Concerning lossy, compressible, magneto-ionic media-General formulation and equation decoupling

The governing equations for electromagnetic phenomena in lossy, compressible, magneto-ionic media are formulated in terms of a newly introduced compressivity tensor. The matrix forms of both the permittivity tensor and the compressivity tensor are given. From the new governing equations, a three-dimensional vector wave equation and a dispersion equation are derived. In a source-free region, a set of three simultaneous wave equations in the longitudinal components of the electric and magnetic fields and in the pressure distribution can be written. These equations can be decoupled in the lossless case by effecting a transformation. The required transformation matrix and the resulting uncoupled, second-order, differential equations are given. Formulas for the determination of the transverse components of the electric and magnetic fields are also derived.     

Analysis of finite-differencing errors to determine cell size when modeling ferrites and other lossy electric and magnetic materials using FDTD

The focus of this paper is the modeling of materials that have both significant electric and magnetic losses, such as ferrites, using finite-difference time domain (FDTD). The primary contribution is identifying appropriate cell sizes when modeling these types of materials. It is shown that finite-differencing errors increase in lossy media compared to lossless media when sampling at the same number of cells per wavelength. Losses in a medium are defined by the ratio of the attenuation constant, /spl alpha/, to the phase constant, /spl beta/, since that ratio accounts for all losses, whether they be electric or magnetic. In addition to a detailed finite-differencing error analysis, a simple approximation is given for selecting a cell size in a lossy material that will give the same finite-differencing error as ten cells per wavelength in a lossless material. This paper also presents a means for deriving pure real constitutive parameters from complex constitutive parameters. Being able to make such calculations is useful in cases where complex constitutive parameters are given for a material, and the FDTD model being used only accepts pure real constitutive parameters, as is the case for several contemporary models. Comparisons of theoretical and FDTD-modeled reflection and transmission show that the derived, real constitutive parameters are valid.     

Quasi-TEM analysis of multilayered, multiconductor coplanarstructures with dielectric and magnetic anisotropy including substratelosses

A quasi-TEM (transverse electromagnetic) analysis of multiconductor planar lines embedded in a layered structure involving lossy iso/anisotropic electric and/or magnetic materials is achieved. Conditions under which a quasi-TEM assumption is valid are theoretically determined. An efficient spectral-domain analysis is used to determine the complex capacitance and inductance matrices characterizing the transmission system. computation of the inductance matrix is reduced to the computation of an equivalent capacitance matrix when media characterized for a fully general permeability tensor are present. It is also shown that most actual monolithic microwave integrated circuit (MMIC) microstrip-type structures (where semiconductor substrates are present) and possible future applications including lossy magnetic materials can be analyzed by using the simple quasi-TEM model. The validity of the results has been verified by comparison with full-wave theoretical and experimental data on microstrip lines on magnetic substrates and slow-wave structures     

A volume-surface integral equation method for solving Maxwell'sequations in electrically inhomogeneous media using tetrahedral grids

Starting with the solution of Maxwell's equations based on the volume integral equation (VIE) method, the transition to a volume-surface integral equation (VSIE) formulation is described. For the VSIE method, a generalized calculation method is developed to help us directly determine E fields at any interface combination in three-dimensional (3-D) electrically inhomogeneous media. The VSIE implementation described is based on separating the domain of interest into discrete parts using nonuniform tetrahedral grids. Interfaces are described using curved or plane triangles. Applying linear nodal elements, a general 3-D formulation is developed for handling scatter field contributions in the immediate vicinity of grid nodes, and this formulation is applicable to all multiregion junctions. The special case of a smooth interface around a grid node is given naturally by this formulation. Grid nodes are split into pairs of points for E-field calculation, and node normals are assigned to these points. The pairs of points are assigned to the elements adjoining the grid node. For each pair of points, the correct field jumps on the interface are given by a surface integral over the polarization surface charge density     

A Vector-Fitting Formulation for Parameter Extraction of Lossy Microwave Filters

In this letter, a formulation based on the vector fitting is applied to extract the equivalent circuit model from the frequency response of lossy cross-coupled microwave filters. By approximating the lossy response with short-circuit admittance parameters in partial fractional expansion form, the proposed method can evaluate the unloaded quality factor of resonators and extract the transversal coupling matrix simultaneously. The methodology of the vector fitting can identify the poles and residues of the short-circuit admittance parameters even when the poles are on the complex plane. And the extracted transversal coupling matrix can further transform into the prescribed form corresponding to the physical layout. The proposed method can be used in the tuning process of filter designs where the extraction of a coupling matrix is essential. To verify the method, a cross-coupled quadruplet filter is used as an example     

Self-Adjoint Vector Variational Formulation for Lossy Anisotropic Dielectric Waveguide

This paper presents the derivation of a new self-adjoint variational formula for complex propagation constant in a lossy anisotropic dielectric waveguide, in terms of the magnetic field and real frequency. The ability to include loss and anisotropy (into the permittivity tensor) while preserving the self-adjointness of the system is achieved by using the less common real-type inner product. When used as a basis of Rayleigh-Ritz or finite-element methods, the formula leads to the canonical eigenvalue eqnation of the form Ax= gamma/sup 2/Bx.     

