99

CCAUV.U-K3.1 9.1 1063 14750 9.4 105 10.6 108 97

The linking procedure is described in detail in [5], but will be briefly explained here:

From the results for CCAUV.U-K3 (abbreviated and indexed as “K3” in the following) of all laboratories

listed in Table 15, the weighted means ḠK3,i are calculated for each FPS (i=1…8), as well as the respective

expanded uncertainties u2(ḠK3,i).

K3, = ∑ K3,, K3,, ∑ K3,,

, (9a)

K3, = ∑ K3,, (9b)

Here, N = 7 (N = 8 for FPS 1 to FPS 3) is the number of participants, GK3,i,k is the radiation conductance value

for frequency-power setting i reported by participant k, and u(GK3,i,k) is the respective standard uncertainty.


Table 15: Measurement results within CCAUV.U-K3 of the participating NMIs for the acoustic radiation

conductance G and declared uncertainties ku(G) (k = 2) after the correction of the step for the first three

NMIs: PTB, UME and INRIM [1]. Results from the linking labs are shaded in green.

FP

S

M1

PTB

M3

INRIM

M2

UME

M4

VNIIFTRI

M5

NIM

M9

NPL

M10

NMIA

M7

KRISS

1 G / mS 5.816 5.804 5.535 5.805 5.885 5.78 5.891 5.615

ku(G) /% 2.9 6.3 5.1 3.1 9.6 3.9 3.6 5.8

2 G / mS 5.827 5.771 5.682 5.668 5.873 5.81 5.921 5.740

ku(G) /% 2.8 3.1 5.0 3.3 3.4 3.4 3.0 4.5

3 G / mS 5.855 5.736 5.928 5.658 6.018 5.82 5.982 5.811

ku(G) /% 2.8 5.9 5.0 4.7 4.6 4.2 3.1 4.6

4 G / mS 6.632 6.626 6.493 6.687 6.896 6.51 6.660 ---

ku(G) /% 3.4 6.9 6.1 4.3 9.4 3.8 3.6 ---

5 G / mS 6.620 6.594 6.377 6.593 7.000 6.54 6.628 ---

ku(G) /% 3.4 4.1 6.1 3.7 9.4 3.4 2.9 ---

6 G / mS 6.994 7.130 6.746 7.268 7.004 6.77 6.966 ---

ku(G) /% 4.6 8.0 7.2 5.6 4.4 3.9 3.6 ---

7 G / mS 6.991 7.038 6.821 7.041 6.891 6.83 6.925 ---

ku(G) /% 4.6 4.1 7.2 5.1 5.8 3.8 3.1 ---

8 G / mS 7.635 7.817 7.577 7.737 7.628 7.35 7.532 ---

ku(G) /% 8.7 7.0 7.2 6.2 7.6 3.5 3.2 ---

Table 16: Measurement results within CCAUV.U-K3.1 of the participating NMIs for the acoustic radiation

conductance G and declared uncertainties ku(G) (k = 2). Results from the linking labs are shaded in green

and outlying results are shaded in grey.

FPS

M1

PTB

M4

INRIM

M2

NMIJ

M3

KRISS

M5

NPLI

M6

INMETRO

1 G / mS 5.80 5.87 6.357 5.86 5.827 6.04

ku(G) /% 3.2 8.66 6.0 6.0 4.88 10

2 G / mS 5.83 5.71 6.172 5.86 5.892 6.19

ku(G) /% 3.0 3.1 6.0 4.9 4.30 6

3 G / mS 5.90 5.86 6.072 5.94 5.901 6.29

ku(G) /% 3.0 6.3 6.2 5.7 4.76 5

4 G / mS 6.55 6.53 6.371 6.54 6.355 6.03

ku(G) /% 4.4 7.5 5.2 6.0 5.26 10

5 G / mS 6.54 6.60 6.693 6.51 6.414 6.60

ku(G) /% 3.6 4.0 4.4 5.3 4.66 5

6 G / mS 6.77 6.88 6.344 6.70 6.886 6.21

ku(G) /% 5.5 8.42 6.4 6.0 5.58 10

7 G / mS 6.78 6.78 6.405 6.73 6.918 6.74

ku(G) /% 4.7 4.3 5.8 5.3 5.12 5

8 G / mS 7.09 7.00 6.406 7.05 7.484 7.24

ku(G) /% 8.6 7.02 7.9 6.2 5.27 5


Next, from the results of the two linking laboratories only (PTB and INRIM) for CCAUV.U-K3.1 (abbreviated

and indexed as “K3.1” in the following), the weighted means G K3.1,i are calculated for each FPS (I = 1…8),

again with the respective absolute standard uncertainties u(G K3.1,i). The symbol G (weighted mean from the

linking laboratories) is used here to distinguish from Ḡ, which denotes weighted means from all participants

of a key comparison.

7K3.1, = K3.1,,PTB K3.1,,PTB ;K3.1,,INRIM K3.1,,INRIM K3.1,,PTB ; K3.1,,INRIM , (10a)

7K3.1, = K3.1,,PTB+ K3.1,,INRIM (10b)

In Equations (9a) and (9b), the values for G and u(G) from Table 15 (i.e. for CCAUV.U-K3) have to be used

and in Equations (10a) and (10b) the green-shaded values for G and u(G) from Table 16 (i.e. for CCAUV.U-

K3.1) have to be used.

From the values derived from Equations (9) and (10), a transformation factor ri and its expanded relative

uncertainty u2rel(ri) are calculated for each FPS as

@ = K3,7K3.1, (11)

and

,rel @ = ,rel K3, + ,rel 7K3.1, − 2 ∙ ,rel K3, ∙ ,rel 7K3.1, (12)

∙ ∑ K3,(K3,,C( ∙ 7K3.1,(K3.1,,C( ∙ rel K3,rel K3,,C ∙ rel 7K3.1,rel K3.1,,C ∙ D,EE .

Here, l = 1 (PTB) and l = 2 (INRIM) denote the two linking laboratories and ρi,l is a term that accounts for the

correlation between the result of linking lab l for FPS i between the two key comparisons (ρ = 0 means no

correlation and ρ = 1 a perfect correlation). It can generally be assumed that the correlation factors here

are all close to 1 due to the high reproducibility of measurements conducted by the linking labs, but not

exactly 1, due to possible temporal drifts of the measurement setups during the time span of

approximately 6 years between the measurements for the two key comparisons and due to the slightly

different defined measurement settings (see Table 14). Generally, the correlation factor ρ between two

measurement series, GA and GB, can be calculated as the quotient of the covariance cov(GA,GB) and the

product of the standard deviations σ(GA) and σ(GB):

DA, B = GHIA ,BJA∙JB (13)

According to [6], the covariance in this case can be calculated as

KLMA, B = ∑ NANOP ∙ NBNOP ∙ , QRR , (14)

where the qj are quantities on which GA and GB depend (i.e. the frequency, the input voltage and others in

this case). However, the above calculation is not straightforward here, since the dependence of the

radiation conductance on these quantities is not precisely known. Therefore, the correlation factors were

all assumed to be 1 here with the following remarks:

1) The particular choice of the correlation factors does not contribute to the transformation factors ri

or to the transformed radiation conductance values, but only to their uncertainties.


2) The influence of the particular choice of the correlation factors on the uncertainties of the

transformed radiation conductance values was empirically tested by setting ρi,l to different values

between 1 and 0 and was found to be at maximum 1 % per change of 0.1 of the correlation factors.

3) Several empirical correlation factors were calculated, e.g. between the first and the last re-

measurement series of PTB or between the results from PTB for CCAUV.U-K3 and for CCAUV.U-

K3.1. All correlation factors obtained in this way were between 0.99 and 1, so that possible errors

in the calculated uncertainties due to the use of ρi,l=1 can be assumed to be much smaller than 1 %.

The values calculated according to Equations (9) – (12) are listed in Table 17. Note that the values for ḠK3,i

and ku(ḠK3,i) are the same as the key comparison reference values in Table 7 in [1] (except for rounding

differences in the last digit of ku(ḠK3,i) in some cases), as can be expected.

Table 17: Results for linking quantities.

Quantity Eq.

