AMTA Paper Archive

Temperature change cause thermal expansion of the antenna materials and will have an important impact on antenna performances. In some applications it is sufficient to calculate the antenna deformation due to temperature by mechanical analysis and determine the RF impact by EM analysis tools. However, if the environmental conditions of the final antenna are stringent and considered critical as in some military and civil applications in the space and aeronautics domain, the thermal performance of the antenna must be determined by experiment. Typical temperature testing ranges for civil applications are often between -50°C and +80°C but can be much more extensive for special applications. This paper present a simple and easy method for thermal testing of antennas in a fast spherical near field measurement facilities such as multi-probe system. During the thermal testing, the antenna is maintained inside a RF transparent thermally insulated container including the local heating and cooling equipment. The fast testing provided by the multi-probe system allow to measure the temperature dependence of the antenna at several different temperatures within the investigation range. The method will be illustrated for the cold measurement case but the extension to the full cold-hot temperature range is trivial.

For high speed and high data-rate communications, operating frequency bands of wireless communication systems have been moving to submillimeter frequency range and their bandwidths have been broadening. IEEE 802.15 THz Interest Group (IEEE 802.15 IGthz) has been performing a channel characteristics study for future indoor millimeter and submillimeter wireless communications in the frequency range of 75 - 110 GHz and 270 - 320 GHz. Specular reflectance data of indoor interior materials is a prerequisite to analysis of the channel characteristics of new indoor millimeter and submillimeter wireless communications. Specular reflectiondescribed by the law of reflection states that the direction of the incident wave and the direction of the reflected wave make the same angle with respect to the surface normal, thus theangle of incidence is equal to that of reflection. This paper describes a specular reflectance measurement system and shows measurement result of dielectric plates in the frequency range from 110 GHz to 325 GHz. Specular reflectance measurement system consists of an S-parameters measurement system and a specular reflectance measurement apparatus. The S-parameters measurement system consists of a 67 GHz vector network analyzer used as the main frame and three frequency extenders which are operating at three frequency bands (D-band (110 -170 GHz), G-band (140-220 GHz) and J-band (220-325 GHz)), respectively. The specular reflectance measurement apparatus consists of a transmitting part, a receiving part, and a MUT holder which is positioned in the middle of the transmitting and receiving parts. During the specular reflectance measurement, the transmitting part is fixed while the MUT holder and receiving part are coaxial-rotating with 1:2 speed ratio. The transmitting and receiving frequency extenders are installed on the transmitting and receiving parts, respectively. For the specular reflectance measurement, one measures the transmission coefficient (S21_MUT) corresponding to the specular reflectance of an MUT mounted on the MUT holder. After replacing the MUT with a metal plate, one measures the transmission coefficient (S21_metal) corresponding to the specular reflectance of the metal plate, assumed to be -1. Specular reflectance of the MUT is obtained by taking the ratio (S21_MUT/S21_metal) of the respective transmission coefficients corresponding to the specular reflectance of the MUT and the metal plate. Multiple reflection effects between the transmitting and receiving antennas can be averaged out and minimized by averaging the transmission coefficients measured with changing the separation distances between the two antennas by ?/8 interval (i.e. initial distance + n·?/8, n=0,1,2,3). Specular reflectances of dielectric plates are measured in the 30° to 70° incident angle range with the developed measurement system in the frequency range from 110 GHz to 325 GHz. Description of the detailed measurement system and measurement result will be presented at the symposium.

Several instances in antenna design are known where an anisotropic material is useful ; however, finding a naturally occurring anisotropic material with the required dielectric tensor is often an impossibility. Therefore, artificially engineered anisotropic dielectric materials must be designed, tested, and implemented. In a previous paper by the authors [1], the design and initial measurement of an anisotropic material in Cartesian coordinates was presented along with predictions of how the material could be used to extend the bandwidth of a simple antenna structure.             In this paper we shall present the final implementation of the anisotropic material (with a tensor implemented in cylindrical coordinates) along with data on the material properties, the resulting antenna bandwidth, and radiation pattern. Design considerations for implementation of this approach shall be discussed along with practical limitations. Data shall also be presented on an unexpected result showing that that a reduced volume of anisotropic material produces favorable results. Measured data shall be compared with values predicted using finite difference time domain (FDTD) software and applications of this new broadband antenna for range operations will be discussed. [1]. D. Tonn, S. Safford, M. Lanagan, E. Furman, S. Perini, “DESIGN AND TESTING OF LAYERED ANISOTROPIC DIELECTRIC MATERIALS”, AMTA 2015 Proceedings, Long Beach CA, October 2015.