Equivalent circuits for electrically small antennas using LS-decomposition with the method of moments

As part of an investigation into methods for accelerating the process of filling the method-of-moments impedance matrix [Z], it was found that [Z] could be decomposed into three parts: a real inductance matrix [L] from the magnetostatic vector potential, a real elastance matrix [S] from the electrostatic static scalar potential, and a complex impedance matrix [z(ω)] of residual frequency-dependent contributions. By neglecting [z(ω)] at sufficiently low frequencies, static and quasi-static charge and current distributions were obtained. For electrically small antennas, a complete RLC circuit was obtained directly from a single quasi-static solution rather than as an approximate characterization of the impedance as a function of frequency. This gives a precise definition of the circuit parameters limiting the performance of electrically small antennas     

A simplified formulation to analyze inhomogeneous waveguides withlossy chiral media using the finite-element method

In this paper, an efficient finite-clement formulation is presented for the analysis of the propagation characteristics in arbitrarily shaped lossy inhomogeneous waveguides loaded with chiral media. It is a simplified form of the one proposed for the bi-anisotropic media. In this formulation, showing no spurious modes, the frequency or the propagation constants may be treated as eigenvalues of a resulting sparse quadratic eigenproblem. However, in order to handle losses easily and to facilitate computation of complex modes, the frequency is specified as an input parameter and the eigensystem is solved for the complex propagation constant as the eigenvalue. This sparse eigensystem is further transformed into a generalized one, thus maintaining the sparse properties of the matrices. New numerical finite-element results are presented     

A finite-element time-domain method using prism elements formicrowave cavities

A finite-element time-domain (FETD) method for solving Maxwell's equations was developed by combining prism-based edge elements with central differencing in the time domain. This method solves for the electric field as a vector function of space and time in finite cylindrical cavity geometries of arbitrary geometry. Two stability analyses of this method are performed using the growth factor technique and the Z-transform. Furthermore, the computational complexity of the present approach is also investigated, This method has been implemented and its validity tested by studying the resonant frequencies of various microwave cavities     

High frequency scattering by a conducting ring

Asymptotic formulae are derived for the Fourier coefficients of the thin wire kernel in the integral equation for the electric current on an electrically large, thin circular loop. The total current induced on the ring by a plane electromagnetic wave is approximated by a modified physical optics term proportional to the incident field, plus resonant terms of lossy circulating waves. Numerical evaluation of the dominant poles and residues of the ring transfer function provides the amplitudes and complex propagation constants of these natural modes.     

A 3-D tensor FDTD-formulation for treatment of sloped interfaces in electrically inhomogeneous media

A general integral finite-difference time-domain (FDTD) formulation on cubical grids for the modeling of electrically inhomogeneous media of arbitrary shape is derived. The simple cubical structure is maintained and no modifications of the integral paths are necessary. Instead, a three-dimensional tensor relationship between the average electric flux density and electric field is determined beforehand and used during the simulation to account for discontinuities in the neighborhood of sloped interfaces. The accuracy of the method is confirmed by comparisons with analytical solutions.     

Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

For a point current source placed at the interface between two half-space media, investigation is made of the far-zone asymptotic fields in the frequency domain and their transient waveforms. The media are electrically uniaxial with the uniaxis normal to the interface. The leading-order fields contributed by the stationary-phase points serve as good approximations well off the critical angles. Near the critical angles, the uniform asymptotic techniques need to be employed for a proper approximation. Unlike the ordinary wave, the extraordinary wave cannot be correctly described merely by taking into account the proximity of the stationary and branch points, except in some rare cases. Consideration must also be given to the combined effect associated with the pole introduced in the formulation. The validities of the asymptotic approximations are examined in the time domain by comparing the asymptotic-field waveforms with the wavenumber-synthetic waveforms, around the critical angle of the extraordinary wave.     

