A protocol for the evaluation of the SAR probe calibration coefficients and the uncertainty estimation is given in Annex B. The uncertainty of the probe sensitivity shall be estimated by assuming a normal probability distribution.
7.2.2.2 Probe isotropy
E-field probe isotropy is a measure of the deviation in probe response to arbitrary field polarization. In general, fields emitted by a handset are of arbitrary polarization. However, the fields induced in the tissue-equivalent liquid have a predominant polarization component parallel to the phantom surface, due to the physics of the absorption mechanism [138].
Hemispherical isotropy uncertainty (uhemispherical isotropy) is related to arbitrary field polarization (includes axial isotropy uncertainty), and axial isotropy uncertainty (uaxial isotropy) is related to fields normal to the probe axis.
The isotropy of the probe shall be measured according to the protocol defined in Annex B.
The uncertainty due to isotropy (uisotropy) shall be estimated with a rectangular probability distribution given by Formula (22):
( ) [ axialisotropy]2 [hemisphericalisotropy]2
isotropy[%] 100 1 w u w u
u = × − i × + i× (22)
where wi is a weighting factor to account for field incidence angles around an imaginary sphere enclosing the probe tip.
If the probe orientation is essentially normal to the surface (within ± 30° when f ≤ 3 GHz and within ± 20° when 3 GHz < f ≤ 6 GHz) during the measurement, then wi = 0,5. Otherwise, wi = 1 (i.e. the hemispherical isotropy uncertainty dominates).
7.2.2.3 Probe linearity and detection limits
Since the nonlinear response of the probe does not depend on the surrounding media but only on the diode sensors, evaluation of the linearizing functions fi(Vi) for a CW signal may be done either in free space or in the tissue-equivalent liquid (for modulated signals, use the procedure described in 7.2.2.4). This is performed by a power sweep covering the specified SAR detection range or a range at least from 0,12 W/kg to 100 W/kg in steps of 3 dB or less.
Small TEM cells or waveguides are preferable, since high field strengths can be produced with medium power amplifiers. The linearity uncertainty is defined as the maximum deviation in the SAR vs. power characteristic from the best-fit straight reference line going through zero (SAR = a∙P, where a is the best-fit slope of the line, using the method of least-squares) defined over the interval 0,12 W/kg to 100 W/kg. The linearity uncertainty for CW signal is determined as follows:
{ }
−
× ⋅
=
=
∈ = ( ) 1
100 max
[%] CW
W/kg 100 )
(
W/kg 12 , 0 ) , (
y , uncertaint linearity
CW maxCW
CW P a
P SAR SAR
i i j P
SAR
P z SAR y x j
i j i j
(23)
Here, SAR(Pi)CWj is the SAR measured for a CW signal at the i-th power level, Pi. The index j refers to the field sensor for each of which the procedure shall be repeated. A rectangular probability distribution is assumed for probe linearity uncertainty in Table 11, Table 12 and Table 13.
NOTE At SAR levels as high as 100 W/kg, the liquid temperature could rise significantly, causing deviations in the dielectric parameters. To avoid this problem, care should be taken to ensure that the liquid is exposed to high SAR levels only for short periods of time.
The probe detection limit uncertainty is determined by comparing the measured SAR (SARmeas) at a reference power level Pref to the value of the reference SAR, SARref = a∙Pref, at the same power level, using the best-fit slope as determined above.
ref meas ref
limit meas
detection [%] 100 100
P a SAR SAR
U = × SAR = × ⋅ (24)
The reference power level Pref shall be chosen such that the signal to noise ratio (determined at the measurement time) is 6 dB. This shall be verified using the data from the power sweep.
A rectangular probability distribution shall be assumed for detection limit uncertainty in Table 11, Table 12 and Table 13.
7.2.2.4 Probe modulation response
Probe sensor responses to modulated signals that are based on diode detectors can be complex since the diodes are greatly non-linear elements. The diode response theory for complex signals was reported by Nadakuduti et al. [116]. The linearization parameters for a particular modulation should be determined by relative experimental calibration, i.e. power sweep at that particular modulation, as described in Clause B.2. The linearization parameters shall be determined for each sensor separately.
The following uncertainty can be determined by using any source (e.g. waveguide or dipole) with a set-up equivalent to the one described in Figure D.1. The signal generation set-up shall simulate the modulation for which the uncertainty is determined according to the specification of the communication system standard. The power shall be increased for probe sensor voltage equivalent to smaller than P0 = 0,1 W/kg to the equivalent of larger than 10 W/kg for the investigated sensor in 5 dB steps. At each power level, the SAR shall be measured with the modulated signal and with CW at the same RMS power (verification that the power meter uses a true RMS detector and that the amplifier is sufficiently linear for the entire dynamic of the signal is required). This procedure shall be repeated for each field sensor.
