The use of surface impedance concepts in the finite-differencetime-domain method

Surface impedance concepts are introduced into the finite-difference time-domain (FDTD) method. Lossy conductors are replaced by surface impedance boundary conditions (SIBC), reducing the solution space and producing significant computational savings. Specifically, a SIBC is developed to replace a lossy dielectric half-space. An efficient implementation of this FDTD-SIBC based on the recursive properties of convolution with exponentials is presented. Finally, three problems are studied to illustrate the accuracy of the FDTD-SIBC formulation: a plane wave incident on a lossy dielectric half-space, a line current over a lossy dielectric half-space, and wave propagation in a parallel-plate waveguide with lossy walls     

The effect of dielectric loss in FDTD simulations of microstripstructures

The importance of dielectric losses in planar microstrip structures is evaluated with the finite-difference time-domain (FDTD) method. This analysis was previously not possible in many FDTD simulators due to a lack of absorbing boundary conditions (ABCs), which appropriately terminate air/dielectric interfaces for which the dielectric is lossy. The newly proposed lossy two-time derivative Lorentzian material (L2TDLM) model ABC allows for these terminations and is presented and implemented here for three-dimensional FDTD simulations. The effect of dielectric losses on several well-known planar microstrip structures is evaluated. It is shown that the inclusion of these losses in FDTD simulations, which is facilitated by the L2TDLM ABC, is, in fact, important to predict the performance of resonant structure on lossy dielectric substrates     

FDTDSIBC混合方法计算近地导线表面电流

通过在FDTD方法中引进时域表面阻抗界条件来研究瞬态电磁脉冲对有耗地面附近电缆线耦合问题。由频域表面阻抗出发通过拉氏变换得到时域表面阻抗边界条件（SIBC）,并将这种边界条件应用于FDTD方法中来模拟有耗地面的反射。计算结果表明了些方法的有效性。     

Thin-Wire Model Using Subcellular Extensions in the Finite-Difference Time-Domain Analysis of Thin and Lossy Insulated Cylindrical Structures in Lossy Media

Recently, a subcellular thin-wire model for the finite-difference time-domain (FDTD) simulation of resistively coated cylinders with lossless insulating and surrounding media was presented. In this paper, it is shown that this model can be extended to lossy cases. The material discontinuity between lossy insulating and surrounding media is corrected as the time-domain boundary condition. The convolution term of the boundary condition is solved by employing a recursive technique. Applying the contour-path integration to the FDTD unit cells around the wire, one may find the coarse-grid-based equation with the correction term and factors for the material discontinuity and the quasi-static field behavior around the wire. In the 2-D cylindrical coordinates with rotational symmetry, the validity of the proposed model is confirmed by an impedance analysis of insulated and resistive antennas according to the electrical properties of insulating and surrounding media, as well as the choice of cell size.      

二维有耗介质体电磁反演的时域玻恩迭代方法

本文利用时域非线性优化方法求解二维有耗介质的体的逆散射问题获得了很好的结果。并对正散射的求解精度做了改进。     

FDTD Implementation and Application of High Order Impedance Boundary Condition Using Rational Functions

An algorithm is proposed for the implementation of the high-order surface impedance boundary condition using the finite-difference time-domain method. The surface impedance function of a lossy medium is approximated by a series of rational functions in the Laplace domain, whereas the dyadic differential operator is approximated by a second-order power series. By assuming that the fields are piecewise linear, the time-domain convolution integrals are computed using a recursive formula. The impedance function of a coating layer is approximated by a third-order power series. The algorithm can be applied to scattering problems of a three-dimensional coating for both vertically and horizontally polarized waves. The advantage of the proposed method is that the result can be applied to media of arbitrary conductivities, with a wide range of incident angles from zero to graze. Some numerical examples are given to substantiate the theory.      

Incorporation of Conductor Loss in the Unconditionally Stable ADI-FDTD Method

A surface-impedance boundary condition (SIBC) is presented for an unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method. The conformal SIBC formulation based on locally conformal grids is capable of modeling the conductor loss of arbitrarily-shaped lossy metal structures. The work is described in the framework of the finite-integration technique (FIT) formulation of the ADI-FDTD. The paper focuses on the proposed ADI-FDTD SIBC formulation and its extensive validation. For this purpose, cylindrical and spherical cavity resonators are used for numerical tests. The quality factor $Q$ is directly proportional to wall loss and is particularly sensitive to the accuracy of loss calculation. The resonator structure consists only of a vacuum-filled metal cavity and is thus free of additional sources of error that are caused by other extensions to the basic ADI-FDTD algorithm. The formulation is validated by comparison with analytic results and numerical data calculated using CST Microwave Studio (MWS). The convergence rate of the results is of second order, i.e., the error reduces to one quarter as the mesh resolution is doubled.      

