Analysis of frequency selective surfaces through the blazing onsetusing rational Krylov model-order reduction and Woodbury singularityextraction

Rational Krylov model-order reduction techniques are used to accelerate the characterization of frequency selective surfaces (FSSs) over broad spectral ranges, including frequencies at which a higher order Floquet mode stops evanescing and begins to propagate. The procedure comprises three main stages: (1) construction of the spectral Galerkin system at a small set of frequencies, (2) linearization of that system, and (3) reduction of the linearized system using the rational Krylov technique. The inclusion of blazing frequencies in the band of interest complicates the second and third of these steps because of the branch point singularity in the periodic Green's function. This difficulty is avoided by removing the blazing modes contributions to the spectral Galerkin matrix using the Woodbury formula for low-rank updates. The algorithm results in a set of small linear systems producing outputs that are combined to approximate the reflection and transmission coefficients of all propagating modes. The technique is applied to three different frequency selective surfaces and is shown to be accurate and efficient in all cases     

Model-order reduction by dominant subspace projection: error bound, subspace computation, and circuit applications

Balanced truncation is a well-known technique for model-order reduction with a known uniform reduction error bound. However, its practical application to large-scale problems is hampered by its cubic computational complexity. While model-order reduction by projection to approximate dominant subspaces without balancing has produced encouraging experimental results, the approximation error bound has not been fully analyzed. In this paper, a square-integral reduction error bound is derived for unbalanced dominant subspace projection by using a frequency-domain solution of the Lyapunov equation. Such an error bound is valid in both the frequency and time domains. Then, a dominant subspace computation scheme together with three Krylov subspace options is introduced. It is analytically justified that the Krylov subspace for moment matching at low frequencies is able to provide a better dominant subspace approximation than the Krylov subspace at high frequencies, while a rational Krylov subspace with a proper real shift parameter is capable of achieving superior approximation than the Krylov subspace at low frequency. A heuristic method of choosing a real shift parameter is also introduced based on its new connection to the discretization of a continuous-time model. The computation algorithm and theoretical analysis are then examined by several numerical examples to demonstrate the effectiveness. Finally, the dominant subspace computation scheme is applied to the model-order reduction of two large-scale interconnect circuit examples.     

Reduced-order modeling of multiscreen frequency-selective surfacesusing Krylov-based rational interpolation

A method is presented for generating a broad-band rational interpolant approximation of the reflection coefficient of multiple-screen frequency-selective surfaces (FSSs). The technique is structured around a linearization of the system provided by a spectral domain moment method-based analysis of the FSS, followed by a model-order reduction of the linearized system using the dual rational Arnoldi method. This process creates a rational interpolant of the linearized system that matches its transfer function and its derivatives at several expansion points in the Laplace domain. Numerical results indicate that a reduced-order model with a system matrix of dimension less than 20×20 can accurately reproduce the broad-band behavior of multiscreen FSSs originally modeled with several hundreds or thousands of unknowns     

A Complete Finite-Element Analysis of Multilayer Anisotropic Transmission Lines From DC to Terahertz Frequencies

A complete and efficient transmission line simulation framework and the techniques involved are reported in this paper. A highly efficient finite-element quasi-TEM technique with comparable full-wave accuracy is applied as our fundamental simulation method. The fast quasi-TEM analysis is first performed over the entire frequency band with a self-estimation of solution accuracy. Then, depending on the requirement of accuracy, a switch frequency can be determined and a full-wave modal solver is automatically initiated to solve the problem up to the high frequency end. In addition, we apply improved model-order reduction methods in both the quasi-TEM and full-wave analyses to further speed up a simulation. Thus, the quasi-TEM and full-wave techniques as well as their associated model-order reduction methods are integrated to provide an efficient and accurate simulation from dc to very high frequencies. As for the versatility of the solver, the material loss, anisotropism, and frequency dependence are all taken into account in our formulations in order to provide a more complete field-based transmission line modeling.     

A Frequency Selective Surface With Miniaturized Elements

We demonstrate a new class of bandpass frequency selective surface (FSS), the building block of which, unlike the traditional FSSs, makes use of resonant dipole and slot structures that have dimensions much smaller than the operating wavelength. This design allows localization of bandpass characteristics to within a small area on the surface which in turn facilitates flexible spatial filtering for an arbitrary wave phasefront. The proposed FSS is made up of periodic array of metallic patches separated by thin air-gaps backed by a wire mesh having the same periodicity (Ltlambda). The array of metallic patches constitute a capacitive surface and the wire mesh a coupled inductive surface, which together act as a resonant structure in the path of an incident plane wave. Like traditional FSSs, the capacitive and inductive surfaces of the proposed FSS can easily be fabricated using printed circuit technology on both sides of microwave substrates. It is shown that by cascading such bandpass surfaces in a proper fashion, any arbitrary multipole filter or non-commensurate multiband response can be obtained. The frequency response of the proposed miniaturized-element frequency selective surface (MEFSS) is demonstrated for various incident angles and it is shown that one-pole designs are less sensitive than two-pole designs to the angle of incidence. Dual band designs are also possible based on two-pole designs, but are more sensitive to incident angle than single band designs because of their larger (in terms of wavelengths) spacing. Prototypes of single-pole and dual-pole MEFSSs are fabricated and tested in a waveguide environment at X-band frequencies and excellent agreements between the measured and simulated results are demonstrated     