FPS

1 2 3 4 5 6 7 8

ḠK3,I /mS (9a) 5.783 5.799 5.866 6.618 6.592 6.954 6.936 7.527 ku(ḠK3,I) /mS (9b) 0.084 0.069 0.083 0.112 0.097 0.125 0.114 0.143 ku(ḠK3,I) /% 1.5 1.2 1.4 1.7 1.5 1.8 1.7 1.9 G

K3.1,I /mS (10a) 5.808 5.771 5.893 6.545 6.567 6.802 6.78 7.035 ku(G

K3.1,I) /mS (10b) 0.174 0.124 0.16 0.248 0.176 0.313 0.215 0.383 ku(G

K3.1,I) /% 3.0 2.2 2.7 3.8 2.7 4.6 3.2 5.4 ri (11) 0.996 1.005 0.996 1.011 1.004 1.022 1.023 1.07 ρi (13) 1 1 1 1 1 1 1 1 ku(ri) /% (12) 2.5 1.8 2.2 3.2 2.2 4.1 2.7 5.1

With the values in Table 17, the results of CCAUV.U-K3.1 can be transformed to results that can be directly

compared to those from CCAUV.U-K3 as (introducing Ġ as a symbol for a transformed value):

SK3,, = @ ∙ K3.1,, (15)

and

,rel SK3,, = ,rel @ + ,rel K3.1,, + 2 ∙ T,K3.1,,T∙K3.1,, , (16)

where

, @, K3.1,, = U−K3, ∙ ,rel 7K3.1, + @ ∙ K3, ∙ ,rel K3, ∙ (K3.1,,((K3,,( ∙ rel K3.1,,rel K3,, ∙ D,V = 1,… , X0,otherwise .

(17)

The respective results are listed in Table 18 and plotted in Figure 7, together with the original results of

CCAUV.U-K3. Note that for the two linking labs the relative uncertainties of the transformed results are

smaller than the relative uncertainties of the corresponding original results, which is also the case in the

example in [5].


Table 18: Final results of the linking procedure, outlying results of CCAUV.U-K3.1 are shaded in grey.

Participant

FPS PTB INRIM NMIJ KRISS NPLI INMETRO

1

G /mS 5.775 5.844 6.329 5.834 5.801 6.013 ku(G) /mS 0.103 0.487 0.412 0.380 0.319 0.620

ku(G) /% 1.8 8.3 6.5 6.5 5.5 10.3

2

G /mS 5.859 5.738 6.203 5.889 5.921 6.221 ku(G) /mS 0.143 0.143 0.388 0.307 0.275 0.389

ku(G) /% 2.4 2.5 6.3 5.2 4.7 6.3

3

G /mS 5.874 5.834 6.045 5.914 5.875 6.262 ku(G) /mS 0.113 0.342 0.398 0.362 0.309 0.343

ku(G) /% 1.9 5.9 6.6 6.1 5.3 5.5

4

G /mS 6.623 6.603 6.442 6.613 6.426 6.097 ku(G) /mS 0.189 0.437 0.393 0.449 0.395 0.640

ku(G) /% 2.9 6.6 6.1 6.8 6.1 10.5

5

G /mS 6.566 6.626 6.719 6.536 6.439 6.626 ku(G) /mS 0.186 0.219 0.331 0.375 0.332 0.362

ku(G) /% 2.8 3.3 4.9 5.7 5.2 5.5

6

G /mS 6.921 7.034 6.486 6.850 7.040 6.349 ku(G) /mS 0.244 0.510 0.494 0.499 0.489 0.687

ku(G) /% 3.5 7.3 7.6 7.3 6.9 10.8

7

G /mS 6.936 6.936 6.552 6.885 7.077 6.895 ku(G) /mS 0.266 0.232 0.419 0.409 0.409 0.391

ku(G) /% 3.8 3.3 6.4 5.9 5.8 5.7

8

G /mS 7.585 7.489 6.854 7.543 8.007 7.746 ku(G) /mS 0.528 0.359 0.645 0.606 0.588 0.554

ku(G) /% 7.0 4.8 9.4 8.0 7.3 7.2

With the transformed results, the differences di,k to the KCRVs ḠK3,i of CCAUV.U-K3 can now be calculated as

), = SK3,, − K3, (18)

with

,rel ), = SK3,, ∙ ,rel SK3,, + K3, ∙ ,rel K3, − 2 ∙ , SK3,, , K3,, (19)

where

, S_`,, , _`, = K3.1,,7K3.1, ∙ K3, ∙ ,rel SK3,, + K3,` ∙ ,rel K3, (20)

∙ ∑ (K3.1,,C(∙rel K3.1,,C(K3,,C(∙rel K3,,C ∙ a bC7K3.1, − K3.1,,∙rel 7K3.1, K3.1,,C∙rel K3.1,,Cc ∙ DE ,

δkl being 1 for k=l, and 0 otherwise. The results are listed in Table 19.


Figure 7a: Combined results (FPS 1 to FPS 4) of CCAUV.U-K3 and CCAUV.U-K3.1 after the linking procedure.

Full lines denote KCRV values of CCAUV.U-K3, and dashed lines their expanded uncertainty (k = 2); all error

bars denote expanded uncertainties (k=2) and outlying results of CCAUV.U-K3.1 are shaded.


Figure 7b: Combined results (FPS 5 to FPS 8) of CCAUV.U-K3 and CCAUV.U-K3.1 after the linking procedure.

Full lines denote KCRV values of CCAUV.U-K3, and dashed lines their expanded uncertainty (k = 2); all error

bars denote expanded uncertainties (k=2) and outlying results of CCAUV.U-K3.1 are shaded.


Table 19: Deviations d and their expanded uncertainties (k=2) of the transformed results from the KCRV of

CCAUV.U-K3 (*Due to the rounding to three digits, absolute values smaller than 5∙10-4 are denoted as 0).

Outlying results of CCAUV.U-K3.1 are shaded in grey.

Participant

FPS PTB INRIM NMIJ KRISS NPLI INMETRO

1 d /mS -0.008 0.061 0.546 0.051 0.018 0.230

ku(d) /mS 0* 0.007 0.046 0.004 0.001 0.044

2 d /mS 0.060 -0.061 0.404 0.090 0.122 0.422

ku(d) /mS 0.001 -0.001 0.030 0.004 0.005 0.032

3 d /mS 0.008 -0.032 0.179 0.048 0.009 0.396

ku(d) /mS 0* -0.003 0.020 0.005 0.001 0.041

4 d /mS 0.005 -0.015 -0.176 -0.005 -0.192 -0.521

ku(d) /mS 0* -0.001 -0.014 -0.001 -0.015 -0.107

5 d /mS -0.026 0.034 0.127 -0.056 -0.153 0.034

ku(d) /mS 0* 0.001 0.007 -0.004 -0.008 0.002

6 d /mS -0.033 0.080 -0.468 -0.104 0.086 -0.605

ku(d) /mS -0.001 0.010 -0.057 -0.013 0.010 -0.143

7 d /mS 0* 0* -0.384 -0.051 0.141 -0.041

ku(d) /mS 0* 0* -0.034 -0.004 0.012 -0.003

8 d /mS 0.058 -0.038 -0.673 0.016 0.480 0.219

ku(d) /mS 0.03 -0.017 -0.400 0.009 0.277 0.125


7 Conclusions

This key comparison is a subsidiary but independent follow-up of the CCAUV.U-K3 comparison on ultrasonic

power measurement. It should give the participants of this comparison with discrepant values the

possibility to renew their measurements. An ultrasonic transducer was circulated and ultrasonic power and

radiation conductance were determined. Linking the former comparison was prepared, which allows a

direct comparison with the results obtained.

References

[1] C. Koch und K.-V. Jenderka, "Report on Key Comparison CCAUV.U-K3.“, Metrologia 51, Tech. Suppl.

09001, 2014.

[2] CIPM, "Measurement comparisons in the CIPM MRA", CIPM MRA-D-05 (Version 1.5): Comité

International des Poids et Mesures, 2014.

[3] L. Nielsen, "Evaluation of measurement intercomparisons by the method of least squares", Technical

Report DFM-99-R39.: Danish Institute of Fundamental Metrology, 2000.

[4] M. G. Cox, "The evaluation of key comparison data: determining the largest consistent subset.“,

Metrologia 44, pp. 187-200, 2007.

[5] C. Elster, A. Link und W. Wöger, "Proposal for linking the results of CIPM and RMO key comparisons.“,

Metrologia 40, pp. 189-194, 2003.

[6] JCGM, "JCGM 100: Evaluation of measurement data - Guide to the expression of uncertainty in

measurement, First Edition“, Joint Committee for Guides in Metrology, Sèvres, F, 2008.

[7] JCGM, "JCGM 200: International vocabulary of metrology – basic and general concepts and associated

terms, 3rd Edition“, Joint Committee for Guides in Metrology, Sèvres, F, 2012.


Annex A: Description of the measurement setups of the participants

PTB For all measurements including the re-measurements, the PTB primary standard radiation force balance

setup was used.

