Efficient analysis of frequency selective surfaces using the Ewald transform

This work presents an analysis of frequency selective surfaces (FSSs) with Dürer's pentagon pre-fractals patch elements. The proposed FSSs are composed by a 2-D periodic array of metal pre-fractals elements printed on a dielectric substrate. A parametric analysis is performed using Ansoft Designer commercial software in terms of the FSS periodicity and of the fractal iteration number used in the FSS elements. The structures are proposed to behave like stop-band spatial filters and exhibit interesting features to be used in the design of compact FSSs with broadband or dual band responses.

This paper presents an analysis of the characteristics of the frequency selective surface (FSS) by means of equivalent circuit models. In order to determine the circuit element parameters of the FSS with resonant elements of arbitrary shape, the eigenvalue problem of the matrix equation is solved and the Q curve of each resonance is derived from the frequency dependence of the reactance obtained from the characteristic current distributions at resonance. By equating this Q curve with that for the equivalent circuit, the circuit parameters are derived. As an example of analysis by the present method, the circuit element parameters of patch-type resonant elements designed by us using the genetic algorithm (GA) are derived. The characteristics of the dielectric-loaded FSS for the C/Ka band are analyzed by means of the equivalent circuit. The usefulness of the proposed method is verified by comparison of the frequency characteristics obtained by the method of moments and by the equivalent circuit. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 88(6): 9–17, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20162

In this paper a modified method based on FDTD method is used to analyze frequency selective surfaces with periodic boundary condition. Computation results are compared to that from other scholars. Good agreement has been observed. Multiplexer, which consists of two sheets of FSS, is simulated and good performance has been obtained over a band from 100 GHz to 450 GHz.

A loaded gridded Jerusalem cross element is analyzed and predicted its plane-wave transmission/reflection characteristics for a normal and oblique angle of incidence using an equivalent circuit model. Further, the structural behaviour of its conformal bent is analyzed by bending the structure at a conformal radius of 25 mm. The modes of resonance of the structure are examined, current is largely confined at the E-plane arm at the resonance frequency. The deviation in the EM performance of planar and conformal structures have been studied for different design parameters. A Commercial full-wave simulator is employed to validate the designed analytical expressions of the element and for further analysis.

Computer programs for simulation of microwave structures are becoming accessible. However, to understand electromagnetic fields behavior and to comprehend the numerical model limitations, a solid theoretical basis and computational expertise to enable the implementation of the own programs remains indispensable. The wave concept iterative procedure, WCIP, is a numerical technique easy to understand, that can be implemented without great efforts. In this work the WCIP is applied to analysis of frequency selective surface, FSS, with Koch Island patch elements. Obtained numerical results are compared to others obtained by the use of Ansoft Designer <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">™</sup> software and to experimental ones.

In this paper, combined elements method is introduced to achieve dual stop-band frequency selective surface (FSS). Later, a dual-band WLAN antenna is designed and the centre frequency is at 2.4GHz and 5.4GHz which accord with the FSS in this paper. We use FSS as dual-band WLAN antenna's reflection plan to improve the performance of antenna. The analysis and results of antenna and FSS are given. The results show that antenna's gain can be improved after the FSS is placed as the reflection plane. This is a new research area which have great prospect in the design of antenna combined with FSS.

This paper presents a design of dualband frequency selective surface (FSS) element design based on SIW cavity (SIWC) technology and its performance analysis. The proposed dualband FSS is modelled using a combination of two FSS elements. A cross-slot element has been enclosed by a square slot to design the proposed shape. The structure shows dualband response at two different frequency bands C- and Ku-bands with sharp roll-off performance characteristics. The performance of the structure has been estimated using commercial CST Microwave studio. The simulation results show the higher selectively, very good isolation between the bands and stable performance characteristics compared with its equivalent conventional planar version.

