Correction of errors due to airgaps for microwave complexpermittivity measurement using a coaxial line

Microwave complex permittivity of PTFE (Teflon) was measured using a transmission/reflection (TR) method and a coaxial sample fixture. A range of sample dimensions were prepared in order to examine the effect of airgaps on the measured permittivities. The measurements were compared with calculated values using a formula derived by considering the total capacitance     

Microwave Dielectric Properties of Ceramic and Nanocomposite Titanates of Transition Metal

Ceramic and nanocomosite samples of the titanates of transition metals have been synthesized and their microwave dielectric properties have been investigated. Frequency and magnetic field dependences of the transmission and reflection coefficients in centimeter and millimeter wavebands were measured. It is established for most of studied ceramic titanates that transmission coefficient increases and reflection coefficient decreases when frequency increases. An absorption maximum has been found for ceramic sample made of Co_0.9Fe_0.1TiO₃. The real and imaginary parts of complex dielectric permittivity were determined from measurements of transmission and reflection coefficients. On the whole, real part of dielectric permittivity of nanocomposite titanates based on an opal matrix is less than for ceramic titanates.     

Scattering by a Cylindrical Post of Complex Permittivity in a Waveguide

An exact solution of the discontinuity problem of a circular cylindrical post of arbitrary complex permittivity centered in a rectangular waveguide with the axis parallel to the electric field vector of the dominant mode has been set up and numerical results based directly on this solution have been found rising an electronic computer. The method used divides the waveguide up into three different regions by introducing two imaginary plane walls perpendicular to the waveguide walls. In the center region, which contains the cylindrical rod, the electromagnetic field is expanded in cylindrical waves and in the outer regions the field is expanded in waveguide modes. By setting up the boundary conditions at all discontinuity surfaces and performing numerical matching of the fields at the two imaginary walls, a system of linear equatious determining the coefficients of reflection, transmission, and absorption of the field due to the cylindrical rod is found. The structure which is of most interest in the case of a plasma column is a coaxial structure consisting of an inner dielectric cylinder with complex permittivity (the plasma) surrounded by a dielectric sleeve with real, positive permittivity (the glass tube). The theory is therefore developed to apply generally for such structures. From the numerical results, curves have been obtained showing the relationship between the coefficients of reflection and transmission and the (complex) permittivity of the rod material. Such curves maybe used for deducing the microwave properties of a cylindrical rod from measurements of the reflection and transmission coefficient of the rod.     

液相化学反应介电常数的测量与气泡影响分析

溶液中化学反应的等效介电常数是微波化学研究中的重要内容,等效介电常数的精确测量是研究微波与化学反应系统相互作用的基础.介绍了一种对溶液中化学反应等效介电常数随时间微弱变化跟踪测量的方法并对测量中经常遇到的气泡影响进行了分析.最后制作了一批测量探头,该探头可以有效排除其中的气泡.通过测量得到的反射系数和遗传算法(GA)可以对等效介电常数的微小变化进行精确测量.对稀溶液中的皂化反应测量的结果证实了该测量方法的有效性.     

FDTD算法的子域连接法

本文用ＦＤＴＤ法处理复合型导体结构中电磁场的耦合和传输时,用一种子域连接法建立数学模型,以分析波导元件散射特性和波导口径面天线的辐射特性为例来这种方法的具体运用。这种方法具有节省计算空间和计算时间,建模灵活多样等优点。     

Transmission of horizontally polarized waves and trapped waveguide modes in inhomogeneous media

A generalized Wentzel-Kramer-Brillouin (WKB) approach is used to obtain full wave solutions for horizontally polarized waves in inhomogeneous media when no closed form analytic solutions are known. This approach is suitable for complex permittivity profiles with critical coupling regions even when the permittivity gradient approaches zero. The transmission and reflection coefficients and the characteristic surface impedance for inhomogeneous layers of finite thickness are computed for several permittivity profiles. Excitation of propagating and evanescent waves is considered and the results are shown to satisfy the realizability and reciprocity relationships in electromagnetic theory. Sinusoidal permittivity profiles for which closed form analytical solutions are known are also considered to provide an additonal check on the generalized WKB solutions. For permittivity profiles with several spatial periods, transmission windows with very narrow beamwidths are found to exist. When conditions for total internal reflection in the inhomogeneous dielectric layer are satisfied, the reciprocal of the reflection coefficient vanishes and propagating waves are trapped in the layer. For these trapped waveguide modes the inhomogeneous dielectric is characterized by a surface reactance.     

