NONDESTRUCTIVE COMPLEX PERMITTIVITY AND PERMEABILITY EXTRACTION USING A TWO-LAYER DUAL-WAVEGUIDE PROBE MEASUREMENT GEOMETRY

The permittivity and permeability are important parameters to characterize the electromagnetic characteristics of materials. In order to solve the problem of the limitation of material processing shape and accuracy in the calculation, this paper proposes a method to calculate the complex permittivity and permeability of materials by using CST simulation, trust region algorithm and measured S parameters based on rectangular waveguide method (one of transmission/reflection method). In this paper, the performance of four common CST optimization algorithms in this problem is compared, and the effectiveness of the method is verified by using PTFE material.

A new free-wave method for measuring complex permittivity and permeability of materials at mm-wave frequencies is introduced. The use of time gating for removing the unwanted reflections within the sample, and its advantages in simplifying the calculations and decreasing the dependence of measurement accuracy on frequency are discussed. The error due to imperfect gate parameters is derived by simulation, and the optimum sample thickness is recommended. Examples of results obtained from measurements of ferrite and dielectric samples are presented and discussed. >

A broadband method is reported for the simultaneous measurement of the complex permeability and permittivity of lossy microwave solid materials or liquids that uses an automatic network analyzer technique. Two reflection coefficient measurements are made for two different thicknesses of the same material. It is shown that the most useful cases arise when the pairs of thicknesses d and 2d, d and 3d, or 2d and 4d are used, where d is the smallest available thickness of the material to be measured. Both theoretical and practical aspects of the technique are discussed. >

The Electromagnetic Stirring (EMS) technology has wide applications in the metal continuous casting. Stirring consists of exciting variable magnetic field in metal liquid, the magnetic field generates induction current. The induction current in the metal flow interacts with magnetic filed to generate EM force, which makes perfect motion to improve casting. The EM force strength is proportional with square of the magnetic field strength. The key of the optimized control of EMS is to adjust several parameters for best EM force and deep magnetic penetration. In this paper, we present a new AGILD EMS modeling. We use Maxwell magnetic field differential equation to replace the reduced magnetic field equation. We present new volume magnetic differential integral equation and new boundary strip magnetic field differential integral equation which are proposed by XIe and Li in GLGEO. According to the new AGILD EM modeling in [1], we developed 3D AGILD EMS modeling. Our AGILD EMS modeling does not need any complex boundary condition. The matrix equations are decomposed by GILD parallel processes. Therefore, our AGILD EMS modeling is fast and accurate without any boundary error. Our AGILD EMS modeling can simulate multiple strands and EMSs together. The simulation shows that the AGILD EMS modeling is very powerful tool for the design of excellent EMS system in Billent/Bloom and metal continuous casting system. The simulation is performed by using GLGEO’s new GL[2-4] and AGILD EMS modeling software. The EMS is an established technology and installed in Billet, Bloom and metal casters. The stirring consists of exciting variable magnetic field which is penetrating in the steel, iron, and metal liquid. The magnetic field generates induction electric current in the metal liquid. The induction current in the metal liquid interacts with the magnetic field to generate EM force which drives the metal liquid flow motion such that the casting is perfectly performing. The casting quality is improved by reduced segregation and porosity through transformation to an equiaxed solidification structure. The steel and iron productions are increasing due to the increased casting speeds. The temperature and carbon component are key factors for high quality steel. The magnetic field penetrating distribution depends on the material properties and high temperature. Moreover, the electromagnetic properties depend on the temperature. The temperature difference between outer and insider of the caster mold is very large. We consider the magnetic conductivity be space variable. The reduced magnetic field equation is no longer to govern this case. In this paper, we use the magnetic field Maxwell equation to replace the reduced magnetic equation. Moreover, we present a new strip magnetic field differential integral equation which is proposed by Xie and Li in [1]. We use the new strip integral equation on the double layered boundary and the magnetic field Garlekin equation in the internal domain to construct the AGILD EMS modeling for the metal continuous casting. It has more advantages over FEM and FD modeling. The AGILD and GL EMS modeling, GL and AGILD nondestructive testing, GL and AGILD heating modeling, and GL and AGILD heavier viscosity flow modeling for the continuous casting are developed by Xie and Li in GLGEO. Many EM research works on motor need the condition that the magnetic resistivity monotone increasedly depends on the magnetic induction. It is very strong and unpractical condition. In practice, magnetic resistivity is not monotone increasing but has a minimum point at B = B0. Our nonlinear FEM EM modeling [10-12] are available for the above practical condition, i.e. the magnetic resistivity is not monotone increasing. We prove that if H(B) monotone increasedly depends on B, the nonlinear FEM is convergent. Because H(B) = υ(B)B, so, we only need that υ(B)B monotone increasedly depends on the B, which is widely generalized. Moreover, the H(B)’s monotone property is the practical physical property. Our nonlinear FEM magnetic DC modeling is briefly described in this paper. The organization of the paper is as follows. We present the new strip differential integral equation in the section 2 which is proposed in [1]. The double layered collocation FEM equation for the magnetic field is

