A New Probe-Array Approach for Fast SAR Measurements

A. Cozza, 0. Merckel, J.-Ch. Bolomey

Supe'lec DREIEMG, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette, FranceEmail: andrea. cozza(wsupelecffr

ABSTRACT

An innovative system for rapid specific absorption rate (SAR) measurements is here proposed. Measurements are carriedout by means of a two-dimensional array of radio-frequency dual-polarized probes. The plane-wave spectrum method issubsequently used in order to compute the electromagnetic (e.m.) field at any position inside a flat-phantom. Experimentalresults obtained with a linear probe-array prototype validate this new concept both for mapping the e.m. field distributioninside the phantom and for SAR measurements. Furthermore, it paves the way to a real-time approach to SAR assessment.

INTRODUCTION

Nowadays, specific absorption rate (SAR) measurements are required for any hand-held wireless communication device,as specified by several international standards [1, 2]. In particular, the maximum averaged SAR (MAS) of mobile-phonesets (MS) is to be tested under a number of operating conditions, in order to check the power-density they induce into areference phantom simulating a human-head (or other parts of a human-body).

Since the actual standards provide for measurements where a single probe explores the electric field into the phantom,due to the extension of the volume being considered, the average time-lap required to test just one configuration is about15 minutes. Since a grand-total of twelve configurations are to be tested, the overall time needed to completely test anMS is a crucial issue in the industrial domain.

For these reasons, several alternative ways have been proposed for measuring MAS in a more rapid way [3, 4, 5,6]. These methods greatly reduce the test duration while maintaining a good precision, yet they are based on someapproximations on the e.m. field distribution. Actually, it has been shown that the residual errors in the field estimation donot have a great impact on the MAS, thanks to the averaging. Nevertheless, these considerations call for a more rigorousapproach, capable of providing fast SAR results while at the same time maintaining a good accuracy on the electric fieldmeasurements.

On the other hand, MS manufacturers are including concepts oriented towards a SAR-conscious design [8]: ratherthan just testing the MS at the end of its design, SAR limitations are already faced during and even before the prototypingphase. To this end, a sort of camera would be quite useful allowing to have a real-time monitoring of the electric fielddistribution in a phantom as induced by a prototype. This would allow in-depth investigations on the way the MS designinfluences the distribution of the induced e.m. field and, ultimately, the MAS. None of the previously cited methods meetthis target. The only works in this direction have been presented in [4, 9, 10], but they still rely on continuous-wave (CW)sources, as opposed to actual TDMA ones.

In this paper, we present a new approach in fast-SAR measurements inspired by previous works on real-time mi-crowave imaging [7], based on the plane-wave spectrum (PWS) decomposition, but not limited to CW sources. The aimof this approach is to develop a system capable of real-time measurements, yet providing accurate results not only forthe MAS, but rather more insightful local information for the design of a MS, such as the spatial distribution of the threecomponents of the electric field inside a phantom. Flat-phantom will be here considered, since the PWS method can beeasily adapted to rectangular configurations. Furthermore, the use of a flat-phantom is growingly appealing for testingother wireless devices than just MS, such as hand-held computers, laptops and so on.

THEORY FUNDAMENTALS

The system here proposed is based on the well-established idea ofPWS decomposition, which is the basis for near-field(NF) to far-field transformations in antenna measurements. In the present study, the PWS is used for what can be referredto as NF-NF transformations: the e.m. field measured on a plane surface is used in order to reconstruct it in any otherposition of an infinite homogeneous but lossy medium. Let us consider the electric field E(p, z), being p = xx + yy (seeFig. 1 for the reference system); the electric field can be expressed, through the PWS A(k), as [11]:

E(p,z) JJA(k)e -ikPe -k zdkdky (1)

1-4244-1088-6/07/$25.00 02007 IEEE.157

Probe-array out

A_ _ ~~~~~~~~lquicO.,x ( DUT J Probe-arrayv

(a) (b)

Figure 1: The probe-array system: a schematic representation (a) and a picture of the probe-array as mounted on anIndexSar MultiSAR base (b).

where k = k +k ,k = k2 kk - k, and k2 = jw,u(u + jcE). The sign of the square-root in the kz expressionmust be chosen in order to satisfy Sommerfeld's radiation condition.

