Analysis of frequency selective surfaces using two-parametergeneralized rational Krylov model-order reduction

Generalized rational Krylov model-order reduction techniques are applied to the spectral Galerkin system describing frequency selective surfaces, resulting in surface reflection coefficient models that depend on both the frequency and the incident angle of the exciting wave. The procedure is composed of three steps: construction of the spectral Galerkin system, linearization of that system, and reduction of the linearized system. The linearization of the spectral Galerkin matrix is carried out using two-dimensional (2-D) polynomial interpolation and the generation of a “two-parameter” companion form of the polynomial system. The subsequent model-order reduction is based on the concept of generalized Krylov subspaces, which are defined in the text. It results in a small system with a frequency and incident angle dependent output that matches the two-parameter polynomial interpolant system transfer function and its derivatives at many points in the frequency/incident angle plane. The technique is applied to the characterization of several frequency selective surfaces, and numerical results that demonstrate the accuracy of the techniques over a broad band of frequencies and range of incident angles are presented     

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.     

Parameterized Model Order Reduction Techniques for FEM Based Full Wave Analysis

As operating frequencies increase full wave methods such as the finite element method (FEM) become necessary for the analysis of high-frequency circuit structures. Such techniques result in very large systems of equations, and model order reduction (MOR) was proven to be very effective in combating such increased complexity. Using traditional MOR, one has to generate a new reduced model each time a design parameter is modified, thus significantly reducing the CPU efficiency. In this paper, a multidimensional Krylov subspace method is proposed to perform reduction directly on the vector wave equation based FEM system and to generate parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction. In order to accomplish this, second-order Arnoldi methods are extended to include design parameters such as material properties, and geometrical parameters in the reduced order model. In addition, multidimensional moment matching technique is used to address the Krylov incompatibility of FEM problems which include arbitrary frequency dependence in the system. This technique results in significant CPU savings and enables applications such as optimization and design space exploration.      

Low backscattered TM-polarised strip gratings

The development of reflector-backed strip gratings exhibiting properties like the elimination of specular reflections from a conducting surface for normal and near-normal incidence is reported. This is not possibly by conventional corrugated metallic surfaces. Perfect blazing to n = ?1 spectral order is also provided by the developed system. This technique offers a simple and inexpensive method for the simulation of corrugated horns.     

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.     

Study on Frequency Coherence Properties of Light Beams

This paper presents a new concept of frequency coherence in the frequency-time domain to describe the field correlations between two lightwaves with different frequencies. The coherence properties of the modulated beams from lightwave sources with different spectral widths and the modes of Fabry-Perot (FP) laser are investigated. It is shown that the lightwave and its corresponding sidebands produced by the optical intensity modulation are perfectly coherent. The measured linewidth of the beat signal is narrow and almost identical no matter how wide the spectral width of the beam is. The frequency spacing of the adjacent FP modes is beyond the operation frequency range of the measurement instruments. In our experiment, optical heterodyne technique is used to investigate the frequency coherence of the modes of FP laser by means of the frequency shift induced by the optical intensity modulation. Experiments show that the FP modes are partially coherent and the mode spacing is relatively fixed even when the wavelength changes with ambient temperature, bias current and other factors. Therefore, it is possible to generate stable and narrow-linewidth signals at frequencies corresponding to several mode intervals of the laser.     

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.     

Proper Orthogonal Decomposition in the Generation of Reduced Order Models for Interconnects

In this paper, reduced order models are generated using the technique of proper orthogonal decomposition (POD), also known as Karhunen-LoÈve decomposition (KLD) for the simulations of interconnect problems. Model order reduction is achieved by projecting the state-space of the original problems onto a subspace spanned by a few number of proper orthogonal modes (POMs) extracted by the POD procedure from an ensemble of system responses at a series of selected frequencies. The proper orthogonal values (POVs) corresponding to the POMs indicate the level of the importance of each POM and provide a guidance for the number of POMs to be used in the reduced order models in order to have enough accuracy. Numerical experiment results obtained from the simulations of a two-conductor interconnect and a spiral inductor demonstrate that the reduced order models generated in this way can simulate the original system more effectively and faithfully than those generated with the standard Krylov subspace method with moment matching at a single point.      

