Details of dielectric parameter test methods are given in Annex J, and uncertainty estimation methods are given in 7.2.6.5.
In accordance with usual metrological practices, the measurement uncertainty for each of the dielectric parameters is required to be less than or equal to the allowable variations (see 6.2.1) from the target values of the measured dielectric parameters.
7.2.6.2 Liquid density
The electromagnetic parameters of the tissue-equivalent liquids are assumed to have a density of 1 000 kg/m3. This density shall be used for SAR evaluations. For the calculation of the SAR from the E-field distribution measured by the dosimetric probe, the liquid density is merely a numerical parameter which is not related to the actual density of the liquid.
Therefore, no uncertainty need be associated with it.
7.2.6.3 Liquid conductivity uncertainty
The uncertainty due to the liquid conductivity arises from two different sources. The first source of uncertainty is the allowable tolerance from the target value in Table A.3 and the second source of uncertainty arises from the measurement procedures used to assess conductivity. The uncertainty shall be estimated using a normal probability. See 6.2.1 for applicable tolerances and corrections of the liquid dielectrics. Formula (41) shall be used to correct the measured SAR for the deviations in conductivity.
7.2.6.4 Liquid permittivity uncertainty
The uncertainty due to the relative liquid permittivity arises from two different sources. The first source of uncertainty is the deviation from the target value given in Table A.3 and the second source of uncertainty arises from the measurement procedures used to assess relative permittivity. The uncertainty shall be estimated using a normal probability. See 6.2.1 for applicable tolerances and corrections of the liquid dielectrics. Formula (41) shall be used to correct the measured SAR for the deviations in permittivity.
7.2.6.5 Assessment of dielectric liquid parameter measurement uncertainties
The measurement procedures described in Annex J use vector network analysers for dielectric property measurements. Network analysers require calibration in order to account for and remove inherent losses and reflections. The uncertainty budget for dielectric measurement derives from inaccuracies in the calibration data, analyser drift, and random errors. Other sources of errors are the uncertainties of the sample holder hardware, and deviations from the optimal dimensions for the specified frequencies, and sample properties.
This applies regardless of the type of sample holder and the nature of the scattering parameters being measured. Uncertainties due to the straight-line fit in the slotted-line method can be evaluated using a least-squares analysis [141].
An example uncertainty template is shown in Table 5. All influence quantities may or may not apply to a specific test set-up or procedure, and other components not listed may be relevant in some test set-ups. Measurement of well-characterized reference liquids can be used to estimate the dielectric property measurement uncertainty [37], [71], [106], [122], as described in the following procedure.
a) Configure and calibrate the network analyser in a frequency span large enough around the centre frequency of interest, of the liquid used in the SAR measurement.
b) Measure a reference material.
c) Repeat Steps a) and b) at least n times (where n is at least three and is sufficient such that the measurements have stabilized. n should be large enough to keep the repeatability in Step d) within the applicable tolerances as specified in 6.2.1 at all frequencies of interest. Make the measurements at the same liquid temperature at which the dielectric target properties of the reference liquids are known. At each frequency, perform Steps d) to g).
d) Calculate the repeatability as the sample standard deviation divided by the mean value.
For the permittivity, this is given by Formula (37):
[ ] ∑ ( )
=
− ′
− ′
× ′
= n
i i
ity n repeatabil
1 r 2 r
r 11
100 1
% ε ε
ε (37)
where the mean value is defined in Formula (38):
∑=
= ′
′ n
i i
n 1 r
r 1 ε
ε (38)
Do the same for the conductivity.
e) Enter the repeatability in Row 1, Column a, of Table 5. The number of degrees of freedom 1
−
=n
νi is entered in Column e. Determine the deviation of the dielectric parameters from the target values εrrefand σref. For the permittivity, this is given by Formula (39):
[ ]
ref ref r
r 100 r
% ε
ε ε
′
− ′
× ′
deviation = (39)
f) Enter the deviation in Row 2, Column a, of Table 5. The number of degrees of freedom 1
−
=n
νi is entered in Column e. Do the same for the conductivity.
g) Estimate the Type B uncertainties for the other components of Table 5 (and other relevant components if needed) in the frequency range under consideration.
h) Determine the combined standard uncertainty as the RSS of the uncertainty components from Steps d), e), and f). Enter this value in Row 5, Column d of Table 5.
i) For the relative permittivity, choose the frequency that gives the largest value for the combined standard uncertainty in Step g). Enter this uncertainty and the corresponding degrees of freedom νi into the appropriate row of Table 11, Table 12 and Table 13. Do the same for the conductivity.