The transducer was mounted at the bottom of the water tank (volume approx. 4.7 l) and the ultrasound

waves were radiated vertically upwards to the targets suspended from the balance (Mettler Toledo A250,

weighing capacity 51 g, readability 0.01 mg) by a thin wire. The setup corresponds to "Arrangement A"

according to IEC 61161. The tank was filled with deionised, degassed water and the water temperature was

monitored during all measurements. Avoiding air currents, the whole setup, including the balance, was

housed in an acrylic enclosure.

In total, three different types of absorbing targets (diameters 50 mm, 110 mm and 115 mm) were used: at

least two different targets for each frequency-power combination (the only exception was the high power

measurement). Each final value reported was the result of four independent measurements. The use of the

different targets depended on the applied frequency and power Ievel.

The excitation voltage of the transducers was generated by a signal generator R&S SMX and was amplified

by an rf power amplifier ENI 350L (ENI A-300 for the high power level measurements).

The voltage measurement directly at the transducer connecting port was carried out with thermal

converters (Ballantine 1394A) and additionally with an rms-level voltmeter (Racal-Dana 9303) fitted with a

high impedance x100 probe. The voltage was monitored by means of a standard oscilloscope.

The applied measurement cycles consisted of multiple on-periods, two for high power levels and three to

five for low power levels, embedded in off periods. The on-time lasted from 18 s to 36 s, and the off-time

from 30 s to 150 s, depending on the applied power. The measurement cycles, the balance readout and the

acquisition of the voltages were controlled by a PC.

The final results reported were obtained by linear, unweighted averaging of the independent

measurements. Each independent measurement was in fact a series of measurements at various, usually 9

or 15, target distances including subwavelength variations of λ/4, and the zero-distance value was obtained

by empirical extrapolation. On the whole, the distance from the transducer surface to the nearest target

point was between 1.4 mm and 39.5 mm. The water temperature was between 19.5 °C and 21.8 °C. The

oxygen content during the high power measurements was between 2.0 mg/l and 3.6 mg/l.

INRIM The device used for the ultrasonic power measurement is based on the radiation force balance method.

The ultrasonic power is determined from the measurement of the force exerted on a target by the sound

field generated by an ultrasonic source. The absorbing target is connected to a balance which measures the

force variation due to the ultrasonic field when the source is alternately switched on and off.

The balance used is a METTLER TOLEDO, mod. SAG 285, the water vessel is made of plexiglas and has a

volume equal to 3.13 l; the absorbing target is suspended in the vessel by means of nylon wires 0.06 mm

thick.

The force exerted on the target is transferred to the balance pan by a rigid carbon fibre castle mounted

externally to the vessel and put on the balance pan.

A thermal voltage converter (TVC) is used to measure the voltage effective value at the transducer input.

The driving voltage used for the measurements varies from 0 V to 50 V, and this range is covered by means

of 4 different TVCs: TVC 1: 0 V to 2 V; TVC 2: 2 V to 5 V; TVC 3: 5 V to 20 V; TVC 4: 20 V to 50 V. The value of

the ultrasonic power, P, and the frequency, f, for the transducer’s characterization, determine the input

voltage to be sent to the transducer and the TVC to be used.

NMIJ NMIJ carried out the measurements by using the primary standard of the radiation force balance system

based on IEC 61161. The transducer to be calibrated was attached at the bottom of a water vessel with a

diameter of 150 mm and a height of 90 mm. Ultrasonic waves were radiated vertically upwards from the

transducer to the absorbing target (Precision Acoustics, HAM A) with a diameter of 50 mm. The target was


suspended by a thin wire from an electric balance (Cahn, D-101) with a weighing capacity of 100 g and a

resolution of 0.001 mg.

The water temperature during the measurements was monitored by a thermistor thermometer (TECHNOL

SEVEN, D642) in conjunction with a sensor (TECHNOL SEVEN, SXK-67). The water temperature ranged from

21.1 °C to 21.9 °C. For the high power level, the dissolved oxygen level of water was measured by a

dissolved oxygen level meter (Iijima, ID-100). The dissolved oxygen level ranged from 2.0 mg/l to 2.3 mg/l.

The total measurement period depended on the power level: 265 s for the very low, low, and medium

power level, and 260 s for the high power level. The measurement period before ultrasound exposure was

30 s for all the power levels. Then the ultrasonic transducer was driven for a period of 25 s for the very low,

low, and medium power level, and 20 s for the high power level. The period of off-time after ultrasound

exposure was 210 s for all the levels. The change of the weight in the absorbing target was recorded during

the measurement period as the output voltage from the electric balance. The output voltage was measured

by a digital voltage meter (Hewlett Packard, 34420A).

The transducer was driven by a function generator (Agilent, 33250A) through a power amplifier (R&K,

CA010K010-5353R). The input voltage to the transducer was measured with a 50 Ω terminator (Tamagawa

Electronics, CT-50NP) and by an RMS/PEAK voltmeter (ROHDE&SCHWARZ, URE3).

KRISS

Measurements of transducer’s radiation conductance, i.e. the calibration of the transducer, were

conducted by the KRISS radiation force balance system designed to measure an applied voltage and an

acoustic radiation force simultaneously.

A target connected to the underfloor weighing electronic microbalance (Mettler Toledo, XP56, 50 g

capacity, 0.001 mg readability, traceable to mass standards in KRISS) with a 0.05 mm platinum wire and a

nano-voltmeter (Keithley 2182A) with properly selected voltage converters (Ballantine, 1394A series,

traceable to rf-voltage standards in KRISS) was mainly included in the system. Three different absorbing

targets were used: A 70-mm diameter NPL’s HAM-A target was mainly used for all the levels and

frequencies specified in the protocol; a wedged 50-mm diameter absorbing target (PTB manufactured) and

a wedged 52-mm diameter homemade absorbing target were used at high level only.

The water temperature and dissolved oxygen contents were measured by an ASA (Automatic Sigma) Lab

F250 thermometer and a Mettler Toledo SevenGoPro Do meter, respectively.

The transducer excitation was made by 3 periodic switches (on (10 s) and off (30 s)) of the rf signal for every

6 different target distances (5 mm, 5 mm + half wavelength, 10 mm, 10 mm + half wavelength, 15 mm +

half wavelength). The rf signal was generated by an Agilent E8663D analogue signal generator and

amplified by an ENI 3100LA power amplifier.

NPL-I At NPLI, during the last two years, continuous efforts have been made to improve, upgrade and fully

automate the primary standard of total ultrasonic power measurement. The system was improved in many

aspects and fully automated, except the automatic measurement of RF voltage in the full range of

frequency and amplitude being fed to the transducer.

The ultrasonic power of the transducer was measured by the Radiation Force Balance (RFB) principle as per

IEC61161 using a Mettler (model: XP-56) microbalance. The ultrasonic beam from the transducer mounted

at the bottom of a tank filled with degassed water was directed vertically upwards. The water container is

made of Perspex with its length, breadth, and height as 300 mm, 300mm, and 170 mm, respectively. The

absorbing target procured from Precision Acoustics with the dimensions 50 mm x 60 mm x10 mm is

suspended under the pan of the microbalance having a resolution of 1 μg. The separation between the

target and transducer was maintained by moving the tank filled with about 12 l of degassed water up or

down with the help of a micro-movement arrangement. The temperature of the tank water was

maintained close to 23 °C and the actual temperature was measured with an accuracy of ± 0.1 °C by an in-

house developed temperature monitor and data logger which uses a semiconductor sensor (LM 35).

The microbalance is connected to a personal computer via a serial (RS 232) port for continuous recording of

the balance output. The transducer was excited at the desired voltage and frequency using an Agilent

programmable function generator (model: 33250A). If required, a fixed gain (E&I, 50 dB) power amplifier

was used to amplify the function generator output.


The rms voltage fed to the transducer was measured by an NPLI developed dual peak-to-peak detector

module attached at the transducer node and the waveform was analyzed on a Tektronix TDS210 digital

oscilloscope. Continuous balance output was recorded before and during transducer excitation with the

help of control and automation software developed in LabVIEW. Repeated measurements were carried out

at three different transducer-target separations, such as 10 mm, 20 mm and 30 mm.

INMETRO

A radiation force balance method with an absorbing target was used. The transducer was positioned above

the target, facing downwards.

The balance was positioned above the water tank. A specially designed mounting apparatus was used to

keep the target in suspension below the balance. The transducer was positioned between the balance and

the target, facing downwards. The target positioning system has 5 degrees of freedom and a linear

resolution of 1 μm. The absorbing target was a 100 mm square-shaped plate 10 mm thick, composed of a

brownish rubber-like material, not commercially available, which has a surface with 5 mm pyramids.

The radiation force balance was a Sartorius CP224S with 0.1 mg resolution.

The voltage to drive the transducer was generated with a Tektronix Arbitrary Function Generator AFG 3252.