Measuring the RF, microwave or millimeter wave reflectivity of materials and components often requires a substantial length of transmission line or cables to connect the microwave source/receiver to the test apparatus.  Such cables may be subject to environmental variations (e.g. temperature or pressure) that change the overall phase delay and amplitude of signals that travel through said cables. Furthermore, some testing requires physical motion of the cable, which is another source of phase and amplitude error.  When possible, great care is often taken to design a test apparatus or methodology to minimize movement of the test cables so that these position-induced phase errors are small.  However, in some measurements, such as those that require scanning sensors or antennas, position-induced phase and amplitude errors cannot be avoided.  In some situations, temperature variations that change the cable phase response are also unavoidable. The problem of cable-induced errors has been a concern for many different applications and there have been previous attempts to address it.  These previous methods have used specialized microwave circuitry or a separate phase-stable reference device to measure and compensate for phase errors.  In this paper, a new correction method is described, which determines and corrects for phase and amplitude errors in transmission line cables.  Unlike previous published methods, the present technique does not require any specialized circuitry at the device under test (DUT).  Instead it utilizes in-situ reflections that already exist in the measurement apparatus to obtain a reference phase and amplitude signal.  The described algorithm combines these reflections with frequency and time-domain signal processing to compensate for erroneous phase and amplitude shifts that occur during a measurement.  This paper demonstrates the correction methodology with materials measurements examples.  Additionally, this phase and amplitude correction may be applicable for scatter and antenna measurements.  It can be applied to either reflection or transmission measurement data.

BIANCHA (BIstatic ANechoic CHAmber) is a singular facility located at the premises of the National Institute for Aerospace Technology (INTA), Spain, and was devised to perform a wide variety of electromagnetic tests and to research into innovative measurement techniques that may need high positioning accuracy. With this facility, both monostatic and bistatic tests can be performed, providing capability for a variety of electromagnetic measurements, such as the electromagnetic characterization of a material, the extraction of the bistatic radar cross section (RCS) of a target, near-field antenna measurements or material absorption measurements by replicating the NRL arch system. BIANCHA consists of two elevated scanning arms holding two antenna probes. While one scanning arm sweeps from one horizon to the other, the second scanning arm is mounted on the azimuth turntable. As a result, BIANCHA provides capability to perform measurements at any combination of angles, establishing a bistatic, spherical field scanner. In this regard, it is worth noting that in the last years, a renewed interest has arisen in bistatic radar. Some of the main reasons behind this renaissance are the recent advances in passive radar systems added to the advantages that bistatic radar can offer to detect stealth platforms. On the other hand, with the aim of developing new aeronautic materials with desired specifications, research on the electromagnetic properties of materials have also attracted much attention, demanding engineers and scientists to assess how these materials may affect the radar response of a target. Consequently, this paper introduces BIANCHA and demonstrates its applicability for these purposes by presenting results of different tests for different applications: a bistatic scattering analysis of scaled aircraft targets and the extraction of the electromagnetic properties of composite materials utilized in an actual aeronautical platform.

