Ultra-Wideband Wave Reactances of Capacitive Grids

The accuracy of transmission line models of two-dimensional freestanding capacitive grids is studied on a very wide frequency band. The grids are of infinite extent in the transverse directions and are illuminated by a linearly polarized normally incident plane wave. Comparison with reference results deduced from Finite-Difference Time-Domain (FDTD) simulations allows determining the range of validity of commonly used equivalent circuits It is shown that their accuracy strongly depends on the dimensions of the grids and the operating wavelength. Although very convenient, their implementation for calculating the frequency response of multi-layer systems could lead to unreliable results. Two closed-form new models are thus proposed. The first one results from an optimized expression of the well-known Marcuvitz's impedance, and the second one involves a series resonant LC circuit shunted by an additional capacitance. Both formulations are very accurate for a wide range of grid geometries and over the whole visible region (wavelength > grid constant).     

An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

A method is proposed to improve the numerical dispersion characteristics for simulations of the scalar wave equation in 3D using the FDTD method. The improvements are realized by choosing a face-centered-cubic (FCC) grid instead of the typical Cartesian (Yee) grid, which exhibits non-physical distortions of the wavefront due to the FD stencil. FCC grids are the logical extension of hexagonal grids in 2D, and have been shown previously to provide optimal sampling of space based on close packing of spheres (highest density). The difference equations are developed for the wave equation on this alternative grid, and the dispersion relationship and stability for grids of equal and non-equal aspect ratios are derived. A comparison is made between FCC and Cartesian formulations, based upon having an equal volume density of gridpoints in each method (i.e. the computational storage requirements of each method would be the same for the same simulated space). The comparison shows that the FCC grid exhibits a much more isotropic dispersion relation than the Cartesian grid of equivalent density. Furthermore, for an equivalent density, the FCC method has a more relaxed stability criterion by a factor of approximately 1.35, resulting in a further reduction in computational resources.     

A method to select the optimal equivalent electrical circuit applied to study corrosion system of composite coating on magnesium alloy

Mg-Al layered double hydroxides/micro-arc oxidation (Mg-Al LDHs/MAO) composite coating on AZ31 magnesium alloy is fabricated by hydrothermal treatment. Corrosion system is described by ideal equivalent circuit, in which each layer or interface is regarded as the corresponding electronic component. The optimal equivalent circuit is determined by the minimum total error area of electrical parameters. Error areas of phase angle and modulus for experimental and fitting data are calculated for the selected four different kinds of circuit models such as EC1, EC2, EC3 and EC4. The results show that circuit model EC2 is the best because its total error is 1/2, 2/19 and 1/15 of error values for other three kinds of circuit models, respectively. This work reveals that the optimal equivalent electrical circuit can well reflect corrosion system of Mg-Al LDHs/MAO composite coating with the help of electrochemical impedance spectroscopy (EIS) and scanning electron microscope (SEM).     

粒子模拟中激励源的一种等效设置方法

 基于计算电磁学中对强迫激励源消除虚假反射的算法分析,提出了用等效电流和等效磁流在FDTD公式中引入电场激励源和磁场激励源的方法。从粒子模拟方法的基本方程和迭代公式出发,分析了激励源的引入过程,推导出激励源所等效的电流项和磁流项表达式,实现了新的激励源设置方法,并进行了数值验证和结果讨论。研究表明：这类等效模型与标准FDTD公式能紧密结合,引入非常方便;不必专门设置一个附加的散射场区来处理散射场的计算,大大节省了计算时间和计算内存,比常规总场/散射场体系方法的效率高20%以上,对粒子模拟这类耗时的计算较为适用。通过对2维柱坐标系下相对论速调管放大器(RKA)的模拟,证明了此类激励源设置方法的实用性。     

Full-Wave Analyses for Vertical Interconnections of Shielded Coplanar Waveguide

Three dimensional (3D) interconnection plays important role in modern millimeter wave integrated circuit (MMIC). In this paper, vertical interconnections of shielded coplanar waveguides, which appear typically in multichip module MMICs, are analyzed through the full-wave finite-difference time-domain (FDTD) method.     

Parametric model of the BAW resonator phase-noise

Excepted for the very short terms the frequency stability of ultra-stable oscillators is mainly limited by the resonator noise. In this work we proposed a parametric model of the bulk acoustic wave (BAW) resonator phase noise based on an equivalent circuit. This model explains phase noise generated by a BAW crystal from a point of view of parametric fluctuations and proves the f⁻¹ dependences of the crystal noise. The model performance is verified with simulation. Simulation results are compared to experimental data and discussed. Comparison of three existing models is made.     

一种有损非均匀传输线时域分析方法

提出利用等效电路法解决电磁脉冲注入下有损非均匀传输线及其网络端接非线性负载的时域响应问题。采用分段逼近级联方法建立了有损非均匀传输线的等效电路模型。利用设计的快沿电磁脉冲源对有损非均匀微带线端接电阻、瞬态抑制二极管的响应进行了试验和仿真对比分析,验证了该等效电路模型的正确性和解决非线性负载响应问题上的有效性。通过与FDTD法对更复杂的有损非均匀传输线、不等长有损非均匀传输线、有损非均匀传输线网络的仿真结果和计算机运行时间进行对比分析,进一步验证了该等效电路法的正确性以及在解决有损非均匀传输线问题上的普遍适用性和高效性。     

The Huygens subgridding for the numerical solution of the Maxwell equations

The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation.     