Surface electric fields and impedance matrix elements of stratifiedmedia

For the various geometrical configurations of waves in stratified media, we consider the important case when both source and field points are located on the same interface separating two different dielectric media. We denote this configuration as surface electric field case. In this paper, the electric fields are calculated numerically without using potentials. For the surface electric field case the integrand of the electric field grows with k_ρ^3/2 for large κ_ρ making the Sommerfeld integral singular. To calculate the surface electric fields in the spatial domain, we previously applied a technique of higher order asymptotic extraction. In the higher order asymptotic extraction, the higher order asymptotic parts were calculated analytically. The remainder, which has an integrand decays as κ_ρ^-3/2 was calculated numerically along the Sommerfeld contour path of integration. In this paper, we use a different extraction technique, the half-space extraction. After the half-space extraction, the integrand of the Sommerfeld integral of stratified media decays exponentially and the integral is calculated along the Sommerfeld integration path. The half-space extraction part is calculated by numerical integration along the vertical branch cuts. The surface electric fields for stratified media using half-space extraction and higher order asymptotic extraction are in good agreement. To validate the accuracy of the solution, we also compute the impedance matrix elements using surface electric fields, testing, and basis functions all in the spatial domain. The results are then compared with the results of the spectral domain method. The comparisons of the complex impedance matrix elements are tabulated and show that the difference is less than 2%     

Design of NPR DFT-Modulated Filter Banks via Iterative Updating Algorithm

In this paper, an efficient algorithm is proposed to design nearly-perfect-reconstruction (NPR) DFT-modulated filter banks. First, the perfect-reconstruction (PR) condition of the oversampled DFT-modulated filter banks in the frequency domain is transformed into a set of quadratic equations with respect to the prototype filter (PF) in the time domain. Second, the design problem is formulated as an unconstrained optimization problem that involves PR condition and stopband energy of the PF. With the gradient vector of the objective function, an efficient iterative algorithm is presented to design the PF, which is updated with linear matrix equations at each iteration. The algorithm is identified as a modified Newton’s method, and its convergence is proved. Numerical examples and comparison with many other existing methods are included to demonstrate the effectiveness of the proposed method.     

Complex image model for ground-penetrating radar antennas

A method of combining the complex image method with the constant Q assumption is derived, which enables the calculation of complex image parameters once for the whole frequency range in the general half-space case. The mixed potential method of moments is then used to model horizontal wire dipoles near a lossy half-space, using pulse-basis functions and point matching. The method is demonstrated by the modeling of two types of wire dipole. A conductive half-wave dipole shows excellent agreement with NEC-S. The current distribution of a 3.4 m resistively loaded dipole across the frequency range 0-512 MHz is also calculated and transformed to the time domain. The result agrees with published measurements. The time required on a workstation was reduced to 4/s per frequency point     

FDTD方法分析THz波段金属平板的屏蔽特性

研究了室温下金属平板对THz波的透射屏蔽特性。考虑到THz波段金属电导率的频率色散特征,基于Z变换方法处理频域色散媒质本构关系到时域的转化,使FDTD仿真易于编程实现。仿真表明,对不同金属材料,其屏蔽效应随频率呈现出周期振荡,且金属平板厚度在百nm量级时对THz波的屏蔽效应＞60 dB。对不同厚度的金属平板,其屏蔽效应以dB为单位随厚度线性增大,有望利用此特性实现厚度μ＜m级薄层金属的厚度测量。     

Application of the TLM method to half-space and remote-sensingproblems

The problem of scattering and radiation in the presence of a material half-space is solved using the transmission line matrix (TLM) method. The TLM method is a general numerical method for obtaining an approximate solution to the time-dependent form of Maxwell's equations in the presence of complex environments. The method requires the discretization of the entire spatial domain of the problem and provides the transient response as well as (through discrete Fourier transform) the frequency domain response. The three-dimensional symmetric-condensed TLM node is applied. A total/scattered field formulation is applied to excite the space. The source used is an electrically short electric dipole and is described analytically in the time-domain. The method is used to calculate near field distributions (in both the time and frequency domain) and the change in source input impedance of a dipole radiator in the presence of a half-space. Numerical simulations relevant to the detection of buried objects are provided     

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.     

Spectral analysis and synthesis options for short pulse radiationfrom a point dipole in a grounded dielectric layer

Formal exact alternative spectral representations for the electromagnetic fields radiation from a pulsed electric current element embedded in a grounded dielectric layer are derived. Starting from the standard spectral decomposition into the real frequency domain and the real spatial wavenumber domains corresponding to the transverse coordinates perpendicular to the direction of stratification, alternative treatments of the spectral integrands in the various complex spectral planes lead to exact steepest descent path representations which are well suited for subsequent asymptotic reduction into the time domain (TD). Of special interest is the nonconventional synthesis strategy, which performs frequency inversion before spatial wavenumber inversion, thereby utilizing in one of the options TD leaky modes with complex frequency and real spatial wavenumbers, and also TD trapped modes, as basis fields. This is contrasted with the conventional approach built around time-harmonic real-frequency leaky modes with complex spatial spectra. The spectral strategies employed here are applicable also to layered structures