Formula (25) is used to derive the modulation uncertainty of a particular modulation modX.
[ ] { }
( )
( )
−
×
= +
∈max = 100 1
%
X 0 X
0
X cal
dB mod 20 ,
y , uncertaint
modulation max
j j
i i
P i P z P y x
j SARP
P
SAR SAR (25)
where
yX uncertaint modulation
SAR is the uncertainty for the particular modulation modX in percent
( )Pi j
SAR modX is the SAR measured with the modulated signal at power level Pi for sensor index j
( )Pi j
SAR calX is the SAR measured with the calibrated signal at the same RMS power for sensor index j
The SAR uncertainty is determined as the maximum of all SAR( )Pi modX at each step for all three sensors. The index j refers to the field sensor for each of which the procedure shall be repeated. A rectangular probability distribution has been assumed for probe modulation response uncertainty in Table 11, Table 12 and Table 13.
7.2.2.5 Boundary effect
The probe boundary effect introduces measurement uncertainty. For the purposes of this Standard, this uncertainty is negligible if the closest distance between the probe tip and the phantom inner surface is always larger than the probe-tip diameter.
In some cases, the probe may need to be used to measure closer than the probe tip diameter, in order to reduce interpolation and extrapolation uncertainties. Then the boundary effect uncertainty of Clause B.6 shall be assessed preferably by using the waveguide system described in B.3.2.3.3. Alternatively, the temperature method described in B.3.2.3.2 could be used below 800 MHz. The method below is valid assuming the angle between the probe axis and the surface normal line is within the requirements of Table 1 and Table 2. Since the boundary effect is a characteristic of a specific probe, it shall be determined during probe calibration (i.e. influence of the probe tip diameter). If algorithms are applied to compensate for the boundary effect, then the SAR uncertainty shall be determined with the same evaluation hardware and software as used for performing the SAR measurements. The boundary effect uncertainty can be estimated according to the following uncertainty approximation formula based on linear and exponential extrapolations between the surface and dbe + dstep along lines that are approximately normal to the surface:
[ ] ( ) ( ( )), ( ) 10mmand 3GHz
2 e [%] 2
% 2 be step
step step 2 be be
y uncertaint
be + < ≤
∆ +
= − d d f
δ d
d SAR d
SAR d δ (26)
[ ]% [%] , be and >3GHz be be
y
uncertaint d f
δ -d SAR δ
SAR =∆ <δ (27)
where
SARuncertainty is the uncertainty in percent of the probe boundary effect;
dbe is the distance between the surface and the closest measurement point;
dstep is the separation distance between the first and second measurement points that are closest to the phantom surface, assuming the boundary effect at the second location is negligible;
δ is the penetration depth of the head tissue-equivalent liquids defined in this Standard;
∆SARbe the deviation of the measured SAR value in percent, at the distance dbe from the boundary, from the analytical reference SAR value for waveguide systems SARref. SARref is calculated using Formula (B.5).
If waveguide systems are not available for certain frequency ranges, temperature probes should be used to assess the reference values SARref at the locations dbe and dbe + dstep, and the SAR uncertainty of the temperature probe shall be accounted for. If temperature methods are used, then SARref is the value at this location determined using the temperature probe.
Note that the actual calibration shall be performed at distances between the probe tip and boundary that are larger than the probe tip diameter, where the boundary effect is negligibly small. Enter the uncertainty of the probe boundary effect in the appropriate row and column in Table 11, Table 12 and Table 13 using rectangular distribution.
7.2.2.6 Field probe readout electronics uncertainty
Field-probe readout electronics uncertainties shall be assessed for field probe readout electronics. All uncertainties related to the probe readout electronics, including the gain and linearity of the instrumentation amplifier, its loading effect on the probe, and accuracy of the signal conversion algorithm, shall be evaluated to estimate the maximum SAR uncertainty.
One method to determine these uncertainty components is by replacing the probe with an equivalent source having the same source impedance as the probe under consideration according to the manufacturer’s specifications for the probe. This is generally performed by the system manufacturer. Each uncertainty shall be converted to a standard uncertainty using normal probability distribution. The RSS value of these uncertainties shall then be used to determine the overall readout electronics uncertainty.