A Sensitivity Analysis of Frequency Selective Surfaces at Millimeter Wave Band

This work presents a sensitivity analysis for the resonant frequency and bandwidth of frequency selective surfaces (FSS) as a function of the structural parameters. The frequency selective surface structure considered here is composed by crossed dipole conductive patches deposited on an anisotropic dielectric layer. Firstly, the moment method is used in combination with the immittance technique in the spectral domain to determine the frequency response of the analyzed structure. Secondly, numerical techniques are used to obtain the resonant frequency and bandwidth sensitivities as a function of the considered FSS structural parameters.     

A spectral Lanczos decomposition method for solving 3-Dlow-frequency electromagnetic diffusion by the finite-elementmethod

A very efficient three-dimensional (3-D) solver for the diffusion of the electromagnetic fields in an inhomogeneous medium is described. The proposed method employs either the node-based or the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution in the frequency domain. By analyzing some practical geophysical problems, it is shown that the SLDM is extremely fast and, furthermore, the electromagnetic fields at many frequencies can be evaluated by performing the SLDM iteration only at the lowest frequency     

Multishot rosette trajectories for spectrally selective MR imaging

In nuclear magnetic resonance, different spectral components often correspond to different chemical species and as such, spectral selectivity can be a valuable tool for diagnostic imaging. In the work presented here, a multishot image acquisition method based upon rosette k-space trajectories has been developed and implemented for spectrally selective magnetic resonance imaging (MRI). Parametric forms for the gradient waveforms and design constraints are derived, and an example multishot gradient design is presented. The spectral behaviour for this imaging method is analyzed in a simulation model. For frequencies that are near to the resonant frequency, this method results in a lower intensity, but undistorted image, while for frequencies that are off-resonance by a large amount, the object is incoherently dephased into noise. A method by which acquisitions are delayed by small amounts is introduced to further reduce the residual intensity for off-resonant signals. An image reconstruction method based on convolution gridding, including a correction method for small amounts of magnetic field inhomogeneity, is implemented. Finally, the spectral selectivity is demonstrated in vivo in a study in which both water and lipid images are generated from a single imaging data set     

用谱域法分析含介质衬底的频率选择表面

本文用谱域Galerkin法分析分层均匀媒质中的频率选择表面。由于选用了存在Fourier变择换解析表达式的电流基函数集,简化了求解过程。为“十”形贴片阵的了频率选择表面所计算的反射系数频响特性,与文献提供的模式法计算结果符合得很好。文中给出了不同介质衬底厚度时的计算结果并进行了讨际。     

Investigation of millimeter-wave scattering from frequencyselective surfaces

A comparative numerical and experimental analysis of scattering from dielectric-backed frequency-selective surfaces in W-band (75-110 GHz) was carried out. The examples studied include metal (aluminium), resistive (bismuth), and bismuth-loaded I-pole or linearized Jerusalem cross arrays on fused silica, all of which exhibit a band-stop resonance in W-band as a general feature. The arrays were fabricated using standard photolithographic techniques. The numerical analysis involves the solution of an electric field integral equation using subdomain rooftop basis and testing functions within the framework of the Galerkin testing procedure. The lossy nature of the materials was fully accounted for. A comparative analysis of doubly stacked aluminium I-pole arrays was also performed. The numerical analysis exploits a variant of the cascade method in that the immediately adjacent dielectric layers are included in the construction of the scattering matrix for the frequency selective surface. This allows the higher-order evanescent Floquet modes to decay sufficiently at the dielectric boundaries so they can be ignored in the scattering matrix     

Analysis of dielectrically loaded radiators using entire-domainGalerkin technique

The response of various types of dielectrically loaded radiators to a time-harmonic excitation is analyzed, by employing an integral-equation formulation in conjunction with an entire-domain Galerkin technique. Coupled integral equations are derived in the frequency domain. These are written in terms of the conductivity currents or/and the electric fields developed on the conducting surfaces or/and inside the dielectric materials, respectively. They are solved via the method-of-moments technique. In particular, an entire-domain Galerkin technique is employed, and proves very efficient, when rather specific geometries are considered and appropriate “intelligent” basis-function sets are chosen, accelerating the convergence of the method. To prove this claim, three representative antenna structures, of significant practical use, corresponding to the three types of geometries (cylindrical, spherical, and planar), are solved in the resonance region. Parallelization of the developed sequential code is employed, in order to extend the use of Galerkin technique to electrically large structures. The validity of the proposed method is checked, and numerical results are presented for several cases     