With the development of electronic components towards miniaturization and integration, permittivity, permeability, loss tangent and other microwave parameters have become the characteristics of new microwave materials. The relative complex permittivity and relative magnetic permeability of solid materials are the most important for microwave electrical elements, componentsor antennas design. In this paper we introduce the method of measuring relative complex permittivity and relative magnetic permeability of solid materials at 30MHz∼50GHz frequencies using air coaxial line and waveguide. The paper describes how to make phase compensation to solve the issue brought by the calibration of the network analyzer and how to re-calculate the S parameters using phase compensation technology.

We present an extended analytic technique for calculating the permeability and permittivity spectra of granular materials. It addresses the relationship between grain properties, their size relative to the wavelength, and the permeability and permittivity spectra of polycrystalline material. The scattered multipolar fields about a single sphere are related to the polarizability of an ordered congregation of such spheres. The product of the external wave vector k and sphere radius a is small and the product of the internal wave vector ${\mathit{k}}_{\mathit{i}}$ and a unrestricted. The Clausius-Mossotti relation is used in combination with the scattering results to yield an equation that permits us to calculate the effective permeability and permittivity spectra of a cubic array. The result is a variety of possible spectral types, including complex permittivity and permeability spectra that have been measured and explained either by including multiple atomic-level sources or by statistical weighting over an ensemble of grains. This theory predicts both ``classical'' and ``anomalous'' spectra from a single source, as well as certain conglomerate permeability spectra that have been measured and for which no direct explanation is available. Our results show that an understanding of the permeability and permittivity spectra of composite materials cannot be complete without inclusion of a dependence on the ratio of the grain size to the wavelength.

A coaxial-probe-based in-situ broadband measurement system has been established to characterize the complex Electromagnetic (EM) Parameters of magnetic absorbing materials. With an emphasis on key techniques for dispersive materials, the Frequency-variation method (FVM) was further studied for simultaneously measuring the both complex permittivity and complex permeability by intentionally varying the test frequency to obtain two different reflections. Criterions for a right order of the interpolation polynomial used to approximate the frequency-dependent EM parameters; measures to reduce the residual mismatch errors in reflection measurements and to suppress the ambiguities in solving the transcendent equation system were discussed in detail. Several typical dispersive absorbing coatings have been tested via FVM. The good comparison between the measured results and reference ones validate the feasibility of the proposed improved technique.

Magnetodielectric (MD) materials find application in many areas of microwave engineering, and therefore, measurement of their dielectric and magnetic properties is very important. This paper presents a novel MD material characterization method using the cavity perturbation technique (CPT) with substrate-integrated waveguide (SIW) cavity resonators. Frequency dependent complex permittivity and permeability of MD material can be extracted with a single SIW cavity structure by inserting the sample material into different locations. The fundamental theory of CPT is explained and its analysis for SIW cavity is discussed. Cobalt nanoparticles are synthesized with a fluoropolymer matrix to realize the MD materials and their properties are measured in the frequency range 1-4 GHz. The effect of volume fraction and density of the synthesized MD materials on the dielectric and magnetic properties has been studied.