New method for the efficient summation of double infinite series arising from the spectral domain analysis of frequency selective surfaces

When the method of moments (MoM) in the spectral domain is applied to the analysis of frequency selective surfaces, the entries of the MoM matrix are slowly convergent double infinite series. In this paper, a two-step acceleration technique is developed which makes it possible the fast and accurate computation of these double series in the particular case where subsectional rooftops are used as basis functions. The technique is based on a combination of the use of Kummer's transformation, the use of Poisson's transformation, and the determination of judicious Chebyshev polynomial interpolations of some of the spectral discrete functions involved in the infinite series. The results obtained show that when all the double series of the MoM matrix are to be computed with an accuracy of three significant figures, the new acceleration technique turns out to be about one thousand times faster than brute-force computation, and a few times faster than the acceleration technique based on fast Fourier transform.     

“十”字环形缝隙阵频率选择表面的频率特性研究

本文用模匹配法分析了任意角度平面波入射时分析一般单元缝隙阵频率选择表面的频率响应性。这里考虑的ＦＳＳ是一零厚度无限大平面阵。问题的 解是以Ｆｌｏｑｕｅｔ 定理为基础。通过匹配ＦＳＳ表面的切向场分量获得的。     

Robust Formulations of the Cauchy Method Suitable for Microwave Duplexers Modeling

It is well known that a Vandermonde matrix generates an ill-conditioned system matrix when applied with finite numerical precision. This deficiency affects the Cauchy method by restricting its application to only lower order systems. This paper presents innovative, accurate, and robust formulations of the Cauchy method to rectify this limitation and make the Cauchy method suitable for the extraction of a high-order microwave duplexer polynomial model. The techniques employed are: the change of polynomial basis into the Krylov subspace and the precondition technique, both acting on the system matrix of the classic Cauchy method formulation. A novel formulation using the QR algorithm on the two characteristic functions of the duplexer and a suitable combination of the QR method and the precondition technique are then presented. Each of these procedures has been successfully verified by numerical application examples     

查找表联合记忆效应补偿技术的宽带自适应预失真算法

为了能够对记忆型功率放大器线性化处理,并能一定程度克服其记忆效应,该文介绍一种自适应数字预失真器。该数字预失真器采用查找表与记忆效应补偿技术相结合的方法,并且利用内插值方法有效减小了查找表幅度量化过程产生的误差。相比记忆多项式预失真器,这种预失真器的计算复杂度较小,却能够得到与其相近的线性化效果。基于功率放大器记忆多项式模型,利用OFDM(Orthogonal Frequency Division Multiplexing)宽带信号验证该文提出的预失真器对记忆型非线性功率放大器的良好线性化效果。     

十字形频率选择表面单元的传输系数分析

传输系数是频率选择表面的一项重要技术指标。简要介绍了利用谱域Galerkin法计算平面频率选择表面传输系数的方法。该方法以平面波谱展开和傅里叶变换为基础,通过矩量法求解频率选择表面电流,进而求得传输系数。对一个十字形频率选择表面的传输系数进行了测量和计算,并将测量结果和计算结果进行了比较,两者吻合得较好,验证了本方法的正确性。     

多路激光体布喇格光栅光谱合成特性研究

为了研究多路激光体布喇格光栅光谱合成的合成特性,采用建立多路反射式体布喇格光栅光谱合成系统物理模型的方法,得到了具有不同谱宽的光束的衍射效率曲线,以及体布喇格光栅材料的吸收系数和通道间的串扰对总的合成效率的影响曲线。结果表明,在入射光束中心频率不变的情况下,随着光束光谱宽度的增大,衍射效率逐渐减小;随着光束中心频率与光栅中心频率之间偏移量的增加,衍射效率逐渐减小;当光束谱宽与光栅光谱选择宽度大约相等,并且通道之间的间距较小时,通道之间由于发生串扰而损失的衍射效率需考虑,随着合成路数的增加,总的合成效率受体布喇格光栅材料吸收系数的影响越来越大,而受串扰的影响则几乎保持不变。     

频率选择表面大范围角度入射时稳定中心频率的方法

在频率选择表面(FSS)的应用中,往往涉及到大范围角度入射的情况,此时中心频率变得不稳定,会随着入射角度的变化而发生漂移。本文针对此问题,在TE波大范围角度入射FSS时,提出了一种实现中心频率稳定性的方法。计算结果表明,随着入射角度的变化合理调整电介质的介电常数可以使FSS获得稳定的中心频率。此方法可以应用在曲面FSS上以减小中心频率对角度的敏感性,以球壳上应用的FSS为例,给出了应用模型。     

FSS对TE极化波传输特性的实验研究

通过实验测试,从单元的尺寸、形状、介质加载以及各参数对入射角的敏感性等方面,初步探讨了频率选择表面(Frequency Selective Surfaces,简称FSS)对TE波的传输特性.结果表明,FSS的谐振频率主要由单元的尺寸和形状确定;介质加载使得FSS平板的谐振频率降低;加载不同厚度的介质对FSS的透波率和谐振频率影响不同;对称加载介质能提高FSS的传输特性对入射角的稳定性.     

