Mutual Coupling Reduction Techniques in Electronic Steering Antennas in X Band

This work provides the development of an antenna for satellite communications onboard systems based on the recommendations ITU-R S.580-6 [1] and ITU-R S.465-5 [2]. The antenna consists of printed elements grouped in an array, working in a frequency band from 7.25 up to 8.4 GHz (15% of bandwidth). In this working band, transmission and reception are included simultaneously. The antenna reaches a gain about 31 dBi, has a radiation pattern with a beam width smaller than 10oand dual circular polarization. It has the capability to steer in elevation through a Butler matrix to 45

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Operational Modal Analysis on laminated glass beams

Laminated glass is a sandwich element consisting of two or more glass sheets, with one or more interlayers of polyvinyl butyral (PVB). The dynamic response of laminated glass beams and plates can be predicted using analytical or numerical models in which the glass and the PVB are usually modelled as linear-elastic and linear viscoelastic materials, respectively. In this work the dynamic behavior of laminated glass beams are predicted using a finite element model and the analytical model of Ross-Kerwin-Ungar. The numerical and analytical results are compared with those obtained by operational modal analysis performed at different temperatures.

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.

FE–BE Coupling Methods for Elastoplasticity

Non-linear physical systems of infinite extent are conveniently modelled using FE–BE coupling methods. By the combination of both methods, suitable use of the advantages of each one may be obtained. Several possibilities of FEM–BEM coupling and their performance in some practical cases are discussed in this paper. Parallelizable coupling algorithms based on domain decomposition are developed and compared with the most traditional coupling methods.

A computer program for the analysis of the dynamic bending-torsion coupling in bridges using a mini-computer

The analysis of modes and natural frequencies is of primary interest in the computation of the response of bridges. In this article the transfer matrix method is applied to this problem to provide a computer code to calculate the natural frequencies and modes of bridge-like structures. The Fortran computer code is suitable for running on small computers and results are presented for a railway bridge.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Mutual coupling reduction using EBG in steering antennas

In this letter, a dual circular polarized steering antenna for satellite communications in X-band is presented. This antenna consists of printed elements grouped in an array, able to work from 7.25 up to 8.4 GHz in both polarizations: left-handed circular polarization (LHCP) and right-handed circular polarization (RHCP). The module antenna is compact, with narrow beamwidth, and reaches a gain of 16 dBi. It has the capability to steer in elevation to and electronically with a Butler matrix. In order to reduce the mutual coupling between adjacent patches, electromagnetic band-gap (EBG) structures are introduced. These EBGs combine double-layer and edge location via in order to reduce the size, without changing the low-permittivity substrate, and therefore maintaining the high radiation efficiency of the antenna.

Maximum Likelihood Estimation of Modal Parameters in Structures Using the Expectation Maximization Algorithm

This paper presents a time-domain stochastic system identification method based on maximum likelihood estimation (MLE) with the expectation maximization (EM) algorithm. The effectiveness of this structural identification method is evaluated through numerical simulation in the context of the ASCE benchmark problem on structural health monitoring. The benchmark structure is a four-story, two-bay by two-bay steel-frame scale model structure built in the Earthquake Engineering Research Laboratory at the University of British Columbia, Canada. This paper focuses on Phase I of the analytical benchmark studies. A MATLAB-based finite element analysis code obtained from the IASC-ASCE SHM Task Group web site is used to calculate the dynamic response of the prototype structure. A number of 100 simulations have been made using this MATLAB-based finite element analysis code in order to evaluate the proposed identification method. There are several techniques to realize system identification. In this work, stochastic subspace identification (SSI)method has been used for comparison. SSI identification method is a well known method and computes accurate estimates of the modal parameters. The principles of the SSI identification method has been introduced in the paper and next the proposed MLE with EM algorithm has been explained in detail. The advantages of the proposed structural identification method can be summarized as follows: (i) the method is based on maximum likelihood, that implies minimum variance estimates; (ii) EM is a computational simpler estimation procedure than other optimization algorithms; (iii) estimate more parameters than SSI, and these estimates are accurate. On the contrary, the main disadvantages of the method are: (i) EM algorithm is an iterative procedure and it consumes time until convergence is reached; and (ii) this method needs starting values for the parameters. Modal parameters (eigenfrequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using both the SSI method and the proposed MLE + EM method. The numerical results show that the proposed method identifies eigenfrequencies, damping ratios and mode shapes reasonably well even in the presence of 10% measurement noises. These modal parameters are more accurate than the SSI estimated modal parameters.

A canonical UTD solution for electromagnetic scattering by an electrically large impedance circular cylinder illuminated by an obliquely incident plane wave

