M. J. Akhtar

A waveguide-based two-step approach for measuring complex permittivity tensor of uniaxial composite materials

A rectangular waveguide-based two-step approach for measuring the complex permittivity tensor of uniaxial highly lossy nonmagnetic composite materials in the S-band is presented. In the proposed scheme, two independent sets of reflection and transmission coefficient data for each material-under-test (MUT) are measured by aligning the electric field vector of the dominant TE/sub 10/ mode in the rectangular waveguide parallel and perpendicular to the fiber orientation of the uniaxial sample, respectively. The complex permittivity tensor of the MUT is determined from these measured scattering data in two successive steps. The first step uses the newly proposed analytical approach, which can resolve the ambiguity problem, commonly encountered with samples of electrical length larger than a wavelength. In the second step, nonlinear least square optimization algorithms are employed, where the material parameters using the first step are now used as the initial guess. The proposed two-step approach is valid for multilayered structures, and the local minima problem commonly encountered with optimization routines are also avoided. A number of carbon-fiber composite materials along and, transverse to the fiber orientation are measured using the proposed method. Finally, a brief uncertainty analysis, to study the effect of air-gaps on waveguide measurements, is carried out.

Reconstructing permittivity profiles using integral transforms and improved renormalization techniques

Some new ideas for reconstructing permittivity profiles in planar and cylindrical objects illuminated by TEM-, TE- or TM-polarized waves are presented in this paper. For a planar medium, an improved renormalization technique along with a revised version of the nonlinear Riccati differential equation describing the direct problem are introduced. A nonlinear Riccati-similar differential equation for the cylindrical case has also been derived here for the first time, which helps reconstructing radially varying permittivity profiles in a way parallel to that of the planar case. The above-mentioned renormalization technique has been used for the cylindrical case as well to solve the inverse problem making use of a Hankel transform. The method represents fundamental bases for a three-dimensional generalization, which is essential for microwave imaging used, e.g., in biomedical applications and for the diagnostic of diseases in trees and vegetation. A known permittivity profile has been taken to generate synthetic reflection-coefficient data by solving the nonlinear equations describing the direct problems using MATLAB. These data have been used in conjunction with the proposed technique to reconstruct the permittivity profile. About 50-100 data points over the wavelength range from a minimum value (ranging from one-tenth to one-fifth of a typical length in the structure) to infinity have been used for the reconstruction. Reconstructed profiles have been compared to the original ones for a number of cases. Deviations of less than 2% have been achieved.

Design and Application of the CSRR-Based Planar Sensor for Noninvasive Measurement of Complex Permittivity

A novel microwave noninvasive planar sensor based on the complementary split ring resonator (CSRR) is proposed for an accurate measurement of the complex permittivity of materials. The CSRR is etched in the ground plane of the planar microstrip line. Two CSRRs of rectangular and circular cross-sections are chosen for the sensitivity analysis, where the later is found to possess higher sensitivity and hence appears to be more appropriate for the sensor design. At resonance, the electric field induced along the plane of CSRR is found to be quite sensitive for the characterization of specimen kept in contact with the sensor. A numerical model is developed here for the calculation of the complex permittivity as a function of resonant frequency and the quality factor data using the electromagnetic simulator, the Computer Simulation Technology. For practical applications, a detailed air gap analysis is carried out to consider the effect of any air gap present between the test sample and the CSRR. The designed sensor is fabricated and tested, and accordingly the numerically established relations are experimentally verified for various reference samples e.g., teflon, polyvinyl chloride, plexiglas, polyethylene, rubber, and wood. Experimentally, it is found that the permittivity measurement using the proposed sensor is possible with a typical error of 3%.

A Generalized Rectangular Cavity Approach for Determination of Complex Permittivity of Materials

A novel cavity-based unified approach to measure the complex permittivity of dielectric samples placed in the E-plane of a rectangular cavity is presented. The proposed generalized cavity method is not limited to test specimens of smaller electrical dimensions, and requires two basic steps. The first step modifies the conventional cavity perturbation technique, where the effects of possible air gap between the cavity slot and the test specimen are also considered. The second step of the proposed approach employs a numerical optimization scheme, where the actual 3-D geometry of the fabricated cavity is simulated using the numerical field simulator, the Computer Simulation Technology (CST) Microwave Studio. The dielectric properties of the test specimen in this case are determined with the help of a MATLAB-based optimization routine, which calls the CST modules over the component object model interface and minimizes the error between the measured and the simulated scattering coefficients. The permittivity of the test specimen determined using the first step is provided as the initial guess to improve the convergence of the numerical optimization scheme. The proposed unified approach is validated by designing two rectangular cavities having different slot sizes operating in the TE107 mode. A number of standard dielectric samples are measured with the help of a vector network analyzer, and a very good agreement is observed between the measured permittivity values and the published data available in the literature having a typical error of less than 2% for samples of even larger dimensions.