FDTD modeling of lumped ferrites

Implementing ferrites in finite-difference time-domain (FDTD) modeling requires special care because of the complex nature of the ferrite impedance. Considerable computational resources and time are required to directly implement a ferrite in the FDTD method. Fitting the ferrite impedance to an exponential series with the generalized-pencil-of-function (GPOF) method and using recursive convolution is an approach that minimizes the additional computational burden. An FDTD algorithm for a lumped ferrite using GPOF and recursive convolution is presented herein. Two different ferrite impedances in a test enclosure were studied experimentally to demonstrate the FDTD modeling approach. The agreement is generally good     

Analysis of exponential time-differencing for FDTD in lossydielectrics

We determine the stability condition and analyze the accuracy of the exponential and centered time-differencing schemes for finite-difference time-domain (FDTD) in an isotropic, homogeneous lossy dielectric with electric and magnetic conductivities σ and σ*, respectively. We show that these schemes are equivalent and determine that, for accuracy, both schemes must be used with a time step that finely resolves the electric and magnetic conduction current relaxation time scales. The implications of these results for perfectly matched layer (PML)-type absorbing boundary conditions are discussed     

Ground effects for VHF/HF antennas on helicopter airframes

In this paper, the finite element method (FEM) is used to predict the space and surface wave radiation patterns of VHF/HF antennas mounted on a helicopter in the presence of a lossy ground. The equivalent sources of the radiation system are obtained by solving an FEM problem in conjunction with an absorbing boundary condition (ABC) or an impedance boundary condition (IBC). From the equivalent sources, the total radiated field is calculated using the equivalence principle and superposition; the original problem is converted into a set of properly combined Hertzian dipoles referred to as the Sommerfeld problem. Instead of evaluating the Sommerfeld integral rigorously, Norton's approximation is used to improve the overall computational efficiency. The validation of this method is accomplished in two steps: first, the FEM is compared with the finite-difference time-domain method (FDTD) in the absence of a lossy ground; second, the Hertzian dipole problem is solved in the presence of a lossy ground and the results are compared with analytic solutions. Finally, this technique is extended to analyze an antenna on a helicopter above a lossy ground     

SO-FDTD Analysis on Magnetized Plasma

In this paper, a novel finite-difference time-domain (FDTD) method with recursive relationships among operators is developed for magnetized dispersive medium, named as the shift operator FDTD(SO-FDTD). The dielectric property of magnetized dispersive medium is written as rational polynomial function, the relationship between D and E is deduced in time-domain. And its high accuracy and efficiency are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collision plasma slab.     

有损土壤上的多导体传输线的时域分析

将多导体传输线（ＭＴＬ）的土壤复数阻抗拓展为土壤运算阻抗,采用Ｐａｄｅ展开法,提出了计及土壤影响的多导体传输线的时域模型,建立了该模型的时域有限差分（ＦＤＴＤ）算法。通过对计及土壤影响的架空单导体和双导体传输线的波过程计算,表明本文方法的正确性,并可以应用于超高压变电站高压母线和超高压输电线路的瞬态电磁干扰计算。     

Time-domain modeling of high-speed interconnects by modified methodof characteristics

In this paper, a new model of lossy transmission lines is presented for the time-domain simulation of high-speed interconnects. This model is based on the modified method of characteristics (MMC). The characteristic functions are first approximated by applying lower order Taylor series in the frequency domain, and then a set of simple recursive formulas are obtained in the time domain. The formulas, which involve tracking performances between two ends of a transmission line, are similar to those derived by the method of characteristics for lossless and undistorted lossy transmission lines. The algorithm, based on the proposed MMC model, can efficiently evaluate transient responses of high-speed interconnects. It only uses the quantities at two ends of the lines, requiring less computation time and less memory space than required by other methods. Examples indicate that the new method has high accuracy and is very efficient for the time-domain simulation of interconnects in high-speed integrated circuits     

Surface impedance modeling using the finite-difference time-domainmethod

The finite-difference time-domain (FDTD) technique has been used to model the one-dimensional (1D) surface impedance of a lossy Earth plane having discontinuities in two and three dimensions. Using a horizontal magnetic field aperture source located five cells from an absorbing boundary and 35 cells above the lossy Earth plane, the surface impedance was accurately modeled at a distance of λ₀/5000 from the source using both grazing and normal incidence. The technique was validated by comparison with a number of two-dimensional (2D) analytical models. The surface impedance profile in the vicinity of a vertical conductive water filled shaft that extends from the Earth's surface to a conductive basement is presented. Unlike modeling in the frequency domain, a single FDTD solution yields accurate multi frequency surface impedance data providing a number of standard cell size constraints are met. For common Earth electrical constants, the FDTD approach is limited to frequencies above 500 Hz     

