Novel Probes and Evaluation Procedures to Assess Field Magnitude and Polarization

240 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 2, MAY 2000 Novel Probes and Evaluation Procedures to Assess Field Magnitude and Polarization Katja Poković, Thomas Schmid, Jürg Fröhlich, and Niels Kuster Abstract The immense development rate of wireless technologies has also brought new requirements for the RF design of transmitters. The design challenge is to optimize multiband devices with minimal dimensions and weight as well as an appealing appearance, which nevertheless operate well within varyingly complex environments such as frequently changing positions within the closest vicinity of the human body. The optimization of such transceivers requires new analysis tools providing precise measurement of electric and magnetic field strength distributions, even in the closest proximity of RF transmitters. In this study, novel field probes were analyzed, optimized, and constructed enabling not only the assessment of the local field strength, but also information on the polarization of the field. The ellipse parameters are reconstructed by a combination of a downhill simplex and a Givens updating algorithm, which has proven to be fast and robust. The developed probes and procedures greatly enhance the quality of the information needed for analysis and optimization of antennas and transmitters. Index Terms Field polarizations, field probes, near-field evaluations of RF transmitters, pseudovector information. I. INTRODUCTION Recent years have seen significant progress in near-field evaluation tools with respect to precision, spatial resolution, etc. [1]. Subsequently, near-field scanners are employed more and more for analysis and optimization of antennas embedded in complex environments. However, current implementations only enable the assessment of the magnitude of electric and magnetic field strengths, i.e., polarization and phase information are not available. At the same time, the availability of the polarization would increase the quality of the information with respect to antenna design purposes, e.g., information on the current flow, distortion of polarization by nearby scatterers, etc. Although electro-optical probes [2], [3] can measure both the magnitude and phase of the incident field simultaneously, they were not suitable for the targeted applications due to their large dimensions or low sensitivity. The objectives of this study were to develop probes as well as the measurement procedure needed to determine not only information on the field amplitude, but also information on the polarization of the field at any measured location and to incorporate the probe and algorithm into an existing near-field scanning system. The study was divided into two parts. First, an extensive numerical analysis was performed in order to optimize the probe parameters and the measurement procedure. Based on these findings, probe prototypes were built and tested under various conditions. II. NUMERICAL EVALUATION An arbitrarily oriented ellipse in three-dimensional (3-D) space can be numerically described with five parameters: semi-major axis, semi-minor axis, two angles describing the orientation of the Manuscript received September 3, 1999; revised February 2, 2000. This work was supported by Commisson for Technology and Inovation (KTI), Schmid & Partner Engineering AG, Motorola Inc. USA, and Nortel U.K. K. Pokovic and T. Schmid are with Schmid & Partner Engineering AG, Zurich, 8004 Switzerland. J. Fröhlich and N. Kuster are with the Foundation for Research on Information Technologies in Society IT IS, Zurich, 8006 Switzerland. Publisher Item Identifier S 0018-9375(00)04692-5. Fig. 1. Illustration of the angles used for the numerical description of the sensor and the orientation of an ellipse in 3-D space. normal vector of the ellipse (; ), and one angle describing the tilt of the semimajor axis ( ): For the two extreme cases, i.e., circular and linear polarization, only three parameters (a,, ) are sufficient for the description of the incident field. Since the goal of this project was to incorporate the novel probe and procedure into the existing near-field scanner (DASY system described in [1]), several considerations arising from the measurement capabilities and limitations had to be taken into account. Current probe designs employing dipole or loop sensors directly loaded with a detector diode can provide information only on the field amplitude, which means that at least five sensor readings would be necessary to gain sufficient information for the reconstruction of the ellipse parameters. In addition, typical probe readout systems have three