The possibility of reconstructing two‐dimensional electron‐density profiles in the ionosphere with ionospheric tomography is significant. However, due to the nature of the imaging system, there are several resolution degradation parameters. In order to compensate for these degradation parameters, a priori information must be used. This article introduces the orthogonal decomposition algorithm for image reconstruction, which uses the a priori information to generate a set of orthogonal basis functions for the source domain. This algorithm consists of two simple steps: orthogonal decomposition and recombination. In the development of the algorithm, it is shown that the degradation parameters of the imaging system result in correlations among projections of orthogonal functions. Gram–Schmidt orthogonalization is used to compensate for these correlations, producing a matrix that measures the degradation of the system. Any set of basis functions can be used, and depending upon this choice, the nature of the algorithm varies greatly. Choosing the basis functions of the source domain to be the Fourier kernels produces an algorithm capable of isolating individual frequency components of individual projections. This particular choice of basis functions also results in an algorithm that strongly resembles the direct Fourier method, but without requiring the use of inverse Fourier transforms.

Interactive rendering of realistic objects under general lighting models poses three principal challenges. Handling complex light transport phenomena like shadows, inter-reflections, caustics and sub-surface scattering is difficult to do in real time. Integrating these effects over large area light sources compounds the difficulty, and finally real objects have complex spatially-varying BRDF's. Precomputed Radiance Transfer (PRT) encapsulates a family of techniques that partially addresses these challenges. PRT is an active of area of research that has relevance to both the academic research community and practitioners of interactive computer graphics. This technique and its variants are being actively investigated in the game development community and there is quite a lot of interest due to the recent appearance of PRT techniques in games such as Halo 2.This course covers these techniques, compares them and discusses their various strengths and weaknesses. A more rigorous derivation directly from the rendering equation is presented along with practical implementation details, both of which are generally not included in technical papers. After introducing the necessary foundation (rendering equation, basis functions, etc.), we begin with simple PRT for diffuse objects. We continue with general PRT using the concept of transfer matrices, which allow for arbitrary reflectance models. The possible choices for basis functions are discussed as well. Different light source representations are presented and compared. Finally, we discuss practical issues with PRT, such as data compression, spatial sampling, normal mapping, precomputation, and more. By the end of the course the audience will be able to pick the right algorithm for their needs and will hopefully have gained some of the unpublished insights the speakers have gained by working in this area.

Choice of Basis Functions for Continuous and Discrete System Modelling

We address the question of an appropriate choice of basis functions for the self-consistent field (SCF) method of simulation of the N-body problem. Our criterion is based on a comparison of the orbits found in N-body realizations of analytical potential-density models of triaxial galaxies, in which the potential is fitted by the SCF method using a variety of basis sets, with those of the original models. Our tests refer to maximally triaxial Dehnen gamma-models for values of $\gamma$ in the range 0<=gamma<=1. When an N-body realization of a model is fitted by the SCF method, the choice of radial basis functions affects significantly the way the potential, forces, or derivatives of the forces are reproduced, especially in the central regions of the system. We find that this results in serious discrepancies in the relative amounts of chaotic versus regular orbits, or in the distributions of the Lyapunov characteristic exponents, as found by different basis sets. Numerical tests include the Clutton-Brock and the Hernquist-Ostriker (HO) basis sets, as well as a family of numerical basis sets which are `close' to the HO basis set. The family of numerical basis sets is parametrized in terms of a quantity $\epsilon$ which appears in the kernel functions of the Sturm-Liouville (SL) equation defining each basis set. The HO basis set is the $\epsilon=0$ member of the family. We demonstrate that grid solutions of the SL equation yielding numerical basis sets introduce large errors in the variational equations of motion. We propose a quantum-mechanical method of solution of the SL equation which overcomes these errors. We finally give criteria for a choice of optimal value of $\epsilon$ and calculate the latter as a function of the value of gamma.