The use of additive manufacturing (AM) techniques to manufacture microwave and mm-wave passive components has recently been demonstrated through various examples [1]. The term AM comprises all techniques based on the successive building of thin layers of material one on top of each other to create a device. When properly implemented, AM offers the possibility to manufacture light-weight and highly complex devices without generating significant costs increase. Among all AM techniques, Stereo-Lithography (SLA) is the most interesting one for the production of mm-wave components. In SLA, the materials are non-metallic epoxy-based polymers, that require a metallic coating to allow them to become RF functional. In contrast to other AM techniques, SLA manufacturing tolerances and surface roughness permit the design of devices up to 300 GHz. SWISSto12 has recently reported the successful performance of metal plated SLA devices, based on a proprietary chemical plating technology enables the processing of monolithic devices. In this contribution, we aim at exploiting the previously described SWISSto12’s AM-SLA technique [1] to obtain a monolithic directional dual-polarized high-directive Leaky-Wave Antenna (LWA) operating at mm-wave frequencies. The LWA consists of a square cross section waveguide perforated with crossed slots in its top aperture [2]. Moreover, the antenna already includes a side-arm orthomode transducer (OMT) and a smooth waveguide  twist, specifically co-designed with the LWA. The squared waveguide supports the propagation of the two first orthogonal modes, which are radiated through the cross-shaped slots. Thus, the vertically (horizontally) polarized mode inside the waveguide produces theta-polarized (phi-polarized) radiation. The pointing angle is approximately 50°, the same for both beams. The simulated cross-polarization values are very low according to the simulations. Moreover, the directivity of each orthogonal beam is controlled by the dimensions of the cross-shaped slot. Weather observation radars are considered as a privileged potential application of this kind of systems. Two different prototypes of this LWA+OMT subsystem (one operating at 30 GHz and the other one at 60 GHz, both achieving gains above 15 dB) are currently being manufactured by SWISSto12. The prototypes and their performance will be included in the final paper. [1] de Rijk, E.; Silva, J.S.; Capdevila, S.; Favre, M.; Billod, M.; Macor, A.; von Bieren, A.; "Additive Manufactured RF components based of Stereo-Lithography", in Antenna and RF Systems for Space Science 36th ESA Antenna Workshop, 6-9 Oct 2015 [2] M. Garcia-Vigueras, M. Esquius-Morote and J.R.Mosig, "Dual-polarized one-dimensional leaky wave antenna," 9th European Conference on  Antennas and Propagation (EuCAP), Lisbon, Portugal, 13-17 April 2015, pp.1-2.

A number of European Space Agency's (ESA) initiatives planned for the current decade require metrology level accuracy antenna measurements at frequencies extending from L-band to as low as 400 MHz. The BIOMASS radar, the Galileo navigation and search and rescue services could be mentioned among others. To address the needs, the Technical University of Denmark (DTU), who operates ESA’s external reference laboratory “DTU-ESA Spherical Near-Field (SNF) Antenna Test Facility”, in years 2009-2011 developed a 0.4-1.2 GHz wide-band higher-order probe. Even though the probe was manufactured of light-weight materials -- aluminium and carbon-fibre-reinforced polymer (CFRP) -- it still weighs 22.5 kg and cannot be handled by a single person without proper lifting tools. Besides that, a higher-order probe correction technique necessary to process the measurement data obtained with such a probe is by far more demanding in terms of the computational complexity as well as in terms of calibration and post- processing time than the first-order probe correction. On the other hand, conventional first-order probes for SNF antenna measurements utilizing open-ended cylindrical waveguides or conical horns fed by cylindrical waveguides operating in the fundamental TE11-mode regime also become excessively bulky and heavy as frequency decreases, and already at 1 GHz an open-ended cylindrical waveguide probe is challengingly large. For example, the largest first-order probe at the DTU-ESA SNF Antenna Test Facility operates in the frequency band 1.4–1.65 GHz and weighs 12 kg. At 400 MHz, a classical first-order probe can easily exceed 1 cubic meter in size and reach 25-30 kg in weight. In this contribution, a compact P-band dual-polarized first-order probe is presented. The probe is based on a concept of a superdirective linear array of electrically small resonant magnetic dipole radiators. The height of the probe is just 365 mm over a 720-mm circular ground plane and it weighs less than 5 kg. The probe covers the bandwidth 421-444 MHz with more than 9 dBi directivity and |µ| ? 1 modes suppressed below -35 dB. The probe design, fabrication, and test results will be discussed.