A power amplifier RF amplifier E&I 3200L was used to achieve the higher output voltages. The generator

frequency was measured with an Agilent 53131A Universal Counter, which had been calibrated in the

Brazilian National Laboratory for time and frequency quantities.

The voltage measurements were carried out using a Tektronix oscilloscope TDS 3032B. The oscilloscope

was internally calibrated with an Arbitrary Function Generator (Tektronix AFG 3252) which had been

calibrated in a primary national laboratory outside Brazil.

The measurement was carried out in a 250 mm × 250 mm × 220 mm acrylic water tank. The water

temperature was monitored with a Hygropalm 3 thermohygrometer with a calibrated PT-100 probe placed

inside the water, close enough to the propagation path region. Dissolved oxygen was monitored with an

oxygen meter Accumet model XL40. Degassed water was used for all measurements.

For each frequency and voltage amplitude, measurements were performed 4 times, keeping the same

repeatability conditions. The tank water was changed after every repetition, and all devices were

disassembled and assembled again for the next run.

Within a run, the transducer was placed at 3 different distances from the absorbing target (10 mm, 15 mm

and 20 mm). At each position, 2 measurements were performed, slightly moving the transducer ¼ of a

wavelength upwards. For all “Very Low”, “Low”, and “Medium” power outputs, the power was turned on

for 21 s and turned off for 18 s; this is referred to as a “reading”. For “High” output, the ON and OFF periods

were 12 s and 60 s, respectively. For each position, 5 readings were carried out and averaged, resulting in a

measurement result. The measurement results were averaged for each ¼ of a wavelength separation. That

averaging led to the measurement result for a given distance. The result of one run was obtained from the

linear regression applied to results for various distances, yielding the power result at the “zero” distance at

the transducer surface.

The power measurement result for each target was calculated by averaging the individual results of 4 runs.

An uncertainty due to the linear regression error was taken into consideration in the uncertainty budget.

The distances considered in this regression were 10 mm, 15 mm and 20 mm. In addition, the non-plane

field structure was considered in the uncertainty budget development.


Annex B: Measurement uncertainty budgets of the participants

B.1 Detailed descriptions of the uncertainty contributions by PTB

1.) Plane-wave assumption: This is a contribution of urect = 0.8 % for measurements in real acoustic fields

when plane-wave conditions are considered in the calculation of ultrasonic power. The uncertainty

contribution accounts for non-ideal behaviour according to long-term experience.

2.) Sound velocity: The sound velocity is calculated for each measurement from the measured

temperature. An uncertainty limit for the temperature measurement of ΔT = 1 K is assumed

(including thermometer calibration and possible temperature gradients), which yields urect = 0.2 % for

the sound velocity.

3.) Gravity: The uncertainty of the gravity is assumed to be negligible in comparison to all other

contributions: urect = 0.0 %

4.) Balance: This is an uncertainty contribution of urect = 0.7 % according to long-term experience. After

each measurement, this was checked by measuring the gravitational force of a calibrated mass under

conditions that were similar to the previous radiation force measurement (appropriate mass, same

temporal on-off sequence, suspended target). This contribution includes the following effects:

internal calibration factor of the balance, linearity and resolution of the balance, influence of the

target suspension, extrapolation to the moment of switching the ultrasound transducer.

5.) Extrapolation to d=0: This contribution is computed for each measurement as the standard

uncertainty of the logarithmic extrapolation P(deff→0) by a fieng procedure using an appropriate

number of single measurements at different distances. The values reported in the table are the

respective mean of the uncertainty contributions from representative repeated measurements.

6.) Non-ideal target behaviour: This is an uncertainty contribution of urect = 1.9 % for 0.75 MHz < f < 5

MHz; urect = 2.4 % for 5 MHz < f < 8 MHz; urect = 3.5 % for 8 MHz < f < 12 MHz; urect = 7.0 % for 12 MHz

< f < 18 MHz; urect = 10 % for 18 MHz < f < 21 MHz according to long-term experience. This

contribution includes non-ideal target properties, non-ideal target geometry and non-ideal alignment

of transducer and target.

7.) Finite target size: This is an uncertainty contribution of urect = 1.0 % for the finite size of the employed

absorbing targets. The employed targets were all larger by more than 50 % than the width

determined according to the formula given in A.5.3.1 of IEC 61161. It is thus reasonable to assume an

uncertainty contribution of 1 %.

8.) Voltage measurement: This is an uncertainty contribution of urect = 0.5 % for measurement of rms

voltages according to long-term experience of the uncertainty of thermal converter measurement.

For the calculation of the overall uncertainty, the values in the table have to be multiplied by 2 due

to the quadratic dependence of the radiation conductance G on the voltage U.

9.) Adapter influence: The measurement of the rms voltage requires the usage of an adapter at the

transducer input. The influence of this adapter is accounted for by an uncertainty contribution of urect

= 0.1 % for f = 6.7444 MHz; urect = 0.2 % for f = 11.3204 MHz; urect = 0.3 % for f = 15.8785 MHz. For f =

2.013 MHz, the influence is negligible. For the calculation of the overall uncertainty, the values in the

table have to be multiplied by 2 due to the quadratic dependence of the radiation conductance G on

the voltage U.

10.) Repeated measurements: For each of the frequency-power combinations, 4 independent single

measurements of the radiation conductance were performed. The values in the table are the

resulting standard uncertainties. This contribution accounts for possible misalignments,

environmental influences and other sources of uncertainties.

Overall uncertainty: This is the quadratic sum of the single standard uncertainty contributions (No. 7 and

No. 8 multiplied by 2) and hence the overall standard uncertainty of the radiation conductance G.

Expanded uncertainty: This is the overall standard uncertainty of the radiation conductance multiplied by

k = 2.


Table B1.1: PTB uncertainty contributions for key comparison CCAUV-K3.1

For every frequency-power combination the left column contains the width of the interval of a rectangular probability distribution and the right one the deduced

standard uncertainty. In cases where a Gaussian probability distribution applies, values are denoted in italics. Column ‘61161’ lists the respective paragraphs

A.7.XX of IEC 61161, 3rd Edition (2013). Frequency f / MHz 2.015 2.015 2.015 6.7513 6.7513 11.3318 11.3318 15.8942

Nominal input voltage Unom / V 1.25 13.5 50 1.2 4 1.25 4 3.7

No Uncertainty contribution 61161 Type urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ % urect / %

ust

/ %

1 Plane-wave assumption 14 B 0.8 0.46 0.8 0.46 0.8 0.46 0.8 0.46 0.8 0.46 0.8 0.46 0.8 0.46 0.8 0.46

2 Sound velocity 10 B 0.2 0.12 0.2 0.12 0.2 0.12 0.2 0.12 0.2 0.12 0.2 0.12 0.2 0.12 0.2 0.12

3 Gravity 15 B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

4 Balance 2,3,4,15 B 0.7 0.4 0.7 0.4 0.7 0.4 0.7 0.4 0.7 0.4 0.7 0.4 0.7 0.4 0.7 0.4

5 Extrapolation to d=0 10,11 A 0.68 0.28 0.15 1.42 0.56 1.59 0.59 0.97

6 Non-ideal target behaviour

5,8,9 B 1.9 1.1 1.9 1.1 1.9 1.1 2.4 1.39 2.4 1.39 3.5 2.02 3.5 2.02 7.0 4.04

7 Finite target size 13 A 1.0 0.58 1.0 0.58 1.0 0.58 1.0 0.58 1.0 0.58 1.0 0.58 1.0 0.58 1.0 0.58

8 Voltage measurement 16 B 0.5 0.29 0.5 0.29 0.5 0.29 0.5 0.29 0.5 0.29 0.5 0.29 0.5 0.29 0.5 0.29

9 Adapter influence 16 B 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.06 0.1 0.06 0.2 0.12 0.2 0.12 0.3 0.17

10 Repeated measurements 15,19 A 0.02 0.04 0.01 0.03 0.01 0.03 0.01 0.01

Overall uncertainty 1.6 1.5 1.5 2.2 1.8 2.8 2.4 4.3

Expanded uncertainty 3.2 3 3 4.4 3.6 5.5 4.7 8.6


B.2 Detailed descriptions of the uncertainty contributions by INRIM

In order to make it easier to connect the uncertainty budget reported in the following tables with the final

expanded uncertainty value Urel(G) associated with the measured ultrasonic conductance value

G = P/(Veff)2, a summary of the complete uncertainty calculation is reported.

The expanded uncertainty value is calculated as the standard uncertainty times the coverage factor kp.