channels (i.e., maximum three sensors per probe). If there is a need for more information, sequential measurements with different probe positions can be performed, e.g., by rotating the probe around its axis. For the reconstruction of the ellipse parameters out of measured data, the problem can be reformulated as a nonlinear search problem. The semi-major and semi-minor axes of an elliptical field can be expressed as a function of the three angles (; ; ): The vector magnitudes a and b can be uniquely determined in terms of minimizing the error in the least-square sense for the given set of angles and knowing the measured data. In addition, to suppress the noise and increase the reconstruction accuracy, it is desirable to have an overdetermined system of equations. The solution of using a probe consisting of two sensors angled by 1 and 2 and performing measurements at three angular positions of the probe, i.e., at 1, 2, and 3 (see Fig. 1), gives an overdetermined matrix. If there is a need for even higher accuracy, more rotation angles can be added. Furthermore, in order to minimize the mutual coupling, sensors can be set orthogonally (2 = 1 +90 ). It is obvious that some angles 1 must be avoided. Namely, if the sensor angle is equal to 90 sequential probe rotation will not provide any new information. Also, the angle should not be 45 ;, otherwise the two sensors would give identical information for some rotations. A. Optimization of Sensor and Measurement Angles In order to assess the potential dependence of the reconstruction accuracy and the sensitivity on the choice of the sensor and measurement angles, the reconstruction algorithm described in the following paragraph was integrated into a genetic algorithm [4]. The two sensor angles, the number of measurement angles, as well as the measurement angles, were coded as bit sequences in the genotype. The fitness of a genotype was evaluated for 100 arbitrarily generated elliptically polarized fields in terms of reconstruction accuracy and sensitivity to measurement errors or manufacturing deviations in the probe. The genetic algorithm successively improved the genotypes by using genetic operators such as selection, crossover, and mutation. 0018 9375/00$10.00 2000 IEEE

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 2, MAY 2000 241 Fig. 4. Tips of the EV2D and HV2D probes providing pseudo-vector information. Probes are shown without encapsulation. B. Reconstruction Algorithm The measured values for the given ellipse parameters (a; b; ; ; ); sensor angles ( i ;i=1; 2) and measurement angles ( j ;j =1111J) can be analytically expressed in the the following form: f 2 ij = a 2 1 [1 0 2 0 3] 2 + b 2 1 [4 + 5 0 6] 2 (1) where the k ;k=11116 denote the following terms: Fig. 2. Numerical algorithm for reconstructing the ellipse parameters. 1 =cos( ) 1 cos() 1 sin( i ) 2 = cos( i ) 1 sin( ) 1 sin( j 0 ) 3 = cos( i) 1 cos( ) 1 sin() 1 cos(j 0 ) 4 = sin( ) 1 cos() 1 cos( i ) 5 = cos( i) 1 cos( ) 1 sin(j 0 ) 6 = cos( i ) 1 sin( ) 1 sin() 1 cos( j 0 ): (2) Fig. 3. Distribution of the number of trials versus relative accuracy. The best solution was achieved by setting the measurement angles i (i=1;2;3) to 0, 120, and 240, and the sensor angles k (k=1;2) to 30 and 120 : Using an initially chosen set of ellipse angles (; ; and ) and performing measurements at three different angular positions i; an overdetermined system of linear equations is built which can be solved for the best (optimal) set of main ellipse parameters a 2 and b 2 in the least square sense. The most robust algorithm for solving overdetermined systems of equations is the Givens updating algorithm [5]. For the search of the corresponding angles of the ellipse a downhill simplex algorithm was employed [6]. The downhill simplex has been chosen because it only requires function evaluations and has been proven to be very robust. The sketch of the developed reconstruction algorithm is shown in Fig. 2. As an example of the reconstruction accuracy of the developed routine, the distribution of the number of reconstruction trials versus the relative accuracy of reconstruction is shown in Fig. 3. III. PROBE DESIGN AND CHARACTERIZATION Based on the numerical analysis, E- and H-field probe prototypes were built. The novel E-field probe consists of two 3-mm-long dipole sensors placed on their substrates and angled toward the probe axis. Detector diodes at the dipole gap rectify the RF signal and resistive lines connect the dipole sensors to the data acquisition unit. Mutual coupling between the sensors was