Anisotropic material characterization requires versatile sample fixtures in order to provide sufficient measurement diversity for material parameter extraction.  However, extensive sample preparation is often required prior to making a measurement, especially for anisotropic materials.  An alternative nondestructive material measurement approach using a Single Port Waveguide Probe (SPWP) is proposed to simplify measurement of uniaxial anisotropic media.  Instead of cutting a material sample to fit into a given fixture, nondestructively interrogating a sheet of material via the SPWP greatly simplifies sample preparation and measurement.  The SPWP system measures a metal-backed sample of a known thickness.  A flange with a waveguide aperture cut in the center is placed on the metal backed sample (thus forming a parallel plate region) and a length of rectangular waveguide is connected to the flange aperture. A Vector Network Analyzer port is connected to the end of the rectangular waveguide to collect calibration and sample data.  Measurements of two different thicknesses of a sample are performed to provide sufficient data for extracting the sample permittivity tensor.  The sample permittivity tensor is computed via comparison of the measured and theoretical S-parameters using a least squares minimization algorithm.  The theoretical S-parameters are derived using a magnetic field integral equation which utilizes a uniaxial parallel plate Green’s function to constitute the fields in the parallel plate region.  Love’s Equivalence Principle is used to relate the fields in the parallel plate flange region to the fields in the waveguide (assumed to be the dominant TE10 mode only).  In this paper, the SPWP theoretical development, measurement and material parameter extraction are discussed.  Measurements and simulations of isotropic and uniaxial samples are made to assess the SPWP performance.

Indoor antenna ranges must have the walls, floor and ceiling treated with RF absorber. The normal incidence performance of the absorber is usually provided by the manufacturers of the materials, however, the bi-static or off angle performance must also be known. Some manufacturers provide factors at discrete electrical thickness for a discrete range of incident angles. This approximation is based on the curves presented in [1]. In reference [2], a polynomial approximation was introduced. In this paper, a more accurate approximation is introduced. Pyramidal RF absorber is modeled using CST’s frequency domain solver. The numerical results are compared to results from other numerical methods. The highest reflectivity of the two principal polarizations for a given angle of incidence and thickness of material is calculated. Different physical thickness pyramids are modeled. Once the worst case reflectivity is calculated, a polynomial curve fit is done to get a set of equations that provide the bi-static performance for absorber as a function of angle of incidence and thickness of material. The equations can be used to predict the necessary RF absorber to treat the walls of an indoor range.

Recent interest in anisotropic metamaterials and devices made from these materials has increased the need for advanced RF material characterization. Moreover, the quest for measurement of inhomogeneous and anisotropic materials at VHF and UHF frequencies has long been one of the primary stretch goals of the RF materials measurement community. To date, the only viable method for these types of materials has been either fully filled or partially filled VHF waveguides, which are large, expensive, and slow. This paper introduces a new fixture design that greatly simplifies the process of obtaining intrinsic properties for inhomogeneous and anisotropic dielectric materials. The fixture combines low frequency capacitance and high frequency coaxial airline concepts to measure cube shaped specimens, and is termed an “RF Capacitor”. Furthermore, a significant limitation of past measurement methods is their reliance on approximate analytical models to invert material properties. These analytical models restrict the available geometries and frequency ranges that a measurement fixture can have. The present method avoids this limitation by implementing a new inversion technique based on a full-wave, finite difference time domain (FDTD) solver to exactly model the measurement geometry. In addition, this FDTD solver is applied in a novel way to enable inversion of frequency-dependent dielectric properties within seconds. This paper presents the fixture design and calibration for this new measurement method, along with example measurements of isotropic and anisotropic dielectric materials. In particular, 3” cube specimens are measured and the bulk dielectric properties in the three principal planes are determined by measuring the same specimen in three different orientations within the measurement fixture. Finally, calculations are presented to show the relative accuracy of this method against a number of probable uncertainty sources, for some characteristic materials.

In the recent years, the microwave and mm wave communities have been experiencing a strong interest in the characterisation of the RF proprieties of materials used in the manufacture of antennas and structures that, in one way or another, interact with propagating electromagnetic fields. Of particular interest are materials used for for space applications, where antennas face a harsh environment at all times making it challenging to keep antenna performances in all orbital conditions, whether in eclipse or under full sunlight exposure. A particular example is the coming Solar Orbiter mission, where the antenna reflector will be exposed to a high intensity of solar energy. This paper describes a measurement system with a custom-built setup that enables the measurement of reflectivity losses of space antenna materials and coatings at very high temperatures - up to 500 degrees Celsius. The design of the high temperature fixture will be presented in detail, together with the development of the necessary measurement and calibration techniques. The paper will conclude with a critical assessment of the obtained results and system performance and achieved accuracies.

