B.3 Assessment of the sensitivity of the dipole sensors
B.3.2 Two-step calibration procedures
The total field shall be evaluated according to Formula (B.1).
The separation of the probe sensitivity into two factors (ηi and γi) allows the use of certain standardized free-space probe calibration procedures and provides additional validation of the probe performance and calibration set-up.
B.3.2.2 Sensitivity in air (first step)
The most accurate set-ups used for the generation of well-defined fields to simulate free- space conditions for use in probe calibration are waveguides. The reasons are as follows:
• waveguide set-ups require moderate power and less space than far-field calibration set- ups;
• generation of the most accurate fields traceable to power readings is possible;
• the uncertainty produced by the field disturbance due to the probe insertion is negligible for small near-field probes when the waveguide dimensions are considerably larger than probe dimensions;
• the set-ups allow easy access for orienting the probe axis normal or parallel to the field polarization inside the set-up;
• in addition, cross validation of the general field strengths is possible by using a set of waveguides with overlapping frequency ranges.
At lower frequencies (e.g. below 750 MHz), TEM cells can be employed instead. However, the field inside a TEM cell is less well-defined, i.e. there is rather large deviation from the predicted homogeneous field distribution [116].
The probe is generally inserted through small holes in the walls of the TEM cell and positioned at the centre (above or below the septum) where the field is mostly homogeneous over the probe dimensions. Each sensor is evaluated with respect to the field component parallel to the sensor.
As long as the resistive line does not load the dipole-diode sensor and the probe is small compared to the wavelength, the sensitivity in free-space is independent of the frequency.
This gives an additional validation of the calibration set-ups, and checks for possible field perturbations due to the probe. Effects due to probe insertion are typically negligible, if high- quality waveguide couplers and matched sources are used. An additional uncertainty source in the waveguide set-ups is due to reflections from the terminating load, which can result in a standing wave pattern within the set-up. Reflections can be kept below 1 % if high-quality waveguide loads are used. Furthermore, the uncertainty can be compensated for by performing supplementary measurements with a l/4-shifted load and averaging of two readings.
B.3.2.3 Sensitivity in media (second step) B.3.2.3.1 General
The sensitivity in liquid is determined by generating locally-known field values inside the media. Two methods can be used:
a) transfer calibration with temperature probe;
b) calibration with analytical fields.
B.3.2.3.2 Transfer calibration with temperature probes
In lossy liquids SAR is related both to the electric field (E) and the rate of temperature rise (dT/dt) in the liquid having specific heat capacity ch. Hence, based on the relation
h 0 2
d d
=
=
=
t t
c T SAR E
σ ρ (B.4)
the electric field in lossy liquid can be measured indirectly by measuring the rate of temperature rise in the liquid. Non-perturbing temperature probes (optical probes or thermistor probes with resistive lines) with small sensors (< 2 mm) and fast response time (< 1 s) are available and can be easily calibrated with high precision [84]. The set-up and the exciting source have no influence on the calibration; only the relative positioning uncertainties of the temperature probe and the E-field probe to be calibrated shall be considered. However, several problems limit the available accuracy of probe calibrations with temperature probes.
• The rate of temperature rise is not directly measurable but shall be evaluated from temperature measurements performed over a short time duration. Special precaution is
necessary to avoid measurement uncertainties caused by temperature gradients due to energy equalizing effects or convection currents in the liquid. Such effects cannot be completely avoided. With a careful set-up these uncertainties can be kept small.
• The measured volume around the temperature probe is not well defined. It is difficult to calculate the energy transfer into the probe from a surrounding gradient temperature field into the probe (typically, temperature probes are calibrated in liquid with homogeneous temperatures). There is no traceable standard for temperature increase measurements.
• The calibration depends on the assessment of the mass density, the specific heat capacity and the electrical conductivity of the medium. While mass density and specific heat capacity can be measured accurately with standardized procedures (~ ± 2 % for ch; much better for ρ), there is no standard for the measurement of the electrical conductivity.
Depending on the method and liquid, the uncertainty can be ± 5 %.
• Sufficient temperature rise is required to produce measurable temperature rises; therefore calibration is often performed at a higher power level than the E-field methods. The non- linearities in the system (e.g. power measurements, different field components, etc.) shall be compensated.
Considering these problems, the calibration accuracy of E-field probes using temperature rise technique in a carefully designed set-up is about ± 10 % (combined standard uncertainty) [104]. A set-up using a combination of waveguide and temperature rise techniques was presented in [72]. The estimated combined standard uncertainty of this set-up is ± 5 % when the same liquid is used for both the calibration and for actual measurements, and ± 7 % to
± 9 % when not, which is in good agreement with the estimates given in [104]. When performing an uncertainty analysis of the transfer calibration using temperature rise technique, the parameters included in Table B.1 shall at least be considered.