Three-dimensional simulation of eccentric LWD tool response in boreholes through dipping formations

We simulate the response of logging-while-drilling (LWD) tools in complex thee-dimensional (3-D) borehole environments using a finite-difference time-domain (FDTD) scheme in cylindrical coordinates. Several techniques are applied to the FDTD algorithm to improve the computational efficiency and the modeling accuracy of more arbitrary geometries/media in well-logging problems: (1) a 3-D FDTD cylindrical grid to avoid staircasing discretization errors in the transmitter, receiver, and mandrel geometries; (2) an anisotropic-medium (unsplit) perfectly matched layer (PML) absorbing boundary condition in cylindrical coordinates is applied to the FDTD algorithm, leading to more compact grids and reduced memory requirements; (3) a simple and efficient algorithm is employed to extract frequency-domain data (phase and amplitude) from early-time FDTD data; (4) permittivity scaling is applied to overcome the Courant limit of FDTD and allow faster simulations of lower frequency tool; and (5) two locally conformal FDTD (LC-FDTD) techniques are applied to better simulate the response of logging tools in eccentric boreholes. We validate the FDTD results against the numerical mode matching method for problems where the latter is applicable, and against pseudoanalytical results for eccentric borehole problems. The comparisons show very good agreement. Results from 3-D borehole problems involving eccentric tools and dipping beds simultaneously are also included to demonstrate the robustness of the method.     

传输/反射法测量复介电常数的若干问题

研究了传输／反射法测量线性材料复介电常数εr的厚度谐振、多值性等问题，得到了解决这些问题的有效方法。通过改进NRW传输／反射法，由散射参数直接得到了归一化特性阻抗与传播常数，从而可以把已有的三个确定复介电常数的方程用到NRW传输／反射法中。联合应用这三个方程解决了上述问题，这使得人们可以用传输／反射法对任意厚度的样品在任意频率上进行复介电常数的稳定测量。用波导取样器与同轴线取样器分别得到的实验结果证明了此方法的有效性与可实现性。     

Measurement/computation of effective permittivity of dilute solution in saponification reaction

For better application of microwaves in chemistry, the interaction between microwaves and the chemical reaction needs further study. Since the reactants form a complicated mixture, which changes with time, an effective permittivity can be used to describe the molecular polarization of the mixture in the reaction. The effective permittivity is expected to change with microwave frequency, temperature and reaction time. However, in many cases, the change of effective permittivity in a saponification reaction is too small to be detected using traditional methods. In this paper, we present a hybrid experimental/computational method for determining the effective permittivity in a saponification reaction. We use a resonant coaxial sensor to measure the reflection coefficients. To predict its performance, the electromagnetic-field distribution near the sensor and the reflection coefficient are calculated employing a frequency-dependent finite-difference time-domain method. Next, we develop a genetic-algorithm-based inverse-calculation technique and employ it to determine the complex permittivity of pure water from the measured reflection coefficient and compare the results with those obtained from Debye's equation. Finally, the hybrid experimental/computational method is employed to determine the effective permittivity of a dilute solution in a typical saponification reaction. Results are presented and discussed.     

Noniterative stable transmission/reflection method for low-lossmaterial complex permittivity determination

This paper describes a new noniterative transmission/reflection method applicable to permittivity measurements using arbitrary sample lengths in wide-band frequencies. This method is based on a simplified version of the well-known Nicolson-Ross-Weir (NRW) method. For low-loss materials, this method is stable over the whole frequency range: no divergence is observed at frequencies corresponding to integer multiples of one half wavelength in the sample. The accuracy on the dielectric permittivity is similar to that obtained with a more recently proposed iterative technique. A general equation for complex permittivity determination including the Stuchly, NRW, and new noniterative methods, is also proposed     

An application of FDTD in studying the end effects of slotline andcoplanar waveguide with anisotropic substrates

In this paper, the finite-difference time-domain (FDTD) method is applied in conjunction with the generalized pencil of function (GPOF) technique to evaluate the reflection coefficient from shorted slotlines and coplanar waveguides (CPW) on anisotropic substrates, and to extract the propagation constant along the line from these data. For each frequency, the field solutions at different locations are processed by using the GPOF technique to extract two complex exponents that correspond to the forward and backward traveling waves, which provide all the information about the reflection coefficient and the dispersion characteristic of the transmission line. The advantage of combining the GPOF technique with the FDTD method is that the reflection coefficients can be obtained with a single run. Recognizing that there is a dearth of results for the reflection coefficients of slotline and CPW-line discontinuities with anisotropic substrates, the present problem is also solved by using the spectral-domain method for the purpose of validation, and the two results are found to compare quite well with each other. For further validation, the FDTD and GPOF solutions are derived for isotropic substrates, and are compared with the published theoretical and experimental results     

Characterization of building materials for propagation modelling: frequency and time responses

We propose original data processing methods for the dielectric characterization of frequency-dependent reflection coefficients of construction materials considering a very wide frequency band. Two types of approaches have been developed to obtain, from spectral measurements, estimates of the equivalent complex permittivity versus frequency or reconstruction of the impulse response. In particular, high resolution (HR) algorithms based on the matrix pencil method have been used in an original way to identify wave multipath inside a sample. Both approaches have been used for the characterization of different types of building materials. A database of dielectric responses of materials is under construction in order to provide the deterministic propagation simulator with the characteristics of building materials.     