As millimeter-wave applications become more widely available technologies, there is a demand to know material properties for design and application purposes.  However, many mass produced materials are either not specified at these frequencies or the price materials can be costly. Therefore the easiest method for characterization is by measurement. Traditional methods of this measurement type involve the reflectivity of a fabric sample placed on a flat metallic reference plate. However, this method has some major difficulties at these high frequencies. For example, the surface of the reference plate must be very flat and smooth and must be carefully oriented such that their surface is precisely facing the transmitting and receive and antennas. Furthermore the electrically large size of the reference plate of this setup makes it difficult to measure in far-field and anechoic range time is expensive.  Resistive and conductive fabrics have applications such as shielding, anti-static, and radio wave absorption. Radio wave absorption and radar cross section engineering is currently of high interest to the automotive industry for testing newly emerging automotive radar systems. Such fabric measurement has already been utilized to accurately characterize artificial skin for radar mannequins to recreate the backscattering of human targets at 77 GHz. This paper presents a new and convenient method for measuring the reflective properties of conductive and resistive materials at millimeter wave frequencies by wrapping fabrics around a metallic reference cylinder. This new approach to fabric characterization method is able to obtain higher accuracy and repeatability despite the difficulties of measuring at high frequency.

Rapid advances in material fabrication capability, such as 3D printing, have made the realization of engineered complex media (i.e., anisotropic and bianisotropic materials) possible.  One of the primary aspects prompting the interest in complex media is the added control over scattered electromagnetic fields due to the increase in the number of constitutive parameters.  Isotropic media are characterized by the 2 well-known scalar parameters of permittivity and permeability.  However, in general, it requires 18 and 36 parameters to describe anisotropic and bianisotropic media, respectively.  Although the increase in parameter space provides more control over electromagnetic response, the penalty to pay is the added complexity in theoretical analysis when compared to isotropic media.  One method that has been developed for the analysis of complex media is the six-vector field formalism which casts Maxwell’s equations into matrix form for ease of manipulation.  Although this formalism handles fully populated permittivity and permeability tensors, inversion of a block 3x3 (i.e., 6x6) matrix is required which is mathematically intensive and physical insight can be obscured since a cofactor-based inversion is often employed in the solution process.  The goal of this work is to develop a scalar potential formulation capable of handling gyrotropic media.  Advantages and limitations of the formulation will be discussed and relevant examples will be provided to demonstrate the simplicity and physically-intuitive nature of the technique.  Future work involving the use of the scalar potential formulation in the analysis of antenna, guided wave structures and material characterization of complex media will also be discussed to demonstrate the promising aspects of the technique.

Crystallographic sample design of complex media influences material tensor properties. These properties offer amplitude, phase and polarization control of the electromagnetic (EM) fields. Previous works have evaluated crystallographic sample designs for isotropic, uniaxial and biaxial anisotropic media, each respective design offering more ways to control the fields.  The tensor elements for these designs are all aligned along the main diagonal of the permittivity and/or permeability tensors.  Additional field control can be obtained by producing materials that have off-diagonal tensor elements in addition to the aforementioned main diagonal elements.  A monoclinic crystal sample design supports the existence of two off-diagonal elements and offers more field control than biaxial anisotropic media.  In this work, field analysis is performed on media that possesses a monoclinic tensor element arrangement, demonstrating the additional control over EM fields as compared to biaxial anisotropic media. A monoclinic sample is then constituted using crystallographic symmetry.  Future work will yield the development and analysis of a monoclinic sample material measurement capability.

In this paper, a patch antenna has been designed based on the complementary split ring resonator (CSRRs), complementary rose curve resonators (CRCRs) and without using these inclusions. Complementary rose curve resonators (CRCRs) are used in design of patch antenna. The Patch antenna based on the complementary rose curve resonators (CRCRs) are achieved by patterning the ground plane under the conductor trace. The perimeter of the Rose curve can be adjusted by tuning the amplitude of the sine function and the radius of the base circle.  With the order of CRCRs, the loading effect of the complementary resonators on the patch antenna is controlled. This works demonstrated that higher order CRCRs allows more compactness of the design and higher miniaturization factor. We proposed a compact patch antenna based on the complementary split ring resonator (CSRRs) and the complementary Rose curve resonator (CRCRs). The proposed patch antenna shows good performances which is designed to operate at 2.4 GHz. The results demonstrate the configurability of the design for a specific size. The results show the effectiveness of using metamaterials in microwave circuit can obtain from n to n+1 of the CRCRs order will result in 0.3 % miniaturization. IndexTerms:  Patch Antenna, Metamaterial, Size Reduction, split ring Resonators, Rose Curve Resonators