By considering (1) at z = 0 and applying the inverse double Fourier transform the PWS can be easily computed as:

A(k) =JJ E(p, O)e±+jkPdxdy (2)

Another advantage of the PWS method resides in the possibility to express the normal component Ez as a function ofthe two tangential components, being A. k = 0; furthermore, the magnetic field can be expressed as a function of thePWS A(k). These results are valid as long as the propagation medium contains no sources. Thus, a probe would onlyneed to measure the components EX and Ey. The knowledge of Ez gets more important when tilt configurations andclam-shell MS are considered, since in this case the dominant polarization does not lay in the tangential plane. For suchconfigurations, methods based only on tangential components like [5] introduce a growing error.

Thanks to (1) and (2) the data obtained through a surface scanning allows the reconstruction of the electric field inthe entire domain. Actually, current measurements are carried out in phantoms, thus a limited homogeneous domain.Nevertheless, thanks to the fact that the tissue-equivalent liquid is quite lossy (about 2.5 dB/cm at 900 MHz), reflectionsfrom the phantom walls are usually negligible as long as the phantom is large enough with respect to the probe-arraydimensions: indeed, 2 cm provide a 10 dB attenuation path. Eventually, these features allow the flat-phantom to beregarded as a sort of anechoic chamber, i.e. a practical approximation to the ideal infinite test facility.

By far more critical is the truncation issue arising from the necessarily limited extension ofthe probe-array. Therefore,the dimensions ofthe scanned surface must be chosen so as to have a relative amplitude dynamics greater than 10 dB (ide-ally 20 dB), otherwise the PWS will be affected by secondary lobes due to the convolution of the Fourier transformationof the scanning window (cardinal sinus) and the actual PWS. This issue will be addressed in the next Section. Moreover,the number of probes is critical too, or better the space-sampling steps Ax and Ay, which should satisfy the conditionmax(Ax, ALy) < A/2, being A the wavelength in the liquid. Therefore, considering the standard characteristics of thephantom liquid for GSM900 tests (Er = 40, or = 1 S/m), the spacing between two adjacent probes should be smaller than26 mm at 900 MHz. The introduction of these practical limitations leads to a discretized version of (2) and (1), which canbe easily computed through FFT algorithms.

THE MEASUREMENT SYSTEM

The PWS method is based on the knowledge of both amplitude and phase measurements, thus radio-frequency (RF)probes have been considered (as opposed to detected ones), as proposed in [4]. Two orthogonal short dipoles (3.5 mmeach branch) are considered as a single probe in order to measure the two tangential components needed. For each dipole,the received signals are transmitted through thin coaxial cables to a balancing, matching and switching network thatallows for the selection of the polarization and of the probe being examined (Fig. 1). The cables being orthogonal to themeasurement-plane, their impact is negligible on the tangential components.

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Measured field at 15 mm130

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40 ...........40 40

60 60 60 10

80 808

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120_ 120_ 0 00 50 _ 100 0 5 10 0 5 100

oo ii ~~~~~~~~~~~~~~~~~~~~~~~~~..._I...... -100 -100 ..................60..

-0 50 100 -0 50 100 -0 50 100040

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-10 5 0 10 -10 5 0 10 -100 -5505 0

Figure 2: Experimental results obtained with the probe-array system. The first row shows Ex modulus, i.e. the componentalong the MS axis. The second row considers the PWS modulus of the above results; the small dashed circles indicate thelimit of the flat part in the Tukey window, whereas the larger ones correspond to a one-half value. All results are expressedin dB units.

The electric field phase has been defined as relative to the signal picked-up by a reference antenna as shown in Fig. 1.Thus, the phase-shift between the probe signals and the reference one is directly related to the propagation delay insidethe phantom. At the same time, the phase-reference antenna is placed near a phantom wall, thus avoiding any potentialnegative impact on the actual measurements. The two output signals X and R are then treated by a detector network whoseoutputs will be the absolute amplitude and the relative phase for the two polarizations of each probe. Another advantageof RF probes is the possibility to dramatically increase their sensitivity by means of low-noise amplifiers. The prototypewe developed can easily measure power-densities as low as a few ,uW/kg. as compared to 50 mW/kg for detected probesas declared in [5] or to 360 ,uW/kg of electro-optic probes in [9]. In the same way, accuracy can be improved by means offilters, thus reducing the noise level.

So far, we just developed a six-probe one-dimensional prototype with a sampling step of 13 mm (i.e. suitable formeasurements up to 1.8 GHz measurements in GSM1800 test liquid), in order to demonstrate the validity of our approach.Thus the array still has to be mechanically moved to cover the necessary scan-surface. Nevertheless, the final aim is todevelop a two-dimensional array sufficiently large to need no mechanical movement.

