In the SAR measurement procedure described in 6.7.4 only one zoom scan produces the peak spatial-average SAR to be compared with basic restrictions. As a consequence of that, a considerable number of zoom scans could be avoided, saving measurement time, if there is a criterion able to forecast that the peak spatial-average SAR for a test configuration will be lower than the highest value of peak spatial-average SAR among all test configurations. By extending this concept to multi-band and multi configuration devices, the measurement time can be further reduced by defining a SAR measurement session not limited by the single band operational mode but extended to all the operational bands and configurations supported by the device and included in the scope of the present test reduction method. The basic idea is to avoid performing the zoom scan session for each single test (Step d) in 6.7.4) if the maximum measured SAR value of the area scan is below a threshold. The threshold is chosen so that the highest peak spatial-average SAR value will be:
• correctly assessed and not underestimated, especially when it could generate a peak spatial-average SAR close to the basic restriction limit;
• correctly identified, even if not executing the zoom scan session.
In order to define the value of the threshold satisfying the first requirement, the peak spatial- average SAR from the zoom scan measurement has been correlated to the maximum measured SAR value found in the corresponding area scan [140]. It was observed that if the maximum measured SAR value in the area scan is lower than a threshold, then the basic limit
IEC
Cheek < 1 GHz
SAR relative to SAR in position with max. SAR in GSM mode
0 0
SAR (W/kg) All phones
Tilt < 1 GHz Cheek > 1 GHz Tilt > 1 GHz 1,4
1,2 1
0,8 0,6
0,4 0,2
0,5 1 1,5 2
for the peak spatial-average SAR is never exceeded; in particular there was a good correlation between the maximum measured SAR of the area scan and the peak spatial- average SAR over 1 g. In [140] choosing a threshold of 1,3 W/kg (80 % of basic 1 g limit of 1,6 W/kg) gives a high probability that the limit for the peak spatial-average SAR is never exceeded. The same threshold can be used also for the evaluation of the peak spatial- average SAR over 10 g.
The following statistical analysis has been performed to address the question of correct identification of the highest peak spatial average SAR [46].
L.3.2 Statistical analysis
The statistical analysis presented here considers handsets operating in the GSM 900 / DCS 1800 and UMTS I bands. The area scan grid spacing parameters used in this analysis were both (x and y) set to 10 mm, so they fit the requirements reported in this International Standard, and area scans were performed at a fixed specified distance (4 mm spacing between sensors and SAM surface in this case) from the SAM internal surface.
Since the maximum SAR value could not be exactly identified after the area scan, because it could be located (in x and y) inside a square region having 10 mm size, it is recommended to first experimentally evaluate the spatial gradient in order to estimate the magnitude of the peak SAR value that could be missed in applying only the area scan. To do this, 420 SAR distributions in the GSM 900 band, 420 distributions in the DCS 1800 band and 300 distributions in the UMTS I band have been considered. The distributions are relevant to mobile phones marketed between 2007 and 2010. All types of mobiles, including clam-shell and slide phones, have been considered in this study. The first step was to identify the "iso- level" as the set of points having a fixed SAR value and then compute the minimum distance Dmin between the iso-level at a fixed SAR level and the position of the interpolated maximum SAR (SARmax, the distance between the two points marked with an X in Figure L.3).
Figure L.3 – Two points identifying the minimum distance between the position of the interpolated maximum SAR and the points at 0,6 × SARmax
Figure L.4 below shows the histogram related to the random variable Dmin in the case of GSM 900 band and 0,6 × SARmax level. In red a normal probability density function (PDF) has been fitted to data using a maximum likelihood estimation procedure.
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0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 SAR (W/kg)
Figure L.4 – Histogram for Dmin in the case of GSM 900 and iso-level at 0,6 × SARmax Even if in some cases data fail the normality hypothesis test (e.g. Jarque-Bera normality test) and data can be more efficiently fitted by using other PDF (e.g. hyperbolic PDF), for the purpose of this analysis only normal fits have been considered in this work. Considering normal PDF, the value Dmin* represents the value for which the probability to have Dmin less than Dmin* is 5 %.
Table L.7 summarizes all the analysis performed, for each frequency band considered in this study. In this table the iso-level is expressed as a percentage, so a value of 90 % means the iso-level at 0,9 × SARmax.
Table L.7 – Distance Dmin* for various iso-level values
GSM 900 DCS 1800 UMTS I
Iso-level
%
Dmin* mm
Iso-level
%
Dmin* mm
Iso-level
%
Dmin* mm
90 4,23 90 3,04 90 1,82
80 6,74 80 4,82 80 4,63
75 7,86 70 6,19 70 6,10
70 8,90 65 6,92 65 6,81
60 10,96 60 7,54 60 7,48
50 13,15 50 9,06 50 8,88
To summarize the results of this analysis considering, for example, the GSM 900 band, we can conclude that it is improbable to find SAR values having the value 0,75 × SARmax if we consider a distance of 7,86 mm from the SARmax point. In particular the values shown in bold have Dmin* values higher than 7 mm, which is the value in the middle of the 10 mm chosen grids. In other words, still considering GSM 900 as an example, it is improbable to miss a SAR value inside a 10 mm area scan grid that is higher than 0,75 times the maximum SAR value measured during the area scan.
To conclude the statistical analysis, the correlation between the measured maximum measured SAR value of the area scan and the peak spatial-average SAR values found after
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Density
0 6
Dmin (mm)
Dmin data Normal Fit
0,02 0,04 0,06 0,08 0,1 0,12 0,14
8 10 12 14 16 18 20 22 24 26
zoom scans has been investigated. To do this, a database of 100 mobile phones operating in the GSM 900 and DCS 1800 bands and 50 handsets operating in the UMTS I band have been considered.