Urel(G) = kp·ucrel(G); kp = 2 (B2.1)

The relative uncertainty of the ultrasonic conductance G is the sum of three main terms:

( ) ( ) ( ) ( )[ ]2

1222 GuGuGuGu SrelALLrelTARrelcrel ++= (B2.2)

• uTARrel(G) is due to the kind of target used in the power measurement;

• uALLrel(G) accounts for the effect of the imperfect target;

• uSrel(G) is the result of the uncertainty propagation on the final ultrasonic conductance value G. It is

calculated as the product of the ultrasonic conductance extrapolated at the transducer surface, G0, and a corrective factor due to the mathematical model for the ultrasonic beam propagation, KPLA.

Table B2.1, Table B2.2 and Table B2.3 show the uncertainty values for the measurement Number 1, f =

2.015 MHz, LEVEL: MEDIUM.

Table B2.1: INRIM uncertainty contributions for key comparison CCAUV-K3.1

N Contribution Description iX ix ixc ( )irel xu ( )irelx xuc

i

( )GU rel Extended uncertainty G 5.71 mS 2 1.55·10-2 3.10·10-2

( )Gucrel Combined uncertainty G 5.71 mS 1 1.55·10-2 1.55·10-2

1 ( )GuTARrel Target (TAR ) n.a. 1 1 0.5·10-2 0.5·10-2

2 ( )GuALLrel Alignment ( ALL ) n.a. 1 1 0.5·10-2 0.5·10-2

3 ( )GuSrel Experimental ( S ) G 5.71 mS 1 1.38·10-2 1.38·10-2

The uncertainty term, uSrel(G), is itself composed of three main contributions:

( ) ( ) ( ) ( )[ ]2

1

02

022 GuGuKuGu relBARrelPLArelSrel ++= (B2.3)

where:

urel(KPLA) is the relative uncertainty of the corrective factor, KPLA;

uBARrel(G0) is the term relative to the uncertainty in the definition of the acoustic “centre of mass”,

that is to say the level at which the radiation absorption or reflection really takes place. It is the point

at which the ultrasonic conductance is extrapolated;

urel(G0) reflects the uncertainty propagation in the calculation of the ultrasonic conductance.

Since the ultrasonic conductance is measured at different transducer-target distances and the

uncertainty of each of those values is calculated, it has been decided to choose the maximum of the

uncertainties as the reference value.

urel(G0) ≈ 1.1· MAX[ urel(de )] (B2.4)

This term is the most significant in determining the magnitude of uSrel(G).


Table B2.2: Uncertainty contributions to uSrel(G)

N Contribution Description iX ix ixc ( )irel xu ( )irelx xuc

i

uSrel(G) Experimental ( S ) G0 5.71 mS 1 1.38×10−2 1.38×10−2

1 uBARrel(G0) Unknown position n.a. 1 1 2105.0 −× 2105.0 −×

2 urel(KPLA) Plane wave approx. KPLA 1 1 2105.0 −× 2105.0 −×

3 urel(G0) Conductance at 0=z G0 5.71 mS 1 1.19×10−2 1.19×10−2

The conductance of the ultrasound transducer, G0, is determined by means of a linear regression algorithm

applied to the data couples (zeffi, Ḡi)i=1,2,…n; with zeffi defined from the equation zeffi = ∆z + zi, where

∆z = 6.7 mm is the distance between the target surface and the acoustic centre of mass and zi are the

transducer-target distances.

The final conductance value, G≡G0≡G(0), is extrapolated at zeff = 0 from the regression line equation:

G(zeff) = G0 + mzeff (B2.5)

The combined uncertainty, uSrel(G), associated with the value of G is calculated directly from the linear

regression algorithm:

uSrel(G) = MAX[ urel(Gi)] (B2.6)

where urel(Gi) is calculated propagating the uncertainties in the relation for the transducer ultrasonic

conductance for each sequence and distance:

= ,f ∙ g ∙ ^ h1ijkk l = ,f ∙ g ∙ ^Ω|o (B2.7)

The variables, affected by the uncertainty, which contribute to the final error on G0, are the water

temperature, T, the gravity acceleration, g, and the ratio, Ω=∆m/(Veff)2, between the apparent mass

variation, ∆m, and the voltage effective value, Veff.

For each transducer-target distance, the uncertainty relative to the ultrasonic conductance is connected to

the relative uncertainty of the former variables by the equation:

urel(Gi) = [cT

2·urel2(T) + urel

2(g) + urel2(Ω)]½ (B2.8)

where the main contribution is:

urel(Ω) = [uRrel2(Ω) + uSrel

2(Ω)] ½ (B2.9)

the value of urel(Ω), the uncertainty on the ratio Ω=∆m/(Veff)2. It is affected by two main terms: the

first one is due to the repeatability of the measures:

,pTqEΩ = r ∙ ∑ ΩR − ΩeR s (B2.10)

The second one is the effect of the propagation of the uncertainty in the evaluation of ∆m and Veff:

uSrel(Ω) = [urel2(∆m) + 4·urel

2(Veff)]½ (B2.11)


The uncertainty of the apparent mass variation, urel(∆m), is the sum of two terms, the first one

accounting for the uncertainty introduced by the analysis time, t (4 s ≤ t ≤ 10 s), uArel(∆m), and the

second one due to the balance calibration, uSrel(∆m):

urel(∆m) = [uArel2(∆m) + uSrel

2(∆m)]½ (B2.12)

And finally the uncertainty on the input voltage effective, urel(Veff), value results to be:

urel(Veff) = [uSrel2(Veff) + urel

2(Kf0)]½ (B2.13)

where the first term represents the uncertainty intrinsic to each voltage reading due to the

measurement process and the second one is the uncertainty due to the frequency dependent

response of the thermal converter used to measure the AC voltage effective value.

Table B2.3: Uncertainty contributions to uSrel(G)

N Contribution Description Xi xi ixc ( )irel xu ( )irelx xuci

uSrel(G) Conductance at z = 0

G0 5.71 mS 1 1.19·10-2 1.19·10-2

1 urel(T) Temperature T 20.2 °C 4.5·10-2 0.2·10-2 9.0·10-2

2 urel(g) Local gravimetry

acceleration g 9.80 ms-1 1 0.3·10-2 0.3·10-2

3 urel(Ω) Statistics link to

ratio Ω=∆m/(Veff)2

∆m/(Veff)2 39.2·10-2 mg/(Vrms)

2 1 5.0·10-2 5.0·10-2

4 uSrel(Ω)

Propagation of

ratio Ω=∆m/(Veff)2

∆m/(Veff)2

39.2·10-2 mg/(Vrms)2

1 1.1·10-2 1.1·10-2

5 urel(∆m) Mass variation ∆m 68.7 mg 1 1.0·10-2 1.0·10-2

6 urel(Veff) RMS voltage Veff 13.23 Vrms -2 2.1·10-2 4.2·10-2


B.3 Detailed descriptions of the uncertainty contributions by NMIJ

Table B3.1 shows the uncertainty budgets at NMIJ. The uncertainty budgets consist of two parts: the

ultrasonic power measurement part, and the applied voltage measurement part to the ultrasonic

transducer. The uncertainties in the ultrasonic power measurement and applied voltage measurement are

calculated separately. The uncertainties are calculated according to the BIPM/IEC/ISO Guide to the

expression of uncertainty in measurement. A more detailed breakdown of each uncertainty component is

given as follows:

u1: A 5 g weight with the traceability to national standards was used for the calibration of the electric

balance. The uncertainty component was calculated by the certificate of calibration for the weight.

u2: This was the uncertainty of the electrical conversion factor to calculate the mass from the output

voltage of the electric balance. The electrical conversion factor was measured from the difference

between output voltages from the electric balance before and after the addition of the 5 g weight.

u3: The uncertainty component showed the linearity of the electric balance. When 5 g to 15 g weights were

serially added to the electric balance, the output voltage from the electric balance was measured.

Then, the uncertainty component was investigated by the difference between the measured output

voltage values and the straight line derived from linear interpolation of actual measured values.

u4: The uncertainty component showed temperature stability and reproducibility of the electric balance.