EXPERIMENTAL RESULTS

The proposed method has been validated by measuring the electric field induced by an actual MS on battery-power, laidflat against the bottom of the phantom, with the screen-side upward. The MS was forced to emit 2 W of peak-power onchannel 50 of GSM900 by a base-station emulator. The electric field has been measured over a region of 143x130 mm,with the MS at its center. These measurements have been carried out from 5 mm to 35 mm deep, with a 5 mm step.

The first validation is about the reconstruction of the electric field by means of the PWS method. To this end, thecomponent Ex, i.e. along the telephone axis, at 5 mm has been computed from the field distribution (amplitude andphase) as measured at 15 mm. The results, shown in Fig. 2, are quite good, with a typical residual error on the electricfield of about 3 %0 and a maximum one equal to 10 %0, over the central area, whereas outside this region (i.e. 15 dB

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Estimated field at 5 mm Measured field at 5 mm

below the absolute maximum) it gets more important, in particular at the corners. Indeed, the accuracy is here limitedby the small dimensions of our flat-phantom: the scanned surface nearly coincides with its physical dimensions, thus anadditional direct contribution comes from the phantom walls which cannot be accounted for by propagation alone.

This result is paramount, because it means that having a probe-array at 15 mm (corresponding to a negligible inter-action with the MS) one can back-propagate the electric field with a good accuracy. Actually, this operation is critical,since the dynamic of the measurement results is limited to 15 dB, therefore the PWS is affected by high secondary lobes,which could be interpreted as fictive evanescent-waves due to truncation. With an ideal PWS knowledge, the z-dependentexponential in (1) would amplify the evanescent waves while back-propagating, thus compensating the media losses. Un-fortunately, the previously recalled limitations in PWS result in a sort of background noise, due to truncation and noise.Thus, the back-propagated PWS would be affected by over-amplified evanescent waves, thus undermining the methodaccuracy.

An convenient solution to this problem is to filter out these convolutional tails: to this end, a Tukey window has beenapplied, as shown in Fig. 2. The same kind of tests have been performed for a forward-propagation: in this case, the PWSis more easily applied, since evanescent waves are attenuated. The residual error is about the same level. Actually, theTukey window we choose is almost degenerated to a Hanning window.

The fact that each plane can be retrieved from another one, implies that the method is auto-consistent, thus validatingthe spectral approach. On the other hand, the overall system has been validated by comparing the MAS obtained withthe proposed method and with a SARA2 base (IndexSar) on a 10 g cube. The former yielded 0.29 W/kg, while the latter0.26 W/kg, hence a 10 00 accuracy. Attention should be paid to the fact that the uncertainty of current SAR measurementsystems is about 20 00, thus this results does not exclude that our system have a better uncertainty. Incidently, Ez accountsfor the 4 00 of the overall SAR results.

Another fundamental issue is the time needed for the MAS estimation. Once the surface-scan is carried out, thetime needed to compute the MAS is about 120 ms on a Pentium III PC, under Matlab with nor compiling neither speed-optimization. This results can be further improved by working in a real-time environment not shared by other programslike actual Window-family operating systems. On the other hand, the electronic scanning poses no problem, since a 10 Hzrate for a square array of 12 probes per side would require an acquisition-rate of about 24 kS/s for TDMA signals, a targetthat can be met by measuring 13 samples per burst.

CONCLUSIONS AND PERSPECTIVES

The results here presented demonstrate the feasibility of a new approach to dosimetry assessment, where not only MASis sought, but also a more detailed information on the e.m. field distribution inside a flat-phantom. The potential impactof such a tool is expected to lead to a better and easier prototyping phase for new MS, improving SAR-oriented designconcepts. The main advantages include a physically accurate reconstruction, an interactive response (thanks to a real-timeapproach), the knowledge of the three components of the electric and magnetic field and an improved sensitivity withrespect to detected probes.

Nevertheless, our current system can be significantly improved with respect to two aspects: the use of a larger flat-phantom, thus reducing the impact oftruncation, and the need for a better calibration procedure. Solving these two simple,yet basic problems will lead to far more accurate results. Another important issue that must be faced is the step from arapid measurement to a real-time one, which concerns informatics rather than electromagnetism.

REFERENCES

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