Design of a Coplanar Sensor for RF Characterization of Thin Dielectric Samples

A multilayered conductor backed coplanar waveguide (MCCPW) sensor for the non-destructive characterization of thin dielectric samples in the RF and microwave frequency band is designed and developed. The newly designed sensor allows the measurement of complex permittivity of thin dielectric samples over a wide frequency band in a non-destructive way as it does not require any special sample preparation except for the fact that the surface of the test sample should be flat for good contact with the coplanar waveguide. The overall procedure is based on the measurement of scattering parameters of the test specimen placed at the top of the designed coplanar sensor in the specified frequency band using the vector network analyzer. The measured scattering data are then employed to compute the effective permittivity of the coplanar (MCCPW) structure using the revised form of the reflection-transmission approach. From the practical point of view, the advantage of the proposed technique is that it employs only two SMA to coplanar end launchers in lieu of the expensive microwave probe stations commonly being used in the past for carrying out such kinds of measurements. The applicability of the designed sensor is tested by extracting the permittivity of a number of reference samples from both the simulated and the experimental data.

Noninvasive Procedure for Measuring the Complex Permittivity of Resins, Catalysts, and Other Liquids Using a Partially Filled Rectangular Waveguide Structure

A waveguide based noninvasive procedure to measure the complex permittivity of epoxy resins and catalysts normally employed in the composite industry is presented. The proposed method combines an analytical approach with a numerical optimization technique, and is based on the injection of the liquid under test beforehand into a cuvette (disposable container) with rectangular cross section. The cuvette filled with the liquid specimen is positioned at the center of a WR-340 rectangular waveguide for measuring the scattering coefficient data in the S-band. The approximate value of the complex permittivity of the specimen is reconstructed from the measured scattering coefficient data using the newly proposed analytical closed-form relations. These analytical expressions are based on derivation of the transcendental equation for the multilayered partially filled waveguide structure using the transverse resonance method. In order to determine quite accurate values of dielectric parameters of the liquid specimen, the experimental setup is simulated with the help of a 3-D full-wave electromagnetic field simulator and accordingly theoretical values of the scattering coefficients are computed. The complex permittivity of the liquid specimen in this case is determined using an optimization algorithm, which minimizes the error between the theoretical and measured values of scattering coefficients. To avoid the local minima problem commonly encountered with optimization routines and to increase the convergence rate, the complex permittivity of the specimen reconstructed using the analytical approach is used as the initial guess. The applicability of the overall procedure is determined by measuring a number of liquid specimens used in the composite industry.

Free-Space Time Domain Position Insensitive Technique for Simultaneous Measurement of Complex Permittivity and Thickness of Lossy Dielectric Samples

A novel time domain measurement technique is proposed to facilitate the simultaneous measurement of electrical properties (complex relative permittivity) and geometrical parameters (thickness) of the material under test (MUT). The overall process is noninvasive and noncontacting, which uses the measured scattering data of the MUT in the equivalent time domain or spatial domain. The effective time domain scattering data are employed to detect the primary and secondary peaks of the overall reflection and transmission coefficients. To this end, a novel algorithm is proposed to obtain the complex permittivity and thickness of the MUT in terms of extracted reflection and transmission power peaks. From the practical point of view, the main advantage of the proposed scheme is that one avoids the complicated calibration procedure normally required to define the reference plane. For increasing the accuracy of the overall reconstruction process, an automated optimization procedure based on parameter sensitivity analysis is proposed, which uses standard time gating procedure to implement the corresponding direct problem. The proposed technique is validated by extracting the relative permittivity, the dielectric loss (effective conductivity), and the thickness of various standard materials, such as polyethylene, Plexiglas, PVC, mortar, nylon, and so on, and comparing the extracted data with their values available in the literature.