Table 5 – Example uncertainty template and example numerical values for dielectric constant (εr′) and conductivity (σ) measurement
a b c d e
ui = (a/b) × (c) Uncertainty
component Uncertainty
(± %) Probability
distribution Divisor ci Standard
uncertainty
(± %) νi or νeff 1 Repeatability of εr′ or σ
(N repeats)
5,2 N 1 1 5,2 4
2 Deviation from reference liquid target
εr′ or σ 3,0 R √3 1 1,73 4
3 Network analyser-drift,
linearity, etc. 0,5 R √3 1 0,29 ∞
4 Test-port cable
variations 0,5 U √2 1 0,35 ∞
5 Combined standard
uncertainty 5,50 5
NOTE Row headings 1 to 5 and column headings a to e are for reference.
In Table 11, Table 12 and Table 13, the sensitivity coefficients ci in Columns f and g for the measurement uncertainties of the conductivity and permittivity of tissue-equivalent liquids are needed. These sensitivity coefficients are cσ for conductivity and cε for permittivity. They are calculated using Formula (42) to Formula (45). The largest sensitivity coefficients over the 300 MHz to 6 000 MHz frequency range were found to be cσ = 0.78 (at 300 MHz) and cε = 0,23 (at 2 000 MHz) for 1 g averaging, and cσ = 0,71 (at 300 MHz) and cε = 0,26 (at 5 500 MHz) for 10 g averaging. These maximum values are entered into Table 11, Table 12 and Table 13. Alternatively, maximum values for specific tested frequency ranges may be entered.
7.2.6.6 Liquid temperature uncertainty
The measurements of both SAR and tissue dielectric parameters shall be carried out at an ambient temperature between 18 °C and 25 °C inclusive. These two measured temperatures shall not differ by more than 2 °C. The following evaluation shall be conducted for each recipe to determine the uncertainty caused by the temperature tolerance. This evaluation is typically done only once per recipe at the frequencies of interest. This evaluation shall be performed for every new recipe or modification to a recipe.
Measurements of the dielectric parameters at liquid temperatures Tlow = 18 °C and Thigh = 25 °C shall be used to compute temperature uncertainty according to the Formulas (40). The conditions that apply here only concern the evaluation of the liquid temperature uncertainty and do not affect the temperature requirements during testing.
[ ]
[ ]
low high low
high
low y high
uncertaint e
temperatur liquid
low high low
r high r
low r high y r
uncertaint e
temperatur liquid
C 2 2
100 [%]
C 2 2
100 [%]
T T ) σ(T ) σ(T
) σ(T ) σ σ(T
T T ) (T ε ) (T ε
) (T ε ) (T ε ε
−
× ° +
−
× ×
=
−
× ° +
−
× ×
=
(40)
where
y uncertaint e temperatur liquid
ε is the temperature uncertainty for the liquid permittivity in percent;
y uncertaint e temperatur liquid
σ is the temperature uncertainty for the liquid conductivity in percent;
εr(Thigh) is the relative permittivity at temperature Thigh; εr(Tlow) is the relative permittivity at temperature Tlow; σ(Thigh) is the conductivity at temperature Thigh; σ(Tlow) is the conductivity at temperature Tlow;
Thigh is the highest temperature in °C at which the dielectric parameters were measured;
Tlow is the lowest temperature in °C at which the dielectric parameters were measured.
These formulas can be used to derive the temperature uncertainty for the particular liquid.
The uncertainty of the measurements for Tlow and Thigh shall be less than 0,1 °C. Note that this tolerance is applicable only for this uncertainty evaluation. They do not affect the temperature requirements during testing.
The values of εliquidtemperatureuncertainty and σliquidtemperatureuncertaintyare entered into Column c of the appropriate rows in Table 11, Table 12 and Table 13. Calculated values for some recipes are provided in Annex I. A rectangular probability distribution has been assumed for the liquid temperature uncertainty in Table 11, Table 12 and Table 13.