Several instances in antenna design are known where an anisotropic material is useful ; however, finding a naturally occurring anisotropic material with the required dielectric tensor is often an impossibility. Therefore, artificial anisotropic dielectric materials must be designed, tested, and implemented.             In this paper we shall present a layered artificial anisotropic dielectric material with a biaxial permittivity tensor. This material is designed to be used in conjunction with an antenna in order to improve antenna bandwidth. The design motivation behind this material shall be discussed, along with its implementation, the measurement of its permittivity tensor, and testing characterization with a prototype antenna. Results from CST Microwave Studio® simulations and the mixing rules from dielectric material science will be compared with the measured data. Test fixture design and instrumentation will also be presented. Predictions on various types of artificial anisotropic dielectrics suitable for future applications will also be discussed.

Constitutive parameter characterization of a biaxial anisotropic material using a rectangular waveguide requires three separate samples; each one a different orientation of the parent biaxial anisotropic sample.  The Waveguide Rectangular to Waveguide Square (WRWS) characterization method is an alternative, more efficient method, to the rectangular waveguide method because the WRWS method requires only one cube sample of biaxial anisotropic material to perform complete parameter extraction. This cube sample fits uniformly without gaps in the waveguide sample holder and can be indexed to accommodate all orientations required for characterization.   The WRWS waveguide transitions insure that only single (TE10) modes are present and thus leads to closed form solutions for the material properties - an advantage over other existing techniques requiring higher-order modal analysis and subsequent numerical root search for extraction.  Each WRWS transition mounts to the sample holder and the waveguide test ports of a Vector Network Analyzer and is calibrated using a TRL technique.  A biaxial anisotropic test sample was designed based upon crystallographic symmetry, mixing theory and verified in rectangular waveguide measurements.  WRWS test data is collected and constitutive parameters are extracted from each orientation of the biaxial anisotropic cube.  This method of extracting biaxial anisotropic constitutive parameters using the WRWS system is evaluated in both experiment, simulation and validates the WRWS method.  Theory, experimental and simulated results are presented to show that a cubic sample and WRWS measurement system can be efficiently and effectively used to measure biaxial anisotropic materials.

A popular method for microwave characterization of materials is the free-space focused beam technique, which uses lenses or shaped reflectors to focus energy onto a confined region of a material specimen. In the 2-18 GHz band, 60 cm diameter lenses are typically spaced 30 to 90 cm from the specimen under test to form a Gaussian focused beam with plane-wave like characteristics at the focal point. This method has proved popular because of its accuracy and flexibility. Another free-space measurement technique that has been employed by some is the use of dielectrically loaded antennas that are placed in close proximity to a specimen. In this alternate technique, the dielectrically loaded antennas are smaller than lenses, making the hardware more compact and lower cost, however this is done at the expense of potentially reduced accuracy. This paper directly compares a standard laboratory focused beam system to a measurement system based on some recently developed RF spot probes. The spot probes are specially designed antennas that are encapsulated in a dielectric and optimized to provide a small illumination spot 3 to 8 cm in front of the probe. Experimental measurements of several dielectric, magnetic, and resistive specimens were measured by both systems for direct comparison. With these data, uncertainty analysis comparisons were made for both fixtures to establish measurement limits and capability differences between the two methods. Understanding these uncertainties and measurement limits are key to implementing compact spot probes in a manufacturing setting for quality assurance purposes.