A measurement technique for the broadband determination of the complex permittivity and permeability of isotropic film‐shaped materials is presented. εr and μr are computed from S‐parameter measurements of microstrip lines propagating in the dominant mode and used as cells. The material under test is the microstrip‐line substrate, which is the original feature of this method in comparison with existing techniques. This leads to a simple and reproducible measurement process. Measurements for several materials in the 0.05–40 GHz frequency range show good agreement between measured and predicted data. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 65–69, 2001.

In the microwave regime, electromagnetic (EM) interference is considered as a crucial problem and EM shielding techniques are widely used to mitigate this issue. Apart from general application in radar cross-section control, EM wave absorbers have become an important element in modern EM devices. As the EM devices are extensively used almost everywhere, the radiation from those devices can interfere with each other and cause a malfunction in results. To avoid this interference, the EM devices need to be well shielded by a metal-backed absorber, where the metal-back layer provides shielding from potential external EM sources, and the absorber helps to reduce the high reflection from metal walls for internal sensors. Modern EM devices are compact and use a wideband of low-microwave frequencies. As the wavelength of EM waves inversely proportional to the operating frequency, the wideband absorber at low-microwave frequencies suffers from the relatively higher thickness and narrow bandwidth. This thesis aims to design, development and characterization of ultra-thin and broadband absorbers operated over low-microwave frequencies for shielding modern compact EM devices and, in doing so, makes five main contributions to the field of EM devices and absorbers.As the designing resonant absorber requires dielectric and magnetic materials with known electric and magnetic properties, the emphasis is given in developing a broadband and accurate characterization technique to measure the complex permittivity and permeability of solid and semi-solid materials, which is the first contribution of this thesis. The proposed technique is based on classical transmission-line analysis, implemented on a strip-line structure. A new calibration technique, namely Object-Reflect-Line (ORL), is proposed to meet the challenge of an extremely low-reflection line for accurate measurement. In the proposed calibration, the Thru standard of conventional Thru-Reflect-Line (TRL) calibration technique is replaced by a standard with a known object. Since the ORL calibration uses only a single device, it reduces the fabrication cost, the measurement complexity, and the potential error in the Thru measurement needed in the TRL method, which uses an additional device. The simulated and measured results with a variety of non-magnetic and magnetic materials demonstrate the effectiveness of the proposed method over broadband at low-microwave frequencies.The second contribution is the development of a low-cost, broadband, and reliable absorptivity measurement system operated over low-microwave frequencies. This measurement system is used to validate the proposed absorbers' performance. The proposed technique is based on parallel-plate waveguide (PPW) and well-suited for frequency selective surface (FSS)-based resonant absorbers. By employing the PPW structure, only a small sample size, i.e. a 1D array of FSS, is required for the measurement. The TRL calibration is implemented to remove the time-gating ambiguity in the conventional PPW-based measurement technique. A measurement system working up to 6 GHz is designed such that its length is adjustable to ensure all three calibration standards (Thru, Reflect, and Line) can be carried out in a single device. Moreover, the height of the PPW is also adjustable to allow the measurement of absorbers with a different periodicity of FSSs.The third contribution is an accurate equivalent-circuit (EC) model-based approach for designing wideband non-magnetic absorbers operating at low-microwave frequencies. The proposed EC model is based on simulated data and synthetic asymptotes for single- and double-layer FSS-based non-magnetic absorbers. Two simple and commonly used resistive FSS, i.e., square patch and single square loop, are considered in this study. Compared to full-wave simulation, the proposed EC model shows more than 95% accuracy. By employing the proposed model and genetic algorithm (GA)-based optimization, several designs of broadband absorbers are demonstrated. The presented non-magnetic absorbers with single- and double-layer FSS show 126% and 161% fractional bandwidth, respectively, with the total thickness very close to the Rozanov limit.The fourth contribution is the design of a thin and broadband FSS-based magnetic absorber for low-microwave frequencies. The design consists of double-layers of FSS with the combination of two different magnetic substrates, which provides a much broader bandwidth compared to existing single-layered designs. The magnetic materials are in-house made by mixing different ratios of carbonyl-iron (CA) powder with a silicone elastomer called polydimethylsiloxane (PDMS). The simple single-square loop structure is used for both FSSs, which are printed on a standard FR4 material using a lossy resistive sheet. This configuration allows the use of a closed-form EC model for fast and efficient bandwidth optimization. Similar to previous non-magnetic absorbers, GA is utilized to obtain the design parameters for broadband absorption with minimum overall thickness. The measured results confirm that the proposed absorber operates from 0.78 to 4.8 GHz with -10 dB reflectivity. The design achieves 144% fractional-bandwidth with a 10.12 bandwidth-to-thickness ratio, which is very close to the optimum value.The last but not least contribution is the design of high performance FSS-based magnetic absorber for EM portable head imaging system [1], which can play a significant role in saving lives by detecting and monitoring stoke. The proposed absorber design is an FSS-based magnetic absorber like the previous design with the same magnetic materials. Instead of using double-layer FSS, only single-layer lossy FSS with simple single square loop geometry is used. As we have fixed operation bandwidth for a specific application (EM Head Scanner), the cost function mainly focuses on having high absorption, light-weight, and ultra-thin design. The proposed absorber provides -15 dB reflectivity (97% absorption) over a wide bandwidth from 0.6 to 2.2 GHz (114.3% fractional bandwidth). The ratio between the theoretical minimum thickness (Rozanov limit) to the actual one is 0.92, which indicates that the proposed design is very close to the optimum one.The developed measurement techniques, absorbers, and other advances reported in this thesis positively contribute to solve the EM interference problem for EM medical imaging systems and other modern compact EM devices.

