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Complex Permittivity of Planar Building Materials Measured with an Ultra-Wideband Free-Field Antenna Measurement System

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Complex Permittivity of Planar Building Materials Measured with an Ultra-Wideband Free-Field Antenna Measurement System Volume 112, Number 1, January-February 2007 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 112, 67-73 (2007)] Complex Permittivity of Planar Building Materials Measured With an Ultra-Wideband Free-Field Antenna Measurement System Volume 112 Number 1 January-February 2007 Ben Davis, Chriss Grosvenor, Building materials are often incorporated to extract the material properties with opti- Robert Johnk, David Novotny, into complex, multilayer macrostructures mization software based on genetic algo- that are simply not amenable to measure- rithms. James Baker-Jarvis, and ments using coax or waveguide sample Michael Janezic holders. In response to this, we developed an ultra-wideband (UWB) free-field meas- Key words: digital signal processing; National Institute of Standards urement system. This measurement system free-field measurement system; genetic and Technology, uses a ground-plane-based system and two algorithm; material properties; TEM half- Boulder, CO 80305-3328 TEM half-horn antennas to transmit and horn antennas; transmission; ultra-wide- receive the RF signal. The material sam- band. ples are placed between the antennas, and [email protected] [email protected] reflection and transmission measurements [email protected] made. Digital signal processing techniques Accepted: December 12, 2006 [email protected] are then applied to minimize environmen- [email protected] tal and systematic effects. The processed [email protected] data are compared to a plane-wave model Available online: http://www.nist.gov/jres 1. Introduction the gated S-parameters. This optimization process uti- lizes a genetic algorithm (GA) [1] that provides accu- The NIST Time-Domain Fields Project has devel- rate estimates of the electrical properties of a sample oped a nondestructive, ultra-wideband (UWB) meas- under test. This system has the marked advantage over urement system to measure complex permittivities of previous systems in that it permits the measurement of building materials. The purpose is to develop a data- very heavy wall samples without the need of a sample base of material permittivities for use by engineers for holder. The system also has high bandwidth, range modeling wireless signal propagation in buildings and (spatial) resolution, and measurement fidelity. related applications. This paper consists of six sections: Section 2 The NIST system consists of an aluminum ground describes the measurement system. Section 3 intro- plane, two TEM horn antennas, precision microwave duces the measurement sequence and the initial data cables, and a vector network analyzer. A wall of sample processing. Section 4 describes the mathematical building material is placed between the antennas, and model and how the GA is used to optimize material both transmission and reflectivity are measured over a parameter estimates for two candidate materials, cross- wide frequency range. The stepped-frequency S- linked polystyrene and concrete. Section 5 compares parameters are then post-processed to isolate the sam- the results obtained thus far with other measurement ple response and reduce systematic effects due to the techniques and published results. Section 6 presents environment. The net result is a set of gated S-parame- conclusions. ters. Material properties are then extracted by an opti- mization process based on plane-wave assumptions and 67 Volume 112, Number 1, January-February 2007 Journal of Research of the National Institute of Standards and Technology 2. The Measurement System order to quantify the scattering from the sample under test, three measurements must be made: (1) a back- Figure 1 is a diagram of the laboratory-based meas- ground measurement with the two boresighted anten- urement system. It consists of an aluminum ground- nas at a specified separation, (2) a reference reflectivi- plane, two TEM half-horn antennas (ground-plane ty measurement with a large aluminum sheet halfway mounted), several material samples, two precision between the antennas, and finally, (3) the building microwave interconnecting cables, and a two-port material sample placed halfway between the antennas. Vector Network Analyzer (VNA). Four S-parameters The processing consists of three principal steps: (1) (S11, S21, S12, S22) are measured at 1601 stepped frequen- The background S-parameters, measured as a function cy points in the range of 30 MHz to 6 GHz. For meas- of frequency with no sample in place, are subtracted urements of plywood, gypsum, and cross-linked poly- from the S-parameters measured with either a sample