242 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 2, MAY 2000 TABLE I GEOMETRICAL SPECIFICATIONS OF THE PROBES TABLE II RF PERFORMANCE OF THE NOVEL PSEUDOVECTOR PROBES eliminated by placing the two dipoles orthogonal to each other. The first prototype of the pseudovector E-field probe (EV2D) is shown in Fig. 4. The same approach was applied for the construction of the novel H-field probe. Two concentric loops each with a diameter of 3 mm were used as sensor elements. The shunt resistance and capacitance are added to flatten the frequency response over the frequency range of interest. Similar to the design of the E-field probe, detector diodes are used to rectify the signals, which are then transmitted via highly resistive lines to the readout electronics (see Fig. 4). For the assessment of the sensitivity of the probe sensors as well as the probe linearity different setups were used. The calibration at frequencies below 0.8 GHz was performed in the TEM cell (ifi110). For the absolute calibration and for higher frequencies, a set of waveguides (R9, R14, R22, and R26) with overlapping frequency ranges was used. By using high-precision components (loads, lines, and adaptors) and error compensation methods, an absolute accuracy of better than 65% was achieved (for more details on the calibration setup see [7]). The linearity over the different frequencies (30 and 3000 MHz) and waveguides was assessed to be better than 62%. Preliminary numerical evaluation revealed that although the choice of the sensor angles is not critical as long as they are not too close to each other and different than 0,45, and 90, it is crucial for the success and accuracy of the reconstruction routine to know the exact sensor angles ( 1; 2) and use them as the input to the reconstruction algorithm. For this reason, the calibration was performed in two steps, e.g., both incident field polarizations with respect to the probe axis were used, whereby the incident field was oriented either normal or parallel to the probe axis. From the two conditions, field sensitivities parallel to the sensors as well as the actual sensor angles could be assessed. Geometrical parameters and the probe calibration data are summarized in Tables I and II, respectively. Since the directivity axis of each sensor is assessed during the calibration procedure and then used in the evaluation, the spherical isotropy is independent of the manufacturing tolerances or field coupling effects. Spherical Fig. 5. E-field vector 5 mm above a dipole radiating at 900 MHz. Measured. Simulated results. Fig. 6. H-field vector 5 mm above a dipole radiating at 900 MHz. Measured. Simulated results. deviation from isotropy for the novel E-field probe was measured in front of an open R9 waveguide at 900 MHz and assessed to be 60.17 db.

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 2, MAY 2000 243 cuboid with a graded mesh ranging from 0.6 mm (around the dipole gap and at the dipole edges) to 2.5 cm with a grading ratio of 1.5. A voltage source was used for the dipole excitation. Measurements using the novel E-field probe were taken at several distances from the central dipole axis. The results for the plane at a distance of 5 mm as assessed by numerical means and measured with novel field probes are shown in Fig. 5. It can be seen that for the extreme near-field region of the dipole, linear polarization is only present in the symmetry plane of the dipole and degrades to elliptical polarization elsewhere. The same example was used to test the performance of the novel H-field probe. The results for the plane at a distance of 5 mm from the dipole is compared to the numerical solution and presented in Fig. 6. B. Multipatch Antenna As a second example, a circularly polarized multipatch antenna operating at 1800 MHz was used. Results assessed using the vector E-field probe for the planes at 30 mm and 100 mm above the ground plane are shown in Fig. 7. At closer distances from the antenna the maximum field values occur above the four antenna patches, while for the greater distance the maximum radiation merges into the center of the multipatch antenna. C. Hybrid 6-dB Coupler Fig. 7. E-field vector over a circularly polarized multipatch antenna at 30 mm and 100 mm away from the ground plane. IV. IMPLEMENTATION AND MEASURED EXAMPLES The most interesting application of the vector H-field probe is the information that can be gained about the current flow over the device, or any other microwave circuit. This information is of particularly great importance for devices which are intended to operate in the closest vicinity of lossy dielectric bodies such as the human body. The reason is that the energy losses are approximately proportional to the square of the magnetic field strength at the surface of these scatterers, i.e., the