Frequency selective surfaces comprised of periodic arrays of two-turn square spiral shaped conductors

The scattering of electromagnetic waves from a frequency selective surfaces (FSSs) composed of a new two-turn square spiral shaped periodic structures are investigated by using modal expansion method. The moment method of Galerkin type is employed by expressing the current induced on the metallic surfaces in terms of Piecewise Sinusoidal (PWS) basis functions to determine the FSS structure reflection and transmission coefficients.     

Circuit-Based Analysis of Electromagnetic Field Coupling With Nonuniform Transmission Lines

This paper presents a new algorithm for simulating electromagnetic (EM) field coupling with nonuniform multiconductor transmission lines in a circuit simulation environment. The proposed algorithm is based on the concept of passive model-order reduction, whereby an algorithmically developed passive reduced-order model, coupled with a set of equivalent sources representing the incident filed, are shown to accurately capture the behavior of the transmission line under EM excitation. The reduced-order model is developed independently from the particular shape of the incident field pulse, in the sense that, in constructing the model, one does not need prior knowledge about the waveform of the incident pulse of the EM field. In addition, it is also shown that the model developed can be used to simulate the transmission line in the absence of the EM field. The derived equivalent sources, representing the field coupling, are given directly in the time domain, thereby making simulation under nonlinear circuit terminations an easy task. Although the proposed work is aimed mainly at simulating nonuniform transmission lines, it can be applied to uniform lines as a special case. The proposed algorithm has been validated numerically with several examples.     

单环频率选择表面的传输系数分析

简要介绍了利用谱域伽略金法计算平面频率选择表面传输系数的方法。该方法以平面波谱展开和傅里叶变换为基础,在谱域中应用弗洛凯定理建立方程。采用屋顶基函数作为子域基函数表示感应电流,通过矩量法求解频率选择表面上的感应电流,进而求得传输系数。给出了某工程使用的单环频率选择表面的设计,计算结果与测试结果一致。     

Reduced-order modeling for hyperthermia: an extendedbalanced-realization-based approach

Accurate thermal models are needed in hyperthermia cancer treatments for such tasks as actuator and sensor placement design, parameter estimation, and feedback temperature control. The complexity of the human body produces full-order models which are too large for effective execution of these tasks, making use of reduced-order models necessary. However, standard balanced-realization (SBR)-based model reduction techniques require a priori knowledge of the particular placement of actuators and sensors for model reduction. Since placement design is intractable (computationally) on the full-order models, SBR techniques must use ad hoc placements. To alleviate this problem, an extended balanced-realization (EBR)-based model-order reduction approach is presented. The new technique allows model order reduction to be performed over all possible placement designs and does not require ad hoc placement designs. It is shown that models obtained using the EBR method are more robust to intratreatment changes in the placement of the applied power field than those models obtained using the SBR method     

Convoluted dipole array elements

Convoluting the conductors of dipole frequency selective surfaces (FSS) while retaining the unit cell dimensions produces a major reduction in the resonant frequency and in the sensitivity of the reflection band to angle of incidence. The separation of this band from the onset of grating responses is correspondingly increased.<>     

3D Micropatterned Functional Surface Inspired by Salvinia Molesta via Direct Laser Lithography for Air Retention and Drag Reduction

Bioinspired functional surfaces are attracting increasing interest in surface engineering, mostly in the field of wettability. The Salvinia-effect is a remarkable example of superficial air retention and drag force reduction caused by selective chemical coating (super-hydrophobic wax and hydrophilic dead cells) and peculiar 3D hierarchical morphological structures. The replication of Salvinia-like patterns at the microscale has always been prevented by limitations in microfabrication techniques, thus hindering relevant technological applications at this dimensional scale. Integrating 3D laser lithography and traditional microfabrication techniques, dimensionally downscaled, 3D micropatterned surfaces inspired for the first time by both morphology and chemical coating of the hairs present on the Salvinia Molesta leaves are reproduced. The effect of design and different surface energies (bare hydrophilic, hydrophobic, selective hydrophilic/hydrophobic coating) on the wettability are modeled and investigated. Bioinspired surfaces demonstrated to be super-hydrophobic in terms of apparent static contact angle (up to 170°) and provide tunable adhesion with roll-off angle from less than 10° to 90°. They successfully proved remarkable underwater air retention capability, sustained by stable Cassie-Baxter state under external hydrostatic pressure up to 4 atm. The proposed surfaces are tested in hydrodynamic conditions: drag force reduction is successfully demonstrated with up to 40% of energy saved.