The uncertainty was calculated from the specifications of the electric balance.

u5: The resolution of the electric balance was 0.001 mg. The uncertainty of the resolution of the electric

balance was calculated from the specifications.

u6: The ultrasonic standard transducer made by PTB was used in the key comparison. The uncertainty

component was calculated from the standard deviation of the measured ultrasonic power of the

ultrasonic transducer. In the case of 2.015 MHz, this represents 1.2% at “very low” level.

u7: Ultrasonic power was obtained by the difference between the extrapolated values of output voltage

from the electric balance before and after ultrasound exposure. The uncertainty was calculated by the

dispersion of the actual measured values from the straight line derived from linear interpolation.

u8: The uncertainty of DVM measuring the output voltage from the electric balance was calculated from

the certificate of calibration.

u9: The reflectance of the absorbing target increased with the frequency. The uncertainty component was

calculated as the 2% maximum acoustic pressure reflectance factor of the absorbing target at 20 MHz.

u10: When using a frequency greater than 2 MHz in the key comparison, the uncertainty was 0.06 % from

the characteristics of the transmission loss of the absorbing target.

u11: This was not relevant for the absorbing target.

u12: The uncertainty component was calculated from the difference between the measured values using

the absorbing target and the reflecting target. At 2.015 MHz, the uncertainty was 1.8 % at “very low”

level.

u13: The target size was calculated on the basis of the formula of IEC 61161. Assuming the worst-case

error, the uncertainty component was 1 % with the diameter of the absorbing target at 50 mm.

u14: The angle of slope of the ultrasonic transducer was assumed within 3 degrees. The uncertainty was

calculated with the cosine of this angle, because the ultrasonic power is proportional to the cosine of

the angle of the transducer to vertical.


u15: The speed of sound was calculated using the formula by Greenspan-Tschiegg. The uncertainty was

calculated using the formula and the certificate of calibration for the thermometer.

u16: The uncertainty component was calculated by the formula of attenuation by Pinkerton.

u17: Applied voltage to the ultrasonic transducer was measured by an RMS/PEAK voltmeter. The

uncertainty was calculated from the certificate of calibration for the voltmeter.

u18: The uncertainty component was calculated from the reflectance ration of the terminator. The

reflectance ratio was 0.13.

u19: The uncertainty component was calculated as the 77 dB/km transmission loss of the coaxial cable at

30 MHz. The type name of the coaxial cable was 3D-2V.


Table B3.1 Uncertainty budgets by the results of 4 independent measurement at NMIJ

Frequency (MHz) 2.015 6.7513 11.3318 15.8942 Ultrasonic power level very low medium high very low low very low low low Uncertainty on ultrasonic power measurement Weight calibration (%) u1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Conversion factor from mass to voltage (%) u2 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Linearity of electric balance system (%) u3 0.79 0.79 0.79 0.79 0.79 0.79 0.79 0.79 Stability of electric balance system (%) u4 0.09 0.00 0.00 0.01 0.00 0.09 0.00 0.09 Resolution of electric balance system (%) u5 0.04 0.00 0.00 0.04 0.00 0.00 0.00 0.00 Stability of typical ultrasonic transducer (%) u6 1.20 1.23 1.55 1.44 0.42 1.47 0.53 0.32 Extrapolation of signal from electric balance system (%) u7 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 Uncertainty of voltage meter (%) u8 0.24 0.00 0.00 0.24 0.00 0.02 0.00 0.02 Reflectance of absorbing target (%) u9 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 Transmittance of absorbing target (%) u10 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Absorbing target misalignment (%) u11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Absorbing target imperfection (%) u12 1.80 1.80 1.80 0.67 0.67 2.01 2.01 3.35 Finite absorbing target size (%) u13 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Ultrasonic transducer misalignment (%) u14 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 Water temperature and speed of sound (%) u15 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 Ultrasonic attenuation (%) u16 0.01 0.01 0.01 0.05 0.05 0.18 0.18 0.33 Combined standard uncertainty of ultrasonic power u(%) 2.53 2.53 2.70 2.05 1.51 2.81 2.45 3.62 Uncertainty of voltage measurement Uncertainty of voltage meter (%) u17 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 Terminator (%) u18 1.44 1.44 1.44 1.44 1.44 1.44 1.44 1.44 Coaxial cable (%) u19 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 Combined standard uncertainty of voltage u(%) 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 Combined standard uncertainty of radiation conductance u(%) 2.98 2.98 3.12 2.59 2.18 3.22 2.91 3.95 Expanded uncertainty of radiation conductance (k=2) U(%) 6.0 6.0 6.2 5.2 4.4 6.4 5.8 7.9


B.4 Detailed descriptions of the uncertainty contributions by KRISS

The expanded uncertainty U is obtained by multiplying the combined standard uncertainty uc(G) by a

coverage factor k :

t = V,G (B4.1)

The combined standard uncertainty for G can be determined by:

,G = u∑ vK,Qw (B4.2)

where Ni ,,1L= is the identification number of input quantities, i ic f q≡ ∂ ∂ is the sensitivity

coefficient, u(qi) is the standard uncertainties of the input quantity qi, and , ≡ |K|,Q is the standard

uncertainty of the radiation conductance, G, as given in Eq. (B4.1). The relative combined standard

uncertainty of the radiation conductance G can be written as:

= u∑ rGO s (B4.3)

Due to eq. (B4.2), the ultrasound power is determined by the balance indication readout (hereafter weight

change) with the mass unit corresponding to radiation force exerted on the target, gravitational

acceleration, sound speed in water, and correction factors, as:

= y ∙ K ∙ KL@ ∙ z ∙ (B4.4)

where F is the acoustic radiation force, c the sound speed, cor the correction factor for diffraction loss, x

the target distance and V the voltage.

y = |g (B4.5)

where m is the balance indication, g is the gravitational acceleration. The sound speed in water was

calculated using the following equation:

Kf, ~1 = M + M + M + M`` + v, + , + ,w × ~1 100⁄ (B4.6)

where

t = T/100, T: water temperature

patm: atmospheric pressure

v0 = 1402.7, v1 = 488, v2 = - 482, v3 = 135

u0 = 15.9, u1 = 2.8, u2 = 2.4

The correction factor for plane wave assumption was calculated by using the following equation in the IEC

61161 standard:

KL@ = 1 + .`~ 1 + .~ ⁄ (B4.7)

where k is the wave number and a is the radius of the transducer.

Hence the relative combined standard uncertainty in Eq. (B4.3) can be expressed as:

= u + GG + GHTGHT + + ii (B4.8)


The standard uncertainties in Table B4.1 and B4.2 are listed as:

- , = u∑ J√`

- , = u,T,J + ,T,Tq + ,T, is less than 0.51 %, where ,T,J. ≈ u∑ 1 − ⁄ for linearity

with target suspension, ,T,Tq for readability of balance, ,T, is for reference weights for balance

calibration.

- ,` ≤ 1.08% is estimated by maximum relative amplitude of the balance indication while varying the

target position with ultrasound sonication.

- , = u∑ , ≈ 1.62 where , = u∑ ,HHHH , ,HH = u , + , , and , ≈u∑ 1 − ⁄ .

- , < 1%, the target radius is sufficiently larger than the calculated minimum target radius

recommended by IEC 61161.

- , = ∞, ≈ %. = 1.0206 × 10 % is negligible

- , = K,T, where K = G NGN = I;I;I;¡;¢×£¤¥¦ ⁄ I§;I;I;I;v§;;w×£¤¥¦ ⁄ and ,T, = 0.5581%

- ,© = K©,T,£¤¥¦ K© = £¤¥¦G NGN£¤¥¦ = ¡§;;¢×£¤¥¦ ⁄ I§;I;I;I;v§;;w×£¤¥¦ ⁄ and ,T,£¤¥¦ = 1.7928%

- , = K ,T,~ where K = GHT NGHTN = −0.6531V ¬ − 0.6531 × 1.407V ®¬ ®, and ,T,~ = 0%

- , = K,T,, where K = ~GHT NGHTN~ = −0.6531V ¬ − 0.6531 × 1.407V ®¬ ® and ,T, = 0.1% (-60 dB harmonic distortion was assumed)

- , = u ~k¥;¯k¥ ~k¥¯k¥° , ≈ ,T, = u¡ ±1 − ± ⁄ ¢ ≈ 0.0012065 %

- , = K,T,, where K = ~k¥∙~k¥∙;¯k¥ and ,T, = b²

- ,` = u∑ i J³√`

- , = ´µ b³i¶¤·j√¸ = u¹º√ = 2.89 × 10 %

- , = u ,T» + ,T¶k¹· + ,i¼¹½¾¥

- , = u,ie¼¹½¾¥ + 10 √12⁄ + ,i¼ + ,i·


Table B4.1. Detailed uncertainty budget of 2.015 MHz frequency.