I. INTRUDUCTION In the heating process of microwave absorbers under incident electromagnetic waves, two disciplines of physics are intertwined, i.e., electromagnetic waves behavior governed by Maxwell’s equations and heat transfer process dictated by laws of thermodynamics. The power density in the absorbers due to the electromagnetic .eld is given by p= s|E|2 =2po0 o ' f|E|2 (1) where, E is the total electric .eld (V/m) in the material, s is electrical conductivity of the material (S/m), o0 is the free space permittivity (8.854 × 10-12 F/m), o' is the imaginary part of the relative dielectric constant, and f is the frequency in Hz. This is point form of the Joule’s law, and is well understood by RF engineers. The EM behavior of the polyurethane absorbers can be numerically computed. The EM .eld acts as the heating source, and its distribution in the absorber can provide a good indication on the locations of hot spots. Polyurethane foam is an excellent insulator, so the conductive heat loss may be minimal. The heat exchanges can be reasonably described by radiation and convection transfers. Radiation takes place in the form of EM wave, mainly in the infrared region. The net power transferred from a body to the surroundings is described by Stefan-Boltzmann’s law [1], prad = osA(T4 -T04 ) (2) where A is the surface area, T is the surface temperature of the radiation body in K, and T0 is the ambient temperature in K. Unfortunately, the conventional symbols used in heat transfer s and o are not the same as those in Eq. (1). s here is the emissivity or emission coef.cient, and is de.ned as the ratio of the actual radiation emitted and the radiation that would be from a black body. o in Eq. (2) is the Stefan-Boltzmann constant (5.67 × 10-8 W/m2 K4 ). The context in the paper should make it clear which symbols the authors are referring to. Otherwise, we will make explicit references. The convective heat transfer is due to the motion of air surrounding the absorbers. Two forms can take place, naturally or by forced air. The relationship is described by Newton’s law of cooling [1]: pconv = hA(T -T0 ) (3) where h is the convection heat transfer coef.cient in (W/m-2 K-1 ). h is often treated as a constant, although it can be a function of the temperature. Eq. (3) assumes that the ambient air is abundant, and is taken to be constant. This is a reasonable assumption, because the heating is typically con.ned to a small localized area in a relatively large anechoic chamber. Combining the two mechanisms of heat transfer, the total heat loss is given by p= osA(T4 -T4 )+ hA(T -T0 ) (4) 0 It is possible to solve for the temperatures from coupled Maxwell’s and heat transfer equations. Realistic results require accurate electrical and thermal properties of the materials. It is often a non-trivial process to obtain the material properties in and of itself. Careful validation is warranted before we can have full con.dence in the results. In this paper, we adopt a measurement approach instead. We conduct a series of experiments to measure the temperature both on the surface of the absorbers using an infrared imaging camera, and internally using thermocouple probes inserted into the absorbers. Temperature pro.les versus applied E .eld are experimentally established. From the measured data, we curve .t to Eq. (4) or other mathematical functions. These functions are useful to calculate results at other .eld levels, e.g., extrapolating to a higher .eld where measurement results cannot be readily obtained. II. FIELD DISTRIBUTION INSIDE THE ABSORBERS Numerical analysis was performed using Ansys HFSS, a commercially available Finite Elements software package. As it was described in [2], symmetry is taken advantage of, so only one quarter of the pyramidal absorber is solved. The quarter pyramid is located inside a square cross section prism that bounds the computational domain. The structure is fed using a port located on the top of the geometry and the side boundaries of the domain are set as perfect electric conductor (PEC) or perfect magnetic conductor (PMC). The base is modeled as PEC. This is exactly the same approach taken in [2]. The structure of a CRV-23PCL-4 is analyzed at 12.4 GHz, the same frequency as used in the measurements. The resulting .eld is extracted at one plane. The plane is one of the two orthogonal planes that cut the pyramid in 4 sections. Fig. 1 shows the .eld distribution at 12.4 GHz. The curvature of the absorber pro.le has been added for clarity. The results are an approximation. The permittivity of the material is assumed to be fairly constant from 6 GHz to 12 GHz. The purpose of the numerical analysis is to check the expected .eld distribution in the pyramid, which we can use to compare with the infrared (IR) images of the absorbers taken during the measurements. Fig. 1. Electric Field distribution at 12.4 GHz The .eld distribution data shows that most of the .eld exists on the upper third of the