Improvement in the Low Frequency Performance of Geometric Transition Radar Absorbers Using Square Loop Impedance Layers

A technique is described for improving the low frequency performance of geometric transition (GT) radar absorbers based on lossy foam pyramids. The technique makes use of the fact that at high frequencies, only the geometric transition region of the absorber is utilized whereas at low frequencies, the whole absorber thickness interacts with the incident wave. Hence the low frequency performance may be improved, without compromising that at high frequencies, by electrically loading the absorber base layer using one or more frequency selective surfaces (FSS) whose elements are typically in the form of single or nested loops. Other advantages of this technique include minimal increases in weight and manufacturing costs. The paper includes comparative predictions of unmodified and loaded GT absorber reflectivity at both normal and oblique incidence and discusses the effect on absorber performance of tolerance variations in the dimensions and location of the loading FSS elements. Finally, free-space reflectivity measurements on unmodified and loaded commercial absorber blocks are made over the frequency range 1-10 GHz and these confirm the validity of the technique.     

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。     

Application of high Tc superconductors asfrequency selective surfaces: experiment and theory

The use of YBa₂Cu₃O_7-x and Tl₂CaBa₂Cu₂O₈ high-temperature superconducting thin films to fabricate frequency selective surfaces (FSS) at millimeter-wave frequencies (75-110 GHz) is discussed. An analytical/numerical model was applied, using a Floquet expansion and the method of moments, to analyze bandstop superconducting frequency selective surfaces. Experimental results were compared with the model, and showed agreement with resonant frequency prediction with an accuracy of better than 1%. The use of the superconducting frequency selective surfaces as quasi-optical millimeter-wave bandpass filters was also demonstrated     

Reflector-backed perfectly blazed strip gratings simulate corrugated reflector effects

Perfect blazing of reflector-backed thin strip gratings to n = ? 1 spectral order for both TE and TM polarisations is compared with corrugated reflection gratings. The strip gratings are shown to be simulating effects of rectangular corrugations in conducting surfaces.     

Effects of various suspended mounting schemes on modecharacteristics of coupled slotlines considering conductor thickness forwideband MIC applications

Propagation characteristics of fundamental and higher-order modes are determined in coupled slotlines with three suspended mounting schemes (pedestal, groove, inverse pedestal) for wideband applications of microwave and millimeter-wave integrated circuits. The analysis is based on a novel enhanced spectral domain approach (ESDA) that combines essentially the conventional spectral domain technique with the power conservation theorem. Numerical results, considering also the influence of finite conductor thickness, are presented for propagation constants and characteristic impedance of the fundamental modes. Effects of different suspended mounting schemes on cutoff frequencies of first higher-order even and odd modes are discussed in detail. Field profiles of the fundamental modes in coupled slotlines with and without pedestals are shown. The inherent mechanism of mode transition is explained with respect to different pedestal sizes, indicating that the monomode bandwidth can be extended by appropriately choosing the dimension of pedestal in coupled slotlines     

Zero-crossing based spectral analysis and SVD spectral analysis forformant frequency estimation in noise

The authors discuss a method for spectral analysis of noise corrupted signals using statistical properties of the zero-crossing intervals. It is shown that an initial stage of filter-bank analysis is effective for achieving noise robustness. The technique is compared with currently popular spectral analysis techniques based on singular value decomposition and is found to provide generally better resolution and lower variance at low signal to noise ratios (SNRs). These techniques, along with three established methods and three variations of these method, are further evaluated for their effectiveness for formant frequency estimation of noise corrupted speech. The theoretical results predict and experimental results confirm that the zero-crossing method performs well for estimating low frequencies and hence for first formant frequency estimation in speech at high noise levels (~0 dB SNR). Otherwise, J.A. Cadzow's high performance method (1983) is found to be a close alternative for reliable spectral estimation. As expected the overall performance of all techniques is found to degrade for speech data. The standard autocorrelation-LPC method is found best for clean speech and all methods deteriorate roughly equally in noise