significant RF currents closest to the tissue should therefore be minimized in order to reduce the energy losses and to gain antenna efficiency [8] [10]. As an illustration, the magnetic field distribution over a four-port hybrid 6-dB coupler at 630 MHz was measured. The H-field was scanned at a distance of 5 mm above the substrate. The results are shown in Fig. 8. The obtained information is significantly better than the information about the magnitude by itself [see Fig. 8]. A reconstruction routine for elliptical and linear polarization have been implemented into the DASY software [1], as has the visualization of the measured vector field. The elegance of the procedure is that the precision can be enhanced by adaptively increasing the number of measurements per position, starting from the initial three angles. The sensitivities parallel to the probe sensors as well as the sensor angles toward the probe axis, as assessed during the calibration procedure, are taken as the input data into the reconstruction routine. In addition, the software gives the possibility to define the termination conditions of the algorithm such as the number of simplex steps, maximum number of simplex initializations, minimum reconstruction accuracy, etc. The probe performance in actual measurements was tested on several examples. A. Benchmark E- and H-field Scans Over a Dipole The first example involved a linearly polarized symmetrical dipole radiating at 900 MHz. As the reference data, numerical simulations based on the in-house finite-difference time-domain (FDTD) code (SEMCAD) have been used. The dipole was modeled as a 3.6-mm V. CONCLUSIONS In the course of this project, novel E- and H-field probes have been developed, analyzed, optimized, and constructed. In combination with the developed and implemented robust and fast numerical algorithm (combination of linear matrix solver and nonlinear search algorithm), the ellipse parameters of the field at any measurement point can be reconstructed. This enables evaluation and visualization not only of the field amplitude at any spatial location, but also of the information on field polarization. The additional information can be of great value in the development and optimization phase of various microwave devices. A further unique characteristic of these probes is that without any loss of performance they can be used for evaluations in basically any homogeneous dielectric material (e.g., human tissues, water, etc.), as long as the calibration parameters for that particular media have been previously determined. The isotropic response of the classical probes will be significantly impaired if the media differs considerably compared to the one for which it was optimized.

244 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 42, NO. 2, MAY 2000 Fig. 8. H-field vector and the H-field magnitude over a hybrid 6-dB coupler operating at 630 MHz. Comparing the two figures clearly demonstrates the improved quality of information that can be obtained with the new probes. ACKNOWLEDGMENT The authors would like to thank O. Egger and Dr. Q. Balzano for their support in this study. REFERENCES [1] T. Schmid, O. Egger, and N. Kuster, Automated E-field scanning system for dosimetric assessments, IEEE Trans. Microwave Theory Tech., vol. 44, pp. 105 113, Jan. 1996. [2] M. Tokuda and N. Kuwabara, Recent progress in fiber optic antennas for EMC measurements, IEICE Trans. Commun., vol. E75-B, no. 3, pp. 107 114, Mar. 1992. [3] M. Kanda, Methodology for electromagnetic interference measurements, IEICE Trans. Commun., vol. E78-B, no. 2, pp. 88 107, Feb. 1995. [4] J. Fröhlich, Evolutionary optimization in computational electromagnetics, Ph.D. dissertation ETH, no. 12 232, Zurich, Switzerland, 1997. [5] G. H. Golub and C. F. Van Loan, Matric Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1990. [6] J. A. Nelder and R. Mead, A simplex method for function minimization, Comput. J., vol. 7, pp. 308 313, 1995. [7] K. Meier, M. Burkhardt, T. Schmid, and N. Kuster, Broadband calibration of E-field probes in lossy media, IEEE Trans. Microwave Theory Tech., vol. 44, pp. 1954 1962, Oct. 1996. [8] N. Kuster and Q. Balzano, Energy absorption mechanism by biological bodies in the near-field of dipole antennas above 300 MHz, IEEE Trans. Veh. Technol., vol. 41, pp. 17 23, Feb. 1992. [9] N. Kuster, Q. Balzano, and J. C. Lin, Mobile Communications Safety. London, U.K.: Chapman Hall, 1997. [10] M. Burkhardt and N. Kuster, Review of exposure assessment for handheld mobile communications devices and antenna studies for optimized performance, in Review of Radio Science 1996 1999, W. R. Stone, Ed. Oxford, U.K.: Oxford Univ. Press, 1999, pp. 873 918.