Frequency /MHz 2.0150

Nominal Power /W 0.01 1 15

Element of uncertainty Symbol u(xi) /% ci uc(xi) / % u(xi) /% ci uc(xi) / % u(xi) /% ci uc(xi) / %

acoustic radiation force u(F) 1 2.78 1 2.18 1 2.62

reproducibility u1 2.30 1 2.30 1.40 1 1.40 1.88 1 1.88

balance system u2 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51

standing wave u3 1.08 1 1.08 1.08 1 1.08 1.08 1 1.08

switching effect u4 0.01 1 0.01 0.61 1 0.61 0.96 1 0.96

finite target size u5 1.00 1 1.00 1.00 1 1.00 1.00 1 1.00

gravitational acceleration u6 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5

sound speed in water u(C) 1 0.56 1 0.56 1 0.56

water temperature u7 0.56 0.9988 0.56 0.56 0.9988 0.56 0.56 0.9988 0.56

atmospheric pressure u8 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4

diffraction loss correction u(Cor) 1 8.79E-4 1 8.79E-4 1 8.80E-4

radius of element u9 - -0.0088 - - -0.0088 - - -0.0088 -

wave number u10 0.10 -0.0088 -8.79E-4 0.10 -0.0088 -8.79E-4 0.10 -0.0088 -8.80E-4

target distance u(x) 1 6.45E-2 1 3.86E-4 1 5.07E-2

extrapolation to zero u11 6.45E-2 1 6.45E-2 3.71E-4 1 3.71E-4 5.07E-2 1 5.07E-2

target distance u12 1.27E-3 1 1.27E-3 1.06E-4 1 1.06E-4 2.63E-4 1 2.63E-4

excitation voltage u(V) 2 0.51 2 0.51 2 0.51

reproducibility u13 0.00 1 0.00 0.00 1 0.00 0.01 1 0.01

voltmeter resolution u14 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6

corr. factor of TVC u15 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51

voltage standard u16 5.10E-3 1 0.01 5.10E-3 1 0.01 5.10E-3 1 0.01

combined uncertainty uc(G) / % 3.01 2.47 2.87

expanded uncertainty U (k=2, CL ~95 %) 6.0 4.9 5.7


Table B4.2. Detailed uncertainty budget of 6.7513 MHz, 11.3318 MHz and 15.8942 MHz frequencies.

Frequency /MHz 6.7513 11.3318 15.8942

Nom. Power /W 0.01 0.1 0.01 0.1 0.1

Symbol u(xi) /% Ci uc(xi) / % u(xi) /% ci uc(xi) /

%

u(xi)

/% ci

uc(xi) /

%

u(xi)

/% ci

uc(xi) /

%

u(xi)

/% ci

uc(xi) /

%

u(F) 1 2.78 1 2.38 1 2.78 1 2.38 1 2.86 u1 2.30 1 2.30 1.80 1 1.80 2.30 1 2.30 1.80 1 1.80 2.40 1 2.40 u2 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 u3 1.08 1 1.08 1.08 1 1.08 1.08 1 1.08 1.08 1 1.08 1.08 1 1.08 u4 0.01 1 0.01 0.08 1 0.08 0.02 1 0.02 0.05 1 0.05 0.08 1 0.08 u5 1.00 1 1.00 1.00 1 1.00 1.00 1 1.00 1.00 1 1.00 1.00 1 1.00 u6 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5 5.21E-5 1 5.21E-5 u(C) 1 0.56 1 0.56 1 0.56 1 0.56 1 0.56 u7 0.56 0.9988 0.56 0.56 0.9988 0.56 0.56 0.9988 0.56 0.56 0.9988 0.56 0.56 0.9988 0.56 u8 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4 1.79 0.0001 1.79E-4 u(Cor) 1 2.46E-4 1 2.46E-4 1 1.44E-4 1 1.44E-4 1 1.02E-4 u9 - -0.0025 - - - - - - - - - - - - - u10 -0.0025 -2.46E-4 0.10 - -2.46E-4 - -1.44E-4 - -1.44E-4 - -1.02E-4 u(x) 1 7.80E-3 1 2.40E-3 1 1.38E-1 1 5.33E-3 1 6.18E-3 u11 7.78E-3 1 7.78E-3 2.20E-3 1 2.20E-3 1.38E-1 1 1.38E-1 4.48E-3 1 4.48E-3 9.26E-4 1 9.26E-4 u12 5.88E-4 1 5.88E-4 9.55E-4 1 9.55E-4 3.15E-3 1 3.15E-3 2.90E-3 1 2.90E-3 6.11E-3 1 6.11E-3 u(V) 2 0.51 2 0.51 2 0.51 2 0.51 2 0.51 u13 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 0.00 1 0.00 u14 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6 2.89E-6 1 2.89E-6 u15 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 0.51 1 0.51 u16 5.10E-3 1 0.01 5.10E-3 1 0.01 5.10E-3 1 0.01 5.10E-3 1 0.01 5.10E-3 1 0.01 uc(G) / % 3.01 2.65 3.01 2.65 3.09 U (k=2, CL ~ 95

%) 6.0 5.3 6.0 5.3 6.2


B.5 Detailed descriptions of the uncertainty contributions for NPL-I

Type ‘A’ evaluation (Ua)

This uncertainty is estimated for each set of measurements. It may be stipulated that ± 0.14 mW at 10 mW

is the maximum uncertainty.

Ua = 1.4%

Type ‘B’ evaluation

The total power is calculated using the following formula:

P= mgc

The radiation conductance is given by the following formula:

G= P/V2

1. Uncertainty due to water temperature.(U1)

Sound velocity at 22°C: 1488.3 m/s

Possible change in temperature: 0.2 °C

Uncertainty due to change in temperature: 0.6 m/s

Uncertainty due to c:

0004.03.1488

6.0 ===

c

dc

P

dP

c

(= 0.04 %)

2. Uncertainty due to acceleration due to gravity g (U2)

The value of g and the associated uncertainty have been taken from the measurements done by

National Geophysical Research Institute, Hyderabad at various locations at NPL-I in 2009. The value

nearest to the Ultrasonic Laboratory is given as follows:

gc = 9.79124 ms-2

Uncertainty due to measurement of gm = 5 µGal = 0.05∙10-6 ms-2

Total uncertainty due to g: U2 = 0.05001 x 10-6 ms-2 (= 5∙10-6 %)

3. Uncertainty due to target size (U3)

The scope of the present measurement is restricted to ka > 30, The absorber target is 50 mm by 60 mm

and hence remains at least 1.5 times greater than the transducer diameter. The uncertainty in

measurement due to the finite size of the target in this case is 1 %. This is assuming that only 98 % of the

radiation force exists if the target were of infinite cross-sectional size.

U3 = 1 %

4. Uncertainty due to target properties(U4) The target is assumed to be a 100 % absorber. Hence uncertainty due to this factor is zero.

5. Uncertainty due to misalignment(U5)

Since the absorber target has been used, the uncertainty due to this factor is zero.

6. Uncertainty due to balance readout (U6)

The uncertainty due to the balance readout is 12 µg. The percentage of uncertainty will be different for

different ranges as given below.

For 10 mW, uncertainty U6 = 1.8 %


For 1 W, uncertainty U6 = 0.018 %

7. Uncertainty due to non-linearity of balance (U7)

Linearity 2 µg in the range of 0.5 mg to 100 mg. This will give the uncertainty in percentage as follows:






8. Uncertainty due to plane wave approximation (U8)

The estimation of this uncertainty is based on the assumption of a rectangular distribution extending

from plane value to the value corrected for non-plane. The maximum value constitutes the lowest

frequency used, that is, 2 MHz. It is given by 0.004391 for ka=80.

The uncertainty has been estimated as U8 = 0.44 %

9. Uncertainty due to attenuation and acoustic streaming: (U9)

Since the value of power measured at a distance has been corrected for attenuation using the

exponential formula given by Eq (7), the uncertainty has been estimated as half of the difference

between the uncorrected power value and the value with full attenuation correction. The corrected

power Pc is derived from the measured power Pm using the following expression:

±G = ±1¿∝ (B5.1)

The uncertainty is given by the following expression:

t = °¦q∝² °¦ (B5.2)

The percentage uncertainty is given by the following expression:

%t = °¦q∝² °¦° . 100 (B5.3)

or

%t = °¦q∝² °¦°¦q∝² . 100 (B5.4)

or

%t = 501 − ¿ ∝ (B5.5)

Using the value of the attenuation coefficient for water as α=0.023 ν2 MHz-2m-1, the percentage

uncertainty was evaluated for various distances at different frequencies. These values are tabulated

below.

Table B5.1. Relative uncertainty U9 due to attenuation and acoustic streaming for different distances and

frequencies.

Distance

d /mm

2 MHz 6.7 MHz 11.3 MHz 15.9 MHz

10 0.045978846 0.513579162 1.447081538 2.824404923

20 0.091915412 1.021883054 2.852282177 5.489264582

30 0.137809735 1.524965859 4.216814018 8.003591386

40 0.183661855 2.022881208 5.541854082 10.37588865

A graph is plotted between distance and uncertainty for various frequencies as shown in Fig. B5.1. All

the curves are nearly straight lines. The equation of the best fitted straight line is written for each

frequency. The intercept of each equation at x=0 yields the percentage uncertainty. These values are

given in Table B5.2. The highest uncertainty in this is at 15.6 MHz and is considered to be ± 0.381

Table B5.2. Relative uncertainty U9 due to attenuation and acoustic streaming at d=0 for different

frequencies.

