Comparison of FDTD algorithms for subcellular modeling of slots inshielding enclosures

Subcellular modeling of thin slots in the finite-difference time-domain (FDTD) method is investigated. Two subcellular algorithms for modeling thin slots with the FDTD method are compared for application to shielding enclosures in electromagnetic compatibility (EMC). The stability of the algorithms is investigated, and comparisons between the two methods for slots in planes, and slots in loaded cavities are made. Results for scattering from a finite-length slot in an infinite plane employing one of the algorithms are shown to agree well with published experimental results, and power delivered to an enclosure with a slot agree well with results measured for this study     

EMI from cavity modes of shielding enclosures-FDTD modeling andmeasurements

Electromagnetic interference (EMI) from slots and apertures resulting from coupling of interior sources through enclosure cavity modes in a rectangular test enclosure is reported. EMI from a specially designed test enclosure with slots or apertures excited by interior sources was studied experimentally and with finite-difference time-domain (FDTD) modeling. The measurements and FDTD modeling agree well. The results indicate that radiation at cavity mode resonances through slots and apertures of nonresonant dimensions can be as significant as the radiation at aperture or slot resonances. The agreement between the FDTD modeling and measurements demonstrates the usefulness of FDTD for investigating aspects of shielding enclosure design such as coupling to slots and apertures and slot interactions     

Generation of FDTD subcell equations by means of reduced order modeling

Adapted finite-difference time-domain (FDTD) update equations exist for a number of objects that are smaller than the grid step, such as wires and thin slots. We provide a technique that automatically generates new FDTD update equations for small objects. Our presentation focusses on 2D-FDTD. We start from the FDTD equations in a fine grid where the time derivative is not discretised. This yields a large state-space model that is drastically reduced with a reduced order modeling technique. The reduced state-space model is then translated into new FDTD update equations that can be used in an FDTD simulation in the same way as the existing update equations for wires and thin slots. This technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method.     

Stable modeling of arbitrarily oriented thin slots in the FDTD method

A subcell model for thin wires in the finite-difference time-domain (FDTD) method using modified telegraphers equations has been developed by Holland et al. Edelvik has previously presented an extension of their algorithm, which allows for arbitrarily located and oriented wires with respect to the Cartesian grid. This is important to be able to accurately model wires that cannot be aligned to the Cartesian grid, e.g., tilted wires and circular loop wires. Recently, a dual set of equations has been proposed for modeling of thin slots. In this paper, we show that using a similar algorithm as for thin wires we can also handle slots of arbitrary location in Cartesian planes. Previous thin slot models have been susceptible for instabilities. We show that a symmetric coupling between field and slot yields a stable time-continuous field-slot system and that the fully discrete field-slot system is stable under a generalized Courant-Friedrich-Lewy (CFL) condition. The proposed method is demonstrated for scattering from a finite-length slot in an infinite conducting wall and a shielding enclosure including a slot. The results are in good agreement with published experimental data.     

PCB上微带线的电磁耦合时域建模分析方法

基于时域有限差分方法和传输线方程,结合高效网格建模技术,文中提出了一种高效的时域建模算 法,它能有效解决微带线的电磁耦合建模问题,实现空间电磁场与微带线瞬态响应的同步计算。首先,结合经验公 式,计算得到微带线的单位长度分布参数,构建适用于微带线电磁耦合分析的传输线方程。然后,采用时域有限差 分(Finite-Difference Time-Domain, FDTD)方法,结合非均匀网格技术和自动网格生成技术,仿真得到微带线激励场, 并在每个时间步进上引入传输线方程获得等效分布源项。最后,对传输线方程使用FDTD 的中心差分格式进行离 散,实现微带线及其端接电路上瞬态响应的迭代求解。为了验证时域建模算法的正确性和高效性,通过自由空间和 屏蔽腔内PCB 上微带线电磁耦合的数值模拟,从计算精度和耗时两方面与传统FDTD 方法的计算结果进行了对比。     

Shielding Characterization of Metallic Enclosures With Multiple Slots and a Thin-Wire Antenna Loaded: Multiple Oblique EMP Incidences With Arbitrary Polarizations

Shielding effectiveness (SE) of metallic rectangular enclosures with thin slots and a thin-wire antenna loaded by an impedance, illuminated by multiple electromagnetic pulses (EMPs) simultaneously, is investigated using a hybrid finite-difference time-domain (FDTD) method. In order to enhance the simulation efficiency of the FDTD algorithm, accurate formulas for handling multiple thin slots, a thin-wire antenna, and a lumped network are integrated together. Numerical results show that for real metallic enclosures, their shielding performance is very sensitive to the variations in direction and polarization angle of the incident EMPs. However, at a given frequency, the resistance and inductance loaded at the terminal of a thin-wire antenna have little effect on the SE level. For two, three, as well as more EMP incidences, common-frequency interferences will result in strong inner field resonance in the enclosure.      

微波脉冲窄缝耦合的数值模拟方法

本文应用一种近似方法，结合时域有限差分法，模拟了微波脉冲与腔体上有限厚度孔缝的线性耦合过程，给出了耦合场对入射波载频、入射场偏振方向、腔体壁电导率以及孔缝尺寸的依赖关系，得出了微波脉冲与孔缝耦合的共振效应和增强效应等规律。     

An Alternative Algorithm for Both Narrowband and Wideband Lorentzian Dispersive Materials Modeling in the Finite-Difference Time-Domain Method

In this study, an alternative algorithm is proposed for modeling narrowband and wideband Lorentzian dispersive materials using the finite-difference time-domain (FDTD) method. Previous algorithms for modeling narrowband and wideband Lorentzian dispersive materials using the FDTD method have been based on a recursive convolution technique. They present two different and independent algorithms for the modeling of the narrowband and wideband Lorentzian dispersive materials, known as the narrowband and wideband Lorentzian recursive convolution algorithms, respectively. The proposed alternative algorithm may be used as a general algorithm for both narrowband and wideband Lorentzian dispersive materials modeling with the FDTD method. The second-order motion equation for the Lorentzian materials is employed as an auxilary differential equation. The proposed auxiliary differential-equation-based algorithm can also be applied to solve the borderline case dispersive electromagnetic problems in the FDTD method. In contrast, the narrowband and wideband Lorentzian recursive convolution algorithms cannot be used for the borderline case. A rectangular cavity, which is partially filled with narrowband and wideband Lorentzian dispersive materials, is presented as a numerical example. The time response of the electric field z component is used to validate and compare the results     

The inclusion of wall loss in finite-difference time-domainthin-slot algorithms

The authors present two methods for incorporating slot wall loss into the finite-difference time-domain (FDTD) calculations. The walls are assumed to be good conductors. Loss is only applied to the current component that flows axially along the slot walls, which is generally the dominant component for slots that are long and narrow. The first method modifies an FDTD equation internal to the slot to include a surface-impedance contribution. This method is appropriate for the usual FDTD thin-slot formalisms. The second method includes the losses into a half-space integral equation that can be used by the recently introduced hybrid thin-slot algorithm. Results based on the two methods are compared for a variety of slot parameters and wall conductivities     

A locally conformed finite-difference time-domain algorithm ofmodeling arbitrary shape planar metal strips

A general algorithm for modeling arbitrary shape planar metal strips by the finite-difference-time-domain (FDTD) method is presented. With this method, fields in the entire computation domain are computed by the regular FDTD algorithm except near metal strips, where special techniques proposed herein are applied. Unlike the case for globally conformed finite-difference algorithms, the computation efficiency of the regular FDTD method is maintained while high space-resolution is obtained by this locally conformed finite-difference method. Numerical tests have verified that a higher computation accuracy is achieved by this scheme than by the conventional staircase approximation. The modeling of electrical characteristics of two crossed strip lines is provided as an example     

Analyzing electromagnetic structures with curved boundaries onCartesian FDTD meshes

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD formulas. Therefore, this new algorithm is more efficient than general nonorthogonal FDTD schemes in terms of computer resources such as memory and central processing unit (CPU) time. Simulation results are presented and compared to those using other methods     

电磁脉冲对目标腔体的孔缝耦合效应数值研究

利用时域有限差分（ＦＤ－ＴＤ）方法研究了超宽带电磁脉冲（ＵＷＢ），快上升前沿电磁脉冲（ＦＲＥＭＰ），核电磁脉冲（ＮＥＭＰ）对目标腔体的孔缝耦合效应。研究表明：对于较小尺寸的目标腔体，在孔缝尺寸也较小的情况下，ＦＲＥＭＰ和ＵＷＢ相对于ＮＥＭＰ更容易通过腔体上的孔缝耦合进入目标腔体，而且更容易引起孔腔共振。     

Accurate Characterization of Shielding Effectiveness of Metallic Enclosures With Thin Wires and Thin Slots

In many electrical and electronic systems, metallic enclosures are used to provide electromagnetic shielding. These enclosures normally contain thin wires, thin slots, and frequency-selective slots (FSS) that degrade the shielding effects. In this paper, integrated FDTD formulations are developed that can model both subcellular thin slots and thin wires simultaneously. The formulations are shown to be capable of accurately predicting shielding effectiveness and inner field distributions of a metallic enclosure in both the frequency- and time-domains when subject to a high-power electromagnetic pulse.      

窄缝耦合共振特性分析

应用时域有限差分法模拟了正弦波和电磁脉冲对窄缝的耦合过程，计算了直缝和扭曲缝的耦合穿透功率和能量，通过分析窄缝的耦合传输系数变化曲线，得出窄缝发生耦合共振的条件和规律。并通过直缝与扭曲缝耦合情况的比较，表明了扭曲缝具有较好的电磁防护能力。     

FDTD modeling of common-mode radiation from cables

Radiation from cables attached to printed circuit boards and shielding enclosures is among the primary concerns in meeting FCC Class A and B limits. The finite-difference time-domain (FDTD) method can be employed to model radiation from printed circuit boards and shielding enclosures with complex geometries, but difficulties in modeling wires and cables of arbitrary radii are encountered. Modeling the wire by setting the axial component of the electric field to zero in the FDTD method results in an effective wire radius that is determined by the mesh discretization. Neglecting the wire radius in applications, such as electromagnetic interference (EMI) or printed circuit board modeling, may result in gross errors because near-field quantities are typically sensitive to wire thickness. Taflove et al. (1988) have developed a subcellular FDTD algorithm for modeling wires that has been shown to work well for plane wave scattering. The method uses a quasistatic field approximation to model wires with a well defined radius independent of the mesh dimensions. The wire model is reviewed and investigated for application to common-mode radiation from cables attached to printed circuit boards, where the source is often a noise voltage at the connector. Also investigated is energy coupling to attached cables through enclosure apertures resulting in common-mode radiation from the cable. The input impedance for a center-fed dipole antenna, as well as a monopole connected to a conducting half-sheet, is computed with FDTD methods and compared to moment method input impedance results. A simulation of a shielding enclosure with an attached cable demonstrates the utility of FDTD analysis in modeling common-mode radiation     

Spherical wave sources in FDTD

A method is described which simulates the propagation of electromagnetic waves as spherical wave modes, approximated by an FDTD method. Modal equations in radius and time are discretized for explicit time-stepping. Angular functions are implemented analytically as required. Computed results for two examples are compared with analytic solutions - a resonator and a dipole near a conducting sphere - to demonstrate the validity of the method with very good agreement. This method is intended as a source condition in total/scattered FDTD methods, to allow for modeling of near-field object interactions without explicitly modeling the source     

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     

FDTD analysis of CPW-fed folded-slot and multiple-slot antennas onthin substrates

Folded slot antennas are attractive for active arrays due to relatively large bandwidth, fabrication simplicity, and ease of integration with devices. Currently, there is little design information for these antennas, especially on thin substrates. The finite-difference time-domain (FDTD) method is applied to the analysis of CPW-fed folded-slot antennas. The paper describes the problems encountered in the analysis, compares the theoretical results and measured data, and provides some design information for folded slots. In addition, it explores the manipulation of input impedance through the use of additional slots, yielding antennas with a broadband 50 Ω input impedance     

Incorporating two-port networks with S-parameters into FDTD

A modeling approach for incorporating a two-port network with S-parameters in the finite-difference time-domain (FDTD) method is reported. The proposed method utilizes the time-domain Y-parameters to describe the network characteristics, and incorporates the Y-parameters into the FDTD algorithm. The generalized pencil-of-function technique is applied to improve the memory efficiency of this algorithm by generating a complex exponential series for the Y-parameters and using recursive convolution in the FDTD updating equations. A modeling example is given, which shows that this approach is effective and accurate. This modeling technique can be extended for incorporating any number of N-port networks in the FDTD modeling