Table B.1 – Uncertainty analysis for transfer calibration using temperature probes
Source of uncertainty Uncertainty
value
± %
Probability
distribution Divisor ci Standard
uncertainty ui ± %
νi or νeff
Positioning of E-field probe R √3 1 ∞
Positioning of temperature probe R √3 1 ∞
E-field probe linearity R √3 1 ∞
Temperature probe drift and noise R √3 1 ∞
Temperature probe linearity R √3 1 ∞
Liquid conductivity R √3 1 ∞
Specific heat of liquid R √3 1 ∞
Liquid density R √3 1 ∞
Temperature probe accuracy R √3 1 ∞
Combined standard uncertainty RSS
NOTE ci is the sensitivity coefficient.
The component tolerances of Table B.1 shall be determined as follows.
a) The positioning tolerances of the temperature and E-field probes are evaluated according to 7.2.3.1 using the actual penetration depth determined from the tissue dielectric parameters measured at the calibration frequency. Since small SAR variations at the peak are expected for directions parallel to the phantom surface, the procedures of 7.2.3.1 are applicable when both temperature and E-field probe movements may be limited to transverse directions only, with no movement required in the surface-normal or z-direction.
b) Linearity uncertainty of the field probe is assessed according to 7.2.2.3 and for calibration shall not exceed 0,1 dB at the calibration field strength.
c) Temperature probe drifts and noise are assessed by temperature measurements at 1 s intervals for 1 h, with an integration time of less than 0,5 s in a constant temperature condition. The temperature tolerance is computed as 100 × [(Tmax – Tmin)/∆Tmin], where
∆Tmin is the minimum temperature rise for the different power levels used for the calibration.
d) The temperature probe linearity tolerance should be determined using the following procedures. The accuracy and linearity of the temperature probe readings are compared against a traceable temperature reference at 10 temperature steps in a range larger than or equal to that used during the calibration. The tolerance is computed as 100 × [(Tmax − Tmin)/∆Tmin], where ∆Tmin is the larger of the minimum temperature rise for the different power levels used for the calibration and the tolerance for the temperature reference.
e) Liquid conductivity measurement tolerance during temperature calibration is determined using the same procedures as in 7.2.6.3.
f) The specific heat tolerance of tissue-equivalent liquids shall be determined using calorimeter procedures ([72], [100]).
g) Liquid density measurement tolerance shall be computed according to the RSS of the volume and weight tolerances obtained using standard measurement methods for volume and weight.
h) The temperature probe shall have a step response time of 1 s or less, which is determined from the time required by the measurement equipment, temperature probe and readout electronics to reach 90 % of the expected final temperature value after a step variation of 5 °C or more has been applied to the temperature probe.
B.3.2.3.3 Calibration with analytical fields (waveguides)
In this method a test set-up is used in which the field can be calculated analytically from measurements of other physical magnitudes (e.g. input power). This corresponds to the standard field method for probe calibration in air; however, there is no standard defined for fields in lossy liquids.
When using calculated fields in lossy liquids for probe calibration, several points shall be considered in the estimation of the uncertainty.
• The net RF power dissipated in the waveguide shall be measured accurately. This requirement implies precise measurements of two out of the following three quantities:
incident power, reflected power, reflection coefficient at the waveguide input port.
• The accuracy of the calculated field strength will depend on the assessment of the dielectric parameters of the liquid.
• Due to the small wavelength in liquids with high permittivity, higher order modes can be excited. The field distribution in the set-up shall be carefully checked for conformity with the theoretical field distribution.
Waveguides can be utilized to generate an analytically known field inside tissue-equivalent liquids, e.g. the set-up presented in [132]. In this set-up (see Figure B.1), the upper part of a vertically-oriented open-ended waveguide is filled with liquid. A dielectric slab at a distance
> l (l refers to the wavelength in the air section of the waveguide) from the feeding coupler provides an impedance match (> 10 dB return loss) between air and liquid. The symmetry of the construction and high losses in the liquid ensure that the field distribution inside the tissue-equivalent liquid follows the TE10 waveguide mode pattern, although higher-order modes theoretically may exist. In [131] the absence of higher modes was carefully validated by measuring the electric field distribution in the volume of the liquid, and this was found to be within ± 2 % of the theoretical TE10 mode pattern.