Implementation of a surface impedance formalism at obliqueincidence in FDTD method

The authors point out that modeling of interfaces between two media, using time-domain surface impedances, permits one to reduce the discretization volume in the finite-difference-time-domain (FDTD) technique. The method presented here is based on an exact formulation of surface impedances, starting from Fresnel reflection coefficients for oblique incidence of the incident wave. The concept, valid for homogeneous and frequency-independent media, is then introduced into an FDTD algorithm where it is converted into a surface-impedance boundary condition (SIBC) for vertical or horizontal polarizations of locally plane waves. Two- and three-dimensional results are compared to those computed with classical FDTD or Fresnel reflection coefficients involving a Fourier transform     

Multiresolution time-domain analysis of plane-wave scattering fromgeneral three-dimensional surface and subsurface dielectric targets

The multiresolution time domain (MRTD) is used to analyze wide-band plane-wave scattering from general dielectric targets embedded in a lossy half-space, with free-space scattering as a special case. A Haar wavelet expansion is used for simplicity, this constituting a generalization of the widely used finite-difference time-domain (FDTD) method. In addition to developing the mathematical formulation, example results are presented for several targets, with the MRTD results validated through comparison with an independent frequency-domain method-of-moments solution and an FDTD model     

Detection of buried dielectric cavities using the finite-differencetime-domain method in conjunction with signal processing techniques

We address the problem of detecting low-dielectric contrast cavities buried deep in a lossy ground by using the finite-difference time-domain (FDTD) method in conjunction with signal processing techniques for extrapolation and object identification. It is well known that very low frequency probing is needed for deep penetration into the lossy ground, owing to a rapid decay of electromagnetic (EM) waves at higher frequencies. It is also recognized that numerical modeling using the FDTD method becomes very difficult, if not impossible, when the operating frequency becomes as low as 1 Hz. To circumvent this difficulty, we propose a hybrid approach in this paper that combines the FDTD method with signal processing techniques, e.g., rational function approximation and neural networks (NNs). Apart from the forward problem of modeling buried cavities, we also study the inverse scattering problem-that of estimating the depth of a buried object from the measured field values at the surface of the Earth or above. Numerical results for a buried prism are given to illustrate the application of the proposed technique     

Scattering from coated targets using a frequency-dependent, surfaceimpedance boundary condition in FDTD

One method for reducing the radar cross section of objects such as aircraft and missiles is the application of a lossy coating. Computing scattering from targets coated with dielectric/magnetic materials is challenging due to the reduced wavelengths of an incident field inside the coating. These smaller wavelengths require finer sampling of the fields. A technique for implementing this calculation without greatly increased memory requirements or computation times has previously been developed using a finite-difference time-domain (FDTD) code which has been tested in one, two, and three dimensions. The method requires knowledge of the frequency behaviour of the complex permittivity and permeability, and the thickness of the dielectric coating and is applicable to thin coatings when one or more reflections from the conducting surface are significant. The impedance at the surface of the coating is computed based on the given information and then approximated using a summation of causal functions. The approximated impedance is Z-transformed and added to the FDTD code in special update equations for the fields at the surface of the coating. No computations are required inside the coatings so the FDTD grid can be sized based on the free-space wavelength. The result obtained is valid over the entire frequency range of interest, assuming that the approximated surface impedance is a good match over the entire range. Comparisons with measurements of a scale model coated missile show good agreement and almost no increase in resource requirements over a standard FDTD calculation for an uncoated metal target     

An efficient surface-impedance boundary condition for thin wires of finite conductivity

To include dispersive loss into a sub-cell thin-wire model, a new implementation of a surface-impedance boundary condition (SIBC) is proposed. The surface-impedance function is approximated in the frequency domain by a series of first-order rational functions allowing straightforward transform into time domain. The contribution of the wire radius is included in the surface-impedance function extending the model to very thin or poorly conducting metal wires. Further, the SIBC includes the direct-current (dc) resistance. The approximation for the SIBC is chosen such that the dependence on the wire radius and conductivity can be removed prior to the computation of the approximation coefficients. Consequently, the wire radius and conductivity can be varied without re-computing the coefficients. The proposed model is compared with an existing SIBC wire model based on the high-frequency approximation and Prony's method, NEC-2 generated reference data, and analytical results. The results indicate enhanced accuracy at a reduced computational cost as compared with an existing model.     

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