7.2.2.7 Signal step-response time uncertainty
Field-probe signal response time uncertainty is evaluated by exposing the probe to an E-field step response producing at least 100 W/kg near the phantom surface. The signal response time is evaluated as the time required by the probe and its readout electronics to reach 90 % of the expected final value produced by the step response by switching the RF power on and off. During the SAR measurement, the probe shall remain stationary at each measurement location for at least twice the assessed response time so that the probe signal response time uncertainty is negligible. Under these measurement conditions, a tolerance value of zero may be entered in the appropriate uncertainty table. Otherwise, the SAR uncertainty due to signal response-time uncertainty shall be assessed, using the signal characteristics of the test device. In this case, the signal step-response time uncertainty is equal to the percentage difference between the SAR measured at the chosen measurement time and the SAR measured at twice the chosen measurement time. A rectangular probability distribution shall be assumed.
7.2.2.8 Probe integration-time uncertainty 7.2.2.8.1 General
Probe integration-time uncertainties may arise when test devices do not emit a continuous signal. When the integration time and discrete sampling intervals used in the probe electronics are not synchronized with the pulsed characteristics of the measured signal, the RF energy at each measurement location may not be fully or correctly captured. This uncertainty shall be evaluated according to the signal characteristics of the test device prior to the SAR measurement.
7.2.2.8.2 Probe integration-time uncertainty for periodic pulsed signals
For signals with periodic pulse modulation and a pulse period greater than 1 % of the probe integration time, additional SAR uncertainty shall be considered when the probe integration time is not an exact multiple of the longest periodicity. The uncertainty shall be assessed according to the maximum uncertainty expected for unsynchronized probe integration time with an assumed rectangular probability distribution. For a signal with an envelope s(t), the
average signal read by the probe during the integration time tint starting at time t0 is given by sint(t0, tint) in Formula (28):
+∫
≤
≤
= 0 int
0
0 , d ) 1 (
) ,
( 0
int int 0 int
t t
t
T t t
t t s
t t
s (28)
Formula (28) assumes that the filtering by the probe does not significantly alter the signal envelope s(t). If t0 is not synchronized with the longest period T of s(t), the probe integration- time uncertainty can be defined as shown in Formula (29):
( )
( )
) (
) ( 100 max
[%] int
int y int
uncertaint s t
t s t
SAR s −
×
= (29)
Here ⋅ denotes the average value. Formulas (28) and (29) can be used to derive the probe integration-time uncertainty of any pulsed signal.
A simple alternative formula for the uncertainty of a TDMA system is shown in Formula (30):
∑
×
=
frames - sub
all total
idle int
frame y
uncertaint [%] 100
slot slot t
SAR t (30)
Formula (30) is an approximation that typically overestimates the uncertainty. Here slotidle is the number of idle slots in a frame with slottotal being the total number of slots. The frame duration is tframe, with tframe < tint. The total probe integration-time uncertainty is the sum of the errors for all subframes in the frame structure that have idle slots. For example, the basic frame for GSM systems has a frame duration tframe = 4,6 ms, with 7 idle slots in an 8-slot frame, and the multiframe duration is tmultiframe = 120 ms, 1 idle slot in a 26-slot frame. For a probe integration time of 0,2 s, the uncertainty is estimated to be 0,020 1 + 0,023 1 = 0,043 2 or 4,32 % for GSM using Formula (30), compared with 3,84 % using Formula (28) and Formula (29). GPRS is the same as GSM, except that the number of idle slots can be 6, 5, …, where 7 idle slots is the worst case.
A rectangular probability distribution shall be assumed for probe integration-time uncertainty.
For continuous or CW-equivalent signals, an uncertainty value of zero shall be entered.
7.2.2.8.3 Probe integration-time uncertainty for non-periodic signals
For signals other than periodic pulsed, the probe integration time should be determined from SAR measurements using a stable source with the same signal characteristics and the same probe type that is used for DUT measurements. Measurements at a single point (where the SAR is at least 1 W/kg) shall be made consecutively using the chosen integration time and progressively larger integration times. The integration time shall be doubled for each consecutive measurement until the last and next to last measurements are within 0,5 % of each other. Each measurement at a given integration time shall be repeated several times to verify that the measurement result is stable, and the average SAR of the repeat measurements shall be used for that integration time. For the probe integration time, a rectangular probability distribution shall be assumed. The uncertainty is the percentage difference between the average SAR at the chosen integration time and the average SAR at the longest integration time.