In situ characterization of building materials for propagation modeling: frequency and time responses

We propose original data processing methods for the dielectric characterization of frequency-dependent reflection coefficients of construction materials considering a very wide frequency band. Two types of approaches have been developed to obtain, from spectral measurements, estimates of the equivalent complex permittivity versus frequency or reconstruction of the impulse response. In particular, high-resolution (HR) algorithms based on the matrix pencil method have been used in an original way to identify wave multipath inside a sample. Both approaches have been used for the characterization of different types of building materials. A database of dielectric responses of materials is under construction in order to provide the deterministic propagation simulator with the characteristics of building materials.     

DC power-bus design using FDTD modeling with dispersive media andsurface mount technology components

DC power-bus modeling in high-speed digital design using the finite-difference time-domain (FDTD) method is demonstrated herein. The dispersive character of the dielectric layers used in printed circuit board substrates is taken into account in this study. In particular, FR-4 is considered. The complex permittivity of the dielectric is approximated by a Debye model. A wide-band frequency response (100 MHz-5 GHz) is obtained through a single FDTD simulation. Good agreement is achieved between the modeled and measured results for a typical dc power-bus structure with multiple surface mount technology (SMT) decoupling capacitors placed on the printed circuit board (PCB). The FDTD method is then applied to investigate some general approaches of power-bus noise decoupling     

A new model for microwave characterization of composite materialsin guided-wave medium

A method of determining the permittivity and the permeability of heterogeneous materials from microwave measurements in a coaxial line or in a rectangular waveguide is presented. Fluctuations are observed in the curves of the transmission and reflection coefficients measured in a guided space cell which are caused by the propagation of modes higher than lowest order. The measuring cell containing the sample is represented by an unperturbed line in series with resonators which model the coupling between the sample and the measurement cell for each higher mode resonating inside the sample. Finally, the intrinsic characteristics of the material are computed from the data for the unperturbed line. Results for several composite materials and measurement cells are presented to demonstrate the capabilities of this model     

New Measuring Apparatus for Complex Permittivity at Millimeter-Wave Frequencies

A dielectric rod resonator excited by a nonradiative dielectric waveguide is used for measuring complex permittivity of low loss dielectric materials. The complex permittivties of single crystal sapphire, polycrystalline Ba (Mg_1/2 W_1/2) O₃ and Mg₂ Al₄ Si₅ O₁₈ (cordierite) have been obtained at 60 and 77 GHz by the new apparatus. The first time the measurement results of complex permittivity of brain grey and white matters from 15 to 50GHz utilizing a two-port microstrip test fixture is presented. S-parameters of Test fixture are simulated employing the finite-element method. A new spectrometer for the precision measurement of dielectric permittivity and loss tangent, which is capable of providing high resolution data for the first time over an extended W-band (68-118 GHz) frequency for specimens with a large range of absorption values, including highly absorbing specimens that otherwise would not be possible.     

FDTD analysis of phased array antennas

This work presents a new application of the finite-difference time-domain (FDTD) method to the generalized analysis of phased array antennas. The generality of the FDTD method brings important advantages to the phased array antenna analysis problem, allowing the modeling of complex conductor and dielectric geometries with relative ease. Additionally, a new broad-band FDTD periodic boundary condition is developed which allows the array problem to be simplified to a periodic unit cell computational domain. This hybrid frequency/time-domain periodic boundary condition enables solution of the periodic phased array problem for arbitrary scan conditions in a broadband fashion. The new method is applied to waveguide and stacked microstrip antenna arrays and the numerical results are compared to experimental or analytic solutions, demonstrating the validity and utility of this method     

同轴探头法测量片状介质材料的微波介电常数

提出了一种可用于测量片状介质材料微波复介电常数的同轴探头技术,该技术将同轴探头紧贴有导电衬底的片状介质,通过测量探头终端的矢量反射系数来确定介质的微波复介电常数。详细介绍了所采用的理论模型和测量系统。测量了一些常见介质材料的介电常数,测量值与理论值基本吻合。文章的同轴探头技术不仅可用于测量厚度较小的片状介质,而且可用测量样品量有限的液体。     

Analysis of Electromagnetic Waves Scattering by a Finite Size Dielectric and Metal Cylinder in a Rectangular Waveguide

The paper presents a rigorous solution of the scattering problem by a circular dielectric and perfectly conducting cylinders of any radius and any height in the rectangular waveguide oriented perpendicularly to a wall. The method is based on the representation of fields in waveguide and dielectric medium by cylindrical eigenfunctions and application of boundary conditions on surfaces of the cylinder to evaluate the fields inside and outside the cylinder. The reflection and transmission coefficients are expressed through the fields. As an example the reflection and transmission coefficients versus frequency for various dielectric and metallic cylinders are computed. The comparison of numerical with experimental data is presented.