For each mobile phone the maximum measured SAR value of the area scan, the peak spatial- average SAR over 1 g and the peak spatial-average SAR over 10 g, as measured after the complete measurement procedure, were collected. Figure L.5 shows the histogram, as well as the normal PDF fit for the random variable Factor1g1800, defined as the ratio between the peak spatial-average SAR for 1 g mass and the maximum measured SAR value of the area scan in case of DCS 1800 band.
Figure L.5 – Histogram for random variable Factor1g1800
In this particular case, it can be shown that the 95 % probability is achieved to find Factor1g1800 in the interval [0,859, 1,015]. In this particular case it can be concluded that if there are two area scans with two different measured peak SAR values (not the interpolated one) and they differ by a factor of 0,859/1,015 = 0,84, then it is improbable that the distribution having the higher maximum SAR value measured during the area scan will have the lower peak spatial-average SAR for 1 g mass. In this particular case, 0,84 can be assumed as an experimental threshold: If two different area scans are considered and the measured peak SAR values measured for each one differ by a factor lower than the threshold, then there is a 95 % probability that the area scan with the higher SAR will yield the higher peak spatial-average SAR.
Similar conclusions can be obtained analysing the other bands as well as the peak spatial- average SAR for 10 g mass.
Table L.8 summarizes the overall results.
Table L.8 – Experimental thresholds to have a 95 % probability that the maximum measured SAR value from the area scan will also have a peak spatial-average SAR
GSM 900 DCS 1800 UMTS I
Threshold 1 g Threshold 10 g Threshold 1 g Threshold 10 g Threshold 1 g Threshold 10 g
0,86 0,76 0,84 0,63 0,74 0,62
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Density
0,8 Factor1g1800
Factor1g1800 data Normal Fit 12
10
8
6
4
2
0 0,85 0,9 0,95 1 1,05
In conclusion, the same thresholds found in Table L.7 (75 % for GSM 900, 60 % for DCS 1800 and UMTS I) are sufficient also to determine (with a 95 % probability value) the fact that the peak spatial-average SAR will be correctly identified even without performing a zoom scan.
L.3.3 Test reduction applicability example
Find below two examples of application of the procedures introduced in 6.7.4. In the first, the test reduction method is applied to a single operational mode (i.e. GSM 900), while in the second a dual mode (GSM 900/DCS 1800 and UMTS I) handset is considered.
Tables L.9 and L.10 show the reported SAR values which are the maximum measured SAR value from the area scan (GSM 900 band).
Table L.9 – SAR values from the area scan (GSM 900 band)
Frequency Position Maximum SAR value
W/kg
Middle Cheek left 1,3
Middle Tilt left 0,6
Middle Cheek right 1,5
Middle Tilt right 0,8
Lower Cheek right 1,0
Higher Cheek right 1,3
For bold rows, according to the proposed test reduction procedure, a zoom scan is not required.
Since this example relates to GSM 900, a threshold of 0,75 should apply. For the first position (cheek left, middle uplink frequency) the zoom scan is needed since the maximum SAR value is 1,3 W/kg (80 % of 1,6 W/kg), while for the tilt left 0,6 W/kg is lower than 0,75 × 1,3, so the zoom scan is not needed. Then in the cheek right position the zoom scan is needed and the new absolute peak SAR (APS) becomes 1,5 W/kg. This new APS precludes the need to perform the zoom scan for tilt right (middle frequency) and cheek right (lower frequency), while it is not high enough to exclude the last zoom scan (cheek right, higher frequency).
Below a second example is presented. For this particular example, the GSM 900 band is tested before DCS 1800 and UMTS I, but in general the order in which the bands are tested may be different.
In this second example, the procedure applied in GSM 900 is repeated considering all the other tests and previous APS found. For each band the user should choose an appropriate threshold (see Table 4). For the first measurement in a different band, the user will use, for the comparison with the maximum measured peak SAR value from the area scan, the previous APS found and the threshold related to the new band. As an example, the first area scan measurement of DCS 1800 has a peak maximum SAR value of 0,9 W/kg that is equal to 60 % (the threshold of DCS 1800) of 1,5 W/kg (the previous APS), so in this case zoom scan is needed.
As can be seen in this example, nine measurements (50 %) do not require a zoom scan to be performed (bold rows in the table). The number of zoom scans that can be avoided depends on maximum measured peak SAR values from the area scans.
Table L.10 – SAR values from the area scan (GSM 900 band)
Frequency Position Maximum SAR value
W/kg
Middle (GSM 900) Cheek left 1,3
Middle (GSM 900) Tilt left 0,6
Middle (GSM 900) Cheek right 1,5
Middle (GSM 900) Tilt right 0,8
Lower (GSM 900) Cheek right 1,0
Higher (GSM 900) Cheek right 1,3
Middle (DCS 1800) Cheek left 0,9
Middle (DCS 1800) Tilt left 0,6
Middle (DCS 1800) Cheek right 0,8
Middle (DCS 1800) Tilt right 0,7
Lower (DCS 1800) Cheek right 1,1
Higher (DCS 1800) Cheek right 0,8
Middle (UMTS I) Cheek left 1,1
Middle (UMTS I) Tilt left 0,7
Middle (UMTS I) Cheek right 1,4
Middle (UMTS I) Tilt right 0,6
Lower (UMTS I) Cheek right 1,2
Higher (UMTS I) Cheek right 1,4