Key
x,y,z Axes of cartesian coordinate system
3δ Liquid depth (> 3 times the penetration depth) a Waveguide cross-section width
b Waveguide cross-section height Pf Incident power
Pr Reflected power
Figure B.1 – Experimental set-up for assessment of the sensitivity (conversion factor) using a vertically-oriented rectangular waveguide
Inside the liquid, the field propagates almost like a TEM wave, because of the low cut-off frequency. The liquid depth (> 3 times the penetration depth) was chosen so that the reflections at the upper surface of the liquid are negligible. Formula (B.5) shows the relationship between the SAR at the cross-sectional centre (x = y = 0) of the lossy waveguide and the longitudinal distance (z) from the dielectric separator:
( ) δ
δ
ρf r e 2 / ) (
4 z
ab P z P
SAR = − − (B.5)
where
ab is the cross-sectional area of the waveguide;
Pf is the forward power inside the lossless section of the waveguide;
Pr is the reflected power inside the lossless section of the waveguide;
z is the distance from the dielectric slab;
ρ is the liquid density;
δ is the penetration depth inside the lossy liquid.
NOTE For the purposes of this standard, the density ρ is assumed to be 1 000 kg/m3.
The penetration depth δ, which is the reciprocal of the waveguide-mode attenuation coefficient α, is determined from a scan along the z-axis and compared with the theoretical value determined from Formula (B.6) using the measured dielectric properties of the lossy liquid.
IEC
>3δ
x y z
Pf Pr Lossy
liquid
Spacer
a
b
( )2 ( ) 1
1 a j 0 j 0 r
δ α = − = ℜ π + ωà σ + ωε ε ′ −
(B.6)
Table B.2 provides design guidelines for calibration waveguides with a return loss of at least 10 dB at the most important frequencies used for personal wireless communications. Values for the penetration depth for these specific fixtures and tissue-equivalent dielectric parameters are also listed in Table B.2.
This technique provides excellent accuracy, with a combined standard uncertainty of
< ± 3,6 % depending on the frequency and media. The calibration itself is reduced to power measurements traceable to a standard calibration procedure. The practical limitation given by the waveguide size to the frequency range between 750 MHz and 6 000 MHz is not severe in the context of compliance testing, because most of the operational frequencies for mobile communications systems are covered within this range. For frequencies below 750 MHz, transfer calibration with temperature probes remains the most practical way to achieve calibration with the lowest uncertainties. When performing an uncertainty analysis of the calibration with analytical fields, at least the parameters included in Table B.2 shall be considered.
When performing an uncertainty analysis of the probe calibration in a waveguide, at least the parameters included in Table B.3 shall be considered.
Table B.2 – Guidelines for designing calibration waveguides
Frequency MHz
Head tissue simulant Waveguide
dimension Penetration
depth Dielectric separator
εr′ σ
S/m a
mm δ
mm εr′ Thickness
mm
300 45 0,87 584,2 45,78 5,5 106,0
450 44 0,87 457,2 42,94 6,0 66,1
835 to 900 42 0,97 247,6 36,16 5,6 34,8
1 450 41 1,20 129,5 28,55 4,7 24,8
1 800 to
2 000 40 1,40 109,2 24,15 4,8 19,4
2 450 39 1,80 109,2 18,59 5,7 12,6
3 000 39 2,40 86,4 13,97 5,7 10,3
3 500 38,0 2,92 58,2 11,42 4,9 9,76
5 400 35,8 4,86 47,5 6,69 5,6 5,73
6 000 35,1 5,48 40,4 5,89 5,4 5,25
Permittivity and thickness of the dielectric separator may vary from the values shown to accommodate commercially available materials. If the dielectric separator permittivity varies from the indicated value by more than 2 %, it is recommended to newly optimize the spacer thickness for the best matching (return loss typically greater than 10 dB).
NOTE 1 By convention, the length of the cross-section short edge is one half that of the long edge, i.e. b = a/2.
NOTE 2 The waveguide dimensions are in accordance with the EIA RS-261-B: 1979 [36].
NOTE 3 These dimensions are also dependent on the frequency bandwidths of interest.
Table B.3 – Uncertainty analysis of the probe calibration in waveguide
Uncertainty component
a b c ui = (a/b) × (c)
Uncertainty
± %
Probability
distribution Divisor ci Standard
uncertainty
± %
νi
Incident or forward power R √3 1 ∞
Reflected power R √3 1 ∞
Liquid conductivity
measurement R √3 1 ∞
Liquid permittivity
measurement R √3 1 ∞
Liquid conductivity deviation R √3 1 ∞
Liquid permittivity deviation R √3 1 ∞
Frequency deviation R √3 1 ∞
Field homogeneity R √3 1 ∞
Field-probe positioning R √3 1 ∞
Field-probe linearity R √3 1 ∞
Combined standard
uncertainty RSS
NOTE Column headings a, b, c are for reference.