Fock states and coherent states have been widely applied in analyses of quantum-optics experiments. In this paper, the application of a set of basis functions that consist of a product of displaced harmonic-oscillator states for the electromagnetic field and atomic states that are eigenfunctions of the momentum operator will be explored. For the case of a single mode, these states are the exact eigenfunctions in the limiting case where the electromagnetic-field mode frequency is much larger than the atomic transition frequency. This choice of basis functions will be used to analyze the interaction of a nonrelativistic, ``two-level'' atom with a single-frequency, quantized electromagnetic-field mode. Since in this basis the sign of the displacement of the electromagnetic-field state depends on the state of the atom, these new basis wave functions exhibit explicitly some aspects of atom-field correlations that are intrinsically quantum mechanical in nature. The analysis will be performed in the electric-dipole approximation for an atomic system that obeys the \ensuremath{\Delta}m=0 selection rule. The rotating-wave-approximation (RWA) terms cannot be made negligible through judicious choice of the field polarization for this system. The diamagnetic term, ${\mathit{e}}^{2}$${\mathbf{A}}^{2}$/2${\mathit{mc}}^{2}$, which is of the same order of magnitude as the RWA terms, is taken into account exactly by slightly modifying the traditional approach to quantizing the electromagnetic field. In this way the physical effects of the diamagnetic term are absorbed into a new electromagnetic cavity mode frequency.An approximate expression for the combined system's energy eigenvalues is found up to third order in the ratio of one-half the atomic transition frequency to the mode frequency. This expression indicates that inclusion of the RWA terms adds a small ``ripple'' on top of the smoothly varying energy eigenvalues when they are plotted as a function of the atom-field coupling constant. The ripple is interpreted as ``interference'' between two displaced oscillator-field states that represent the unperturbed state. When the Fock states are used as the basis for expanding the wave function of this system, a formidable five-term recurrence relation results. However, expanding the wave function in terms of the displaced harmonic-oscillator basis results in a less formidable three-term recurrence relation for the quantum coefficients.

A new paradigm is presented to reconstruct the plasma current density profile in a tokamak in real-time. The traditional method of basing the reconstruction on real-time diagnostics combined with a real-time Grad–Shafranov solver suffers from the difficulty of obtaining reliable internal current profile measurements with sufficient spatial and temporal accuracy to have a complete picture of the profile evolution at all times. A new methodology is proposed in which the plasma current density profile is simulated in real-time by solving the first-principle physics-based equations determining its evolution. Effectively, an interpretative transport simulation similar to those run today in post-plasma shot analysis is performed in real-time. This provides real-time reconstructions of the current density profile with spatial and temporal resolution constrained only by the capabilities of the computational platform used and not by the available diagnostics or the choice of basis functions. The diagnostic measurements available in real-time are used to constrain and improve the accuracy of the simulated profiles. Estimates of other plasma quantities, related to the current density profile, become available in real-time as well. The implementation of the proposed paradigm in the TCV tokamak is discussed, and its successful use in plasma experiments is demonstrated. This framework opens up the possibility of unifying q profile reconstructions across different tokamaks using a common physics model and will support a wealth of applications in which improved real-time knowledge of the plasma state is used for feedback control, disruption avoidance, scenario monitoring and external disturbance estimation.

The intention of this work is to generate a mathematical model of a plate with collocated piezoelectric actuators/sensors to be used for control purposes. The proposed control method is a linear/nonlinear dynamic coupling technique developed by the ConStruct group at the University of Waterloo. The performance of the plate with attached layers of piezoelectric material is evaluated by a finite element model. Test results show that the application of this theory along with an appropriate choice of basis functions allows the analysis of a wide range of thicknesses. This approach avoids shear locking, and provides excellent accuracy, and convergence characteristics.

Efforts to get reliable data about the efficiency of a set of basis functions in representing a Reed-Muller canonical form with the minimum number of coefficients are frustrated by the long computation times necessary for calculation. Using an integrated suite of utility programs employing fast transforms, we provide statistics on the performance of six different algebras for two, three, four and five variables. Based on experimental results we suggest that the choice of basis functions has only a marginal effect for random samples from the entire function space. In addition we provide evidence which suggests that providing additional polarities has a more and more marginal effect upon efficiency.