pyramid. It also shows that there is a region of high .eld existing in the valleys between the pyramids. The surface temperature pro.le from the IR pictures shows that this is an real phenomena. On the other hand, the .eld is higher at the very tip of the absorber. Measurements from the IR images seem to contradict this result. This can be explained. Since the tip is smaller, it cools faster to the surrounding ambient temperature. III. EXPERIMENTAL SETUP AND DATA Experiments were performed on ETS-Lindgren CRV-23PCL-8, and CRV-23PCL-4 absorbers at 12.4 GHz. Both types are 23” long from tips to bases. A piece has a base size of 2’ × 2’. A CRV-23PCL-8 piece consists of 8×8=64 pyramids, whereas a CRV-23PCL-4 piece consists of 4×4=16 pyramids. The two types are designed to have similar RF performances, but the CRV-23PCL-8 is made of slender pyramids to facilitate better heat transfers to the surroundings [2]. The absorbers are mounted on a particle board with metallic backings, and are placed in front a Ku band horn antenna with a circular aperture (the gain is approximately 20 dBi). A 300W ampli.er is used, and the power to the antenna is monitored through a 40 dB directional coupler connected to a power meter. The test setup is shown in Fig. 2. The ambient temperature is at 23.C. Fig. 2. Test setup using a conical horn antenna to illuminate the absorbers As a .rst step, a 200 V/m .eld is generated by leveling to a calibrated electric .eld probe. The distance from the probe to the antenna is 30”. At this distance, near .eld coupling is assumed neglegible, and the incident wave uniform (numerical simulation also validated these assumptions). The power needed to generate 200 V/m .eld is recorded. Next, the .eld probe is replaced with the absorbers under test. The tips of the absorbers are placed at the same distance (30”) from the antenna. Other .eld strengths can be leveled by scaling from the power for 200 V/m. A. Surface Temperature Figs. 3 and 4 show two examples of the infrared images taken after the temperature reached equilibrium under a constant 700 V/m CW at f=12.4 GHz for the two types of absorbers described earlier. There is no forced air.ow during the measurement. Table 1 summarizes the resulting temperatures on the absorber surfaces at different .eld levels. Tests were performed on two .nishes of otherwise identical CRV-23PCL-8 absorbers, i.e., fully covered with rubberized paint, or with latex paint. The data indicates that the paint has minimal effects on absorber temperatures. Table 1 also lists data for the wider CRV-23PCL-4 absorbers (with latex paint). B. Internal Temperature of the Absorber recorded by Thermocouples Three thermocouples are inserted in the CRV-23PCL-8 which are painted with rubberized coating. They are inserted at distances of 4”, 6”, and 8” from the tip of the pyramid, as illustrated in Fig. 5. Fig. 6 shows the temperatures measured by the three sensors. The temperatures at 8” from the tip are consistently higher than at other locations. There is a gap in the data at 700 V/m because RF power was turned off brie.y. Internal temperature reached 115 .C under 1.7 kW/m2 Fig. 3. Infrared camera image for incident electric .eld of 700 V/m. The absorber is the slender CRV-23PCL-8. Fig. 4. Infrared camera image for incident electric .eld of 700 V/m. The absorber is the wider CRV-23PCL-4. (800 V/m). Since the maximum allowed temperature for the polyurethane foam material is 125 .C, the incident power density is recommended to stay less than 1.7 kW/m2 for CRV-23PCL-8 absorbers mounted vertically and with natural convection in a 23.C room. After the temperature reached equilibrium under 800 V/m, additional air.ow was introduced by turning on a 6” diameter fan at 45” in front of the absorbers. The air.ow rate was measured to be approximately 80 ft/min at this distance. Note that this is a rather moderate air.ow, which can arise naturally from air-conditioning vents in a chamber. As shown in Fig. 6, the internal temperature quickly dropped to 102.C from 115.C. TABLE I MAXIMUM SURFACE TEMPERATURE RECORDED BY THE IR CAMERA (AT EQUILIBRIUM). T0 =23. C. E Power CRV-23PCL-8 CRV-23PCL-8 CRV-23PCL-4 (V/m) Density rubberized latex (. C) rubberized (kW/m2 ) (. C) (. C) 200 0.11 24 300 0.24 28 360 0.34 30 400 0.42 35 36 43 500 0.66 41 50 600 0.95 54 67 700 1.30 63 82

Abstract—A new technique is presented to measure the permittivity and permeability of conductor-backed magnetic absorbing materials using a triaxial probe. The probe consists of two coaxial transmission lines that share an aperture in a conducting flange, which is placed against the sample creating a two-port network. By measuring the reflection coefficients at each port and the transmission between the ports, the material parameters may be determined. This paper describes the technique and provides a theoretical method for computing the S-parameters of the triaxial system. Experimental implementation of the system is still under study.