Hemisphere lens-loaded Vivaldi antenna for time domain microwave imaging of concealed objects

Abstract The hemisphere lens-loaded Vivaldi antenna for the microwave imaging applications is designed and tested in this paper. The proposed antenna is designed to work in the wide frequency band of 1–14 GHz, and is fabricated on the FR-4 substrate. The directivity of the proposed Vivaldi antenna is enhanced using a hemispherical shape dielectric lens, which is fixed on the end-fire direction of the antenna. The proposed antenna is well suited for the microwave imaging applications because of the wide frequency range and high directivity. The design of the antenna is carried out using the CST microwave studio, and various parameters such as the return loss, the radiation pattern, the directivity, and input impedance are optimized. The maximum improvement of 4.19 dB in the directivity is observed with the designed hemisphere lens. The antenna design is validated by fabricating and testing it in an anechoic environment. Finally, the designed antenna is utilized to establish a setup for measuring the scattering coefficients of various objects and structures in the frequency band of 1–14 GHz. The two-dimensional (2D) microwave images of these objects are successfully obtained in terms of the measured wide band scattering data using a novel time domain inverse scattering approach, which shows the applicability of the proposed antenna.

Investigation on electromagnetic characteristics, microwave absorption, thermal and mechanical properties of ferromagnetic cobalt–polystyrene composites in the X-band (8.4–12.4 GHz)

The electromagnetic, thermal and mechanical properties of ferromagnetic cobalt–polystyrene composites in the X-band (8.4–12.4 GHz) are investigated in order to explore their usage for wide band microwave absorbers. The cobalt–polystyrene composites are prepared by mechanical blending method using automated injection molding equipment. The microwave absorption properties of cobalt–polystyrene (Co–PS) composites with different cobalt weight ratios are investigated in order to determine the optimum weight ratio for design of efficient microwave absorbers. In order to understand the electromagnetic absorption process at micro level, the X-ray diffraction (XRD) and scanning electron microscopy (SEM) of various samples are carried out to obtain information about the existence and dispersion of Co filler in the Co–PS composite samples, respectively. The thermal stability of the synthesized Co–PS composites is analyzed using the thermo gravimetric analysis (TGA), while the surface hardness is measured using Shore D hardness tool. The tensile and flexural tests are performed to find out the mechanical properties of the molded composites. The complex permittivity (e) and permeability (μ) of the Co–PS composites are extracted from the scattering data obtained using the vector network analyzer (VNA) measurements in the X-band of microwave frequency. The reflection losses (RL) in the composites are calculated using the complex permittivity and permeability parameters. The minimum reflection loss (maximum absorption) of −19.85 dB (98.96%) at 10.22 GHz is achieved for 30 wt% Co–PS composite with thickness of 5 mm, and this value reaches to −31.6 dB (99.93%) at 9.04 GHz with thickness of 10 mm. For 5 wt% Co–PS composite, the minimum reflection loss of −4.90 dB (67.66%) at 10.72 GHz is achieved with thickness of 5 mm. The experimental results reveal that the microwave absorption properties of the synthesized composites in the X-band can be improved by changing the ferromagnetic cobalt weight ratios in the composite.

An Improved Rectangular Cavity Approach for Measurement of Complex Permeability of Materials

An improved rectangular cavity (RC) approach is proposed for the accurate complex permeability determination of materials in the microwave frequency band. The proposed approach assumes the bar-shaped magnetic specimen to be placed along the width of the cavity to increase the sensitivity of the measurement. A generalized closed-form formula is derived accordingly to determine the complex permeability of these bar-shaped samples in terms of the cavity parameters measured under both loaded and unloaded conditions. The proposed formula is found to improve the accuracy of the original RC approach where samples are placed in the H-plane traversing the maximum width of the cavity for permeability measurement. The improvement in accuracy is facilitated by considering the sinusoidal magnetic field variation over the test sample, which is otherwise neglected in most of the earlier approaches. The modified formula is numerically tested for a number of samples having wide range of permeability variations, and the obtained results are typically 40% more accurate than the values obtained using the original formula. Finally, the synthesized magnetic samples, viz., the carbonyl iron-epoxy composite and the manganese ferrite, are measured by placing them inside the fabricated X-band cavity with the help of a vector network analyzer. The proposed approach is quite advantageous for magnetic materials as finite-size samples having sample to cavity volume ratio of less than 3e-3 can be characterized quite accurately with typical errors of 2% and 3% in the real and imaginary parts of the complex permeability, respectively.