This paper provides an equivalent magnetic current approach for near-field to far-field transformation. The method utilizes near-field measured data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents, and method of moments (MoM) procedure is applied to transform the integral equation into a matrix one. Numerical results based on measurement data of phased array antenna are given to demonstrate the accuracy of the proposed method.

Consider an infinitely long slot in a conducting plane in an unbounded medium illuminated by a uniform transverse magnetic (TM) (to the slot axis) plane wave. The theory of characteristic modes for apertures is applied to solve the problem. For a narrow slot, analytic expressions for the first two characteristic currents and the equivalent magnetic current are given. As computed by the method of moments, numerical results for the characteristic currents and fields, the equivalent magnetic current, and the transmitted field pattern are presented for the slot whose width is one wavelength.

Consider an infinitely long slot in a perfectly conducting plane in an unbounded medium illuminated by a uniform transverse electric (TE) (to the slot axis) plane wave. The theory of characteristic modes for apertures is applied to solve the problem. For a narrow slot, analytic expressions for the first two characteristic currents and the equivalent magnetic current are given. As computed by the method of moments, numerical results for the characteristic currents and fields, the equivalent magnetic current, and the transmitted field pattern are presented for the slot whose width is one wavelength.

In this paper, we investigate various methods for solving a time-domain electric field integral equation (TD-EFIE) and a time- domain magnetic field integral equation (TD-MFIE) for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthogonal basis functions that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed TD-EFIE and TD-MFIE formulations are presented and compared.

An efficient multiregion model is extended with the single integral equation (SIE) method to calculate the EM scattering from a dielectric rough surface. In the multiregion model, the rough surface is divided into multiple regions depending on their positions along the rough surface as well as the energy distribution of the incident wave. Two intermediate regions are chosen as the domain region on which the method of moment (MoM) is adopted. The mutual couplings between different regions are considered approximately based on the magnetic and field integral equations, from which closed-form approximations for electric current on other regions are derived.