styrene, the 7.3 m × 7.3 m aluminum ground-plane sys- or metal sheet in place; (2) these subtracted S-parame- tem of the NIST cone and ground-plane time-domain ter sets are then inverse Fourier transformed, time range was used. Measurements of the concrete slab gated, and Fourier transformed by NIST-developed were made on a smaller 3.66 m × 3.66 m aluminum software to yield a set of “gated” S-parameters; and (3) ground-plane. Sample thicknesses were measured with the gated S-parameters are then normalized with either precision calipers at various points around the sample the metal reference for reflectivity or with the antenna- and are accurate to within ±0.1 cm. Figure 2 is a photo- to-antenna reference for transmission [2]. Specifically, graph of the measurement system being used on a sam- we have ple slab of cross-linked polystyrene, and Fig. 3 is a pic- S = 21m ( gated sample ) ture of the concrete slab measurement setup. The TEM S21 (1) half-horns can be seen with their styrofoam wedge S21m ( gated reference ) mounts on either side of the concrete slab. SS− S = 11m ( gated sample ) 11 m ( gated reference ) (2) 11 − 3. Measurement Sequence and Data SS11m ( gated metal ) 11 m ( gated reference ) Processing S11 = S22 ; S12 = S21. (3) The measured S-parameters must be post-processed further before material properties can be extracted. In Fig. 1. Plan view and profile view of sample under measurement. 68 Volume 112, Number 1, January-February 2007 Journal of Research of the National Institute of Standards and Technology Fig. 2. 1.2 m × 1.2 m cross-linked polystyrene in styrofoam holders for measurement on a laboratory ground-plane. Fig. 3. 1.2 m × 1.2 m × 0.2 m concrete measurement between TEM half-horns on portable ground-plane. 69 Volume 112, Number 1, January-February 2007 Journal of Research of the National Institute of Standards and Technology These three steps yield a set of normalized free-field S- domly generating many possible solutions. These solu- parameters (S11, S21, S12, S22) that quantify both the tions are tested with the objective function and ranked reflection and transmission through the sample under by a minimum cost criterion. A certain fraction of the test. best solutions is selected and a new set of solutions is generated. This process is repeated until a desired level of convergence is met or a maximum number of itera- 4. Extraction of Material Electrical tions is achieved. A unique property of the GA is that Properties per iteration, a fraction of the solutions are randomly changed to ensure that the results are not subject to The free-field S-parameters are used in the determi- local minima. The cost function that is used is the nant of the S-matrix [3]: absolute distance per frequency between calculated and 22 measured results and is given by −−γ Γ−z ||S =−=SS SS e2(0 dL ) , (4) 11 22 21 12 −Γ22 1 z |(SSεε′′′ , )|− | | . (9) r r fii() calc f ( meas ) where π The first term in Eq. (9) is equivalent to the right-hand γ = 2 f 0 j , (5) side of Eq. (4), and the second term to the left-hand side clab of Eq. (4). The cost function of Eq. (9) is minimized. where f is the operating frequency, 5. Results z = e–γ L (6) Complex permittivity results are presented for cross- 2πεf * linked polystyrene and concrete. In the case of cross- γ = j r , (7) linked polystyrene, we measured a 1.2 m × 1.2 m sam- cvac ple that was 2.9 cm thick. In this case we know, based and on published data obtained by a Split-Post Resonator ε ′ technique [5], that r = 2.55 at two frequency points, c µ* 1.44 GHz and 2.06 GHz. Using this as a guide, the ini- vac r −1 ε ′ c ε * tial population for the genetic algorithm of r is drawn Γ= lab r ε ′ . (8) from the domain 1 < r <3 and the results are shown in c µ* vac r +1 Fig. 4. This technique does not have sufficient sensitiv- ε * ε ″ clab r ity to measure r for a low-loss material like cross- linked polystyrene. In Eqs. (4) through (8), L is the measured thickness of A series of measurements was also made on a the sample, d is the antenna separation without a sam- 1.2 m × 1.2 m × 0.2 m section of concrete wall. This ple present, and cvac and clab [4] represent the speed of sample weighs approximately 907.18 kg and is an ideal light in vacuum and in the laboratory, respectively. candidate for ground-plane based measurements. The Equation (8) contains the complex relative permittivity results of the concrete measurements are shown in Figs. ε ∗ ε ′ ε ″ r = r – j r and complex relative permeability 5 and 6. The results are in good agreement with inde- µ∗ µ ′ µ ″ r = r – j r of the sample. We assume all sample pendent measurements, using a shielded open-circuit materials are nonmagnetic and do not have conductive technique conducted by the Electrical Properties of µ ′ µ ″ properties, so that r = 1 and r =0. Materials Project, and with published data [2].
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