Frequency

f /MHz

% Uncertainty

2 0.000

6.7 0.013

11.3 0.102

15.9 0.381


Fig. B5.1 Uncertainty as a function of distance from transducer for various frequencies

10. Uncertainty due to voltage measurement: (U10)

U10 = 2 %

11. Uncertainty due to frequency measurement: (U11)

1 in 10-5

Distribution: Normal

Standard Uncertainty: 0.00001

Combined Standard Uncertainty:

√(Ua2+∑Un

2)

The values of the individual uncertainties have been used to estimate the combined standard uncertainty.

The entire uncertainty budget is described in the following Table B5.3.

Using the highest uncertainty value and rounding it off, the combined uncertainty is 2.75 %

Expanded Uncertainty at 95.45 % confidence level, i. e. k = 2:

2.75 % ∙ 2 ≈ 5.5 %

0

2

4

6

8

10

12

0 10 20 30 40

Un

cert

ain

ty (

%)

Distance from transducer (mm)

Uncertainty due to attenuation

correction2 MHz

6.7

MHz


Table B5.3: Uncertainty budget for measurement of total ultrasonic power by microbalance method

using absorber

S.No. Source of

uncertainty

Probability

distribution

factor/ divisor

Standard

Uncertainty

%

Sensitivity

coefficient

Ci

Uncertainty

contribution

%

Degree

of

freedom

1 Standard

deviation

Type A

Normal/ √4

1.4a 1.4 16

2 Temperature Type B

Rectangular/

√3

0.04 1 0.0231 ∞

3 Gravity g Type B

Rectangular/

√3

0.000005 1 0.000003 ∞

4 Target size Type B

Rectangular/

√3

1 1 0.557 ∞

5 Target properties Type B

Rectangular/

√3

0 1 0 ∞

6 Misalignment Type B

Rectangular/

√3

0 1 0 ∞

7 Balance readout Type B

Rectangular/

√3

1.8b 1 1.04 ∞

8 Balance non-

linearity

Type B

Rectangular/

√3

0.3b 1 0.17 ∞

9 Plane wave

approximation

Type B

Rectangular/

√3

0.44 1 0.25 ∞

10 Attenuation and

streaming

Type B

Rectangular/

√3

0.38c 1 0.22 ∞

11 Voltage

measurement

Type B

Normal/ 2

2 2 2 ∞

12 Frequency

measurement

Type B

Normal/ 2

0.001 1 0.0005 ∞

13 Combined

Standard

Uncertainty

2.737

14 Expanded

Uncertainty k=2

5.5

(rounded

off)

a This is only an example. It is evaluated for each case. b This is only an example and has been calculated for minimum power, that is, 10 mW. c This value is estimated for 15 MHz which is the highest. At other frequencies, it will be smaller.


B.6 Detailed descriptions of the uncertainty contributions for INMETRO

The radiation conductance G and the power output P are related to each other through the input driven

voltage V applied to the transducer under calibration according to Eq. B6.1:

2

[S]P

GV

= (B6.1)

The output power is derived from the radiation force measured with a balance and an absorbing target and

the sound velocity in water according to Eq. B6.2:

( ) [W]P c F c T m g= ⋅ = ⋅ ⋅ (B6.2)

The uncertainty for G is

( ) ( )2 2 2 2

2 2

2 3

12G P V G A P V G A

G G Pu u u u u u u

P V V V− −∂ ∂ = ⋅ + ⋅ + = ⋅ + − ⋅ + ∂ ∂

(B6.3)

where G Au − is the type A uncertainty for G and Vu is the uncertainty for the voltage measurement,

defined in 4.

( ) ( ) ( )2 2 2

V V cal V res V linu u u u− − −= + + (B6.4)

The uncertainty for P is

( )

( ) ( ) ( ) ( )

22 22

22 2 2

P c m g P A

c m g P A

P P Pu u u u u

c m g

mg u cg u cm u u

−

−

∂ ∂ ∂ = ⋅ + ⋅ + ⋅ + = ∂ ∂ ∂

= ⋅ + ⋅ + ⋅ +

(B6.5)

where P Au − is the type A uncertainty for P and

2 -11404.3 4.7 0.04 [m s ]c T T= + ⋅ − ⋅ ⋅ (B6.6)

Disclosing uncertainty equations for P :

( ) ( ) ( )2 22

c c md c temp c posu u u u− − −= + + (B6.7)

( ) ( ) ( ) ( ) ( ) ( ) ( )2 22 2 2 2 2

m m cal m lin m res m reg t imp t misal t sizeu u u u u u u u− − − − − − −= + + + + + + (B6.8)

( ) ( ) ( )2 2 2

g g val g res g posu u u u− − −= + + (B6.9)


Table B6.1: Applied uncertainty contributions for INMETRO.

2.5%1.0% [V]

vv V res

V cal V cal

uu u V

n

Vn

−− −

= + ⋅ =

= + ⋅

→ uncertainty for voltage measurement due to calibration and

rms calculation, where 1.0 % is the typical voltage uncertainty due

to calibration, n is the number of points used to calculate rms

value (typically 500n = ) and 2.5 % is the maximum oscilloscope

uncertainty in the worst case (frequency and amplitude ranges

under consideration);

0.1% [V]vV res V resu u V V− −= ⋅ = ⋅ → uncertainty for voltage measurement due to resolution;

0.1% [V]vV lin V linu u V V− −= ⋅ = ⋅ → uncertainty for voltage measurement due to oscilloscope

linearity in the worst case (frequency and amplitude ranges under

consideration); -10.1% [m s ]v

c md c mdu u c c− −= ⋅ = ⋅ ⋅ → uncertainty for sound velocity calculation due to model used;

-10.5% [m s ]vc temp c tempu u c c− −= ⋅ = ⋅ ⋅ → uncertainty for sound velocity calculamon due to imperfect

temperature measurement; -10.5% [m s ]v

c pos c posu u c c− −= ⋅ = ⋅ ⋅ → uncertainty for sound velocity calculamon due to inappropriate

position of temperature sensor;

0.1% [kg]vm cal m calu u m m− −= ⋅ = ⋅ → uncertainty for mass measurement due to balance calibramon;

0.1% [kg]vm lin m linu u m m− −= ⋅ = ⋅ → uncertainty for mass measurement due to balance linearity;

710 [kg] 0.029 [mg]

2 3 2 3

vm res

m res

uu

−−

− = = ≅⋅ ⋅

→ uncertainty for mass measurement due to balance resolution;

m regu − → uncertainty for mass measurement due to regression of mass

measurement, calculated for every regression (typically 910 [kg] 0.001 [mg]m regu −

− < = );

0.5% [kg]vt imp t impu u m m− −= ⋅ = ⋅ → uncertainty for mass measurement due to target imperfections

(absorption etc);

0.5% [kg]vt misal t misalu u m m− −= ⋅ = ⋅ → uncertainty for mass measurement due to target and

transducer misalignments;

0.5% [kg]vt size t sizeu u m m− −= ⋅ = ⋅ → uncertainty for mass measurement due to target finite size;

-20.001% [m s ]vg val g valu u g g− −= ⋅ = ⋅ ⋅ → uncertainty for gravity acceleramon value due to calibramon

(value determined for the Mass Laboratory); -20.01% [m s ]v

g res g resu u g g− −= ⋅ = ⋅ ⋅ → uncertainty for gravity acceleramon value due to resolumon;

-20.01% [m s ]vg pos g posu u g g− −= ⋅ = ⋅ ⋅ → uncertainty for gravity acceleramon value due to the position of

the measurement system, as it is not in the Mass laboratory;

For each measurement at a determined distance and a determined ¼ wavelength position, equations B6.3

and B6.5 are to be used to assess G and P uncertainties. Within a repetition, the standard deviation of P

for different distances yields type A uncertainty P Au − . For different repetitions, the standard deviation of

P for different distances yields type A uncertainty P Au − , and the standard deviation of G discloses the

type A uncertainty G Au − value. The effective number of degrees of freedom is calculated to define the

coverage factor for a coverage probability of 95 %.

The present procedure consists of measurements at 3 different distances from the transducer to the

absorbing target (typically 10 mm, 15 mm and 20 mm) and 2 positions ¼ wavelength apart at each distance.

The whole procedure is repeated 4 times in repeatability conditions.

The uncertainty calculations, as well as the measurements, are fully automated using LabVIEW (National

Instruments), and a screenshot of the input variables as described above is shown below.


Documents

Final Report on Key Comparison CCAUV.U-K3.1