非静力模式中三维网格的计算特性

在线性斜压非静力滞弹性方程组的基础上,从频率和群速方面讨论了10种三维网格的计算频散性,结果表明三维网格EL/CP、C/CP与Z/LZ计算频散性能较好.从而为非静力原始方程大气模式选取三维网格提供指导.     

分析水下目标的大比例变换总场散射场源FDTD方法

为解决探测水下目标的电磁散射问题,提出大比例变换的总场-散射场源时域有限差分（FDTD）方法.该方法包含两次FDTD计算：第一次计算采用细网格得到激励源周围的近场值;第二次计算采用粗网格得到远距离的电磁场值.两次FDTD计算通过总场-散射场边界建立联系.实现细粗网格的大比例变换,例如变换比例N=10,大大节省了计算时间,降低了计算内存的消耗,提高了计算效率.通过算例验证该方法的正确性和有效性.最后,计算水下岩层中存在异常体时的电磁响应,指出当岩层中异常体电导率不同时,接收点处电磁场的幅值和相位均不相同.     

Theoretical models for designing a 220-GHz folded waveguide backward wave oscillator

In this paper,the basic equations of beam-wave interaction for designing the 220 GHz folded waveguide(FW)backward wave oscillator(BWO) are described.On the whole,these equations are mainly classified into small signal model(SSM),large signal model(LSM),and simplified small signal model(SSSM).Using these linear and nonlinear one-dimensional(1D) models,the oscillation characteristics of the FW BWO of a given configuration of slow wave structure(SWS) can be calculated by numerical iteration algorithm,which is more time efficient than three-dimensional(3D)particle-in-cell(PIC) simulation.The SSSM expressed by analytical formulas is innovatively derived for determining the initial values of the FW SWS conveniently.The dispersion characteristics of the FW are obtained by equivalent circuit analysis.The space charge effect,the end reflection effect,the lossy wall effect,and the relativistic effect are all considered in our models to offer more accurate results.The design process of the FW BWO tube with output power of watt scale in a frequency range between 215 GHz and 225 GHz based on these 1D models is demonstrated.The 3D PIC method is adopted to verify the theoretical design results,which shows that they are in good agreement with each other.     

Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker’s algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices.     

光频段多频率域负折射率材料的数值研究

利用电介质材料周期性排列构成二维六角结构光子晶体,用平面波展开法研究了二维光子晶体材料各个能级的等频率曲线图,发现此结构光子晶体在多个频段上存在负折射特性,用时域有限差分(finite difference time domain,FDTD) 数值计算模拟也得到了相同的结果. 关键词： 光子晶体 左手化媒质 负折射 多频段     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.     

三模重叠双间隙耦合腔型输出回路的仿真设计

 为扩展速调管输出回路的带宽,进一步分析了双间隙耦合腔的模式重叠理论,说明了实现三模重叠的可能性,采用等效电路法计算了三模重叠双间隙耦合腔型输出回路的阻抗频率特性。以中心频率3 GHz的输出回路为例,建立了3维计算模型,给出了设计这种输出回路的步骤和结构参数。用场分析法计算了间隙阻抗频率特性,结果表明：此输出回路2 dB相对带宽接近15%,加载滤波器后1.5 dB相对带宽可达19.3%。     

等效折射率为非-1时的亚波长成像

本文采用硅柱子周期性排列构成六角结构光子晶体,用平面波展开方法和FDTD方法研究表明,此结构光子晶体存在等效折射率接近-1的频率区域.在等效折射率趋于-1但不等于-1时,此光子晶体平板结构超透镜能形成一个非近场的像.模拟还发现,此结构平板光子晶体等效折射率为非-1时,可以亚波长成像. 关键词： 负折射 光子晶体 亚波长 成像     

Numerical simulation of Bessel beams by FDTD employing the superposition principle

Finite difference time domain (FDTD) method is adopted to build a Bessel beams simulation model according to homogeneousness and linearity of the Maxwell equations in source-free region. Validation for this model is confirmed by comparing the simulation results with the theoretical results solved with a vector Helmholtz equation in free space and good agreement with maximum error 2% has been demonstrated. It is indicated that FDTD could be an effective approach to analyze other complicated models of Bessel beams in source-free region by means of superposition principle.     

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.     

高斯波束在双负媒质中的传播特性分析

 提出了一种基于Drude色散媒质模型的2维TM模时域有限差分法,数值模拟了高斯波束从自由空间垂直入射和斜入射到双负媒质(介电常数和磁导率同时为负)平板后的折射现象,并给出了平板内外的电场强度分布。模拟结果显示：垂直入射时,双负媒质平板对高斯波束具有汇聚作用,通过改变媒质的折射率,可以控制高斯波束通过组合平板的传播时间而不发生衰减;斜入射时,折射波束与入射波束均位于法线的同一侧,高斯波束在双负媒质与空气交界面处发生了负折射。     

一种可用于分析任意介电常数张量的各向异性波导导模的二维时域有限差分模型

为分析具有任意介电常数张量的各向异性波导的导模，本文通过把简化的二维时域有限差分（２－ＤＦＤＴＤ）法扩展至任意各向异性介质，提出了一种以Ｄ、Ｅ和Ｈ场为基础的统一的简化２－ＤＦＤＴＤ模型．利用该模型，研究了简化的复数２－ＤＦＤＴＤ方法与实变数２－ＤＦＤＴＤ方法之间的关系．文中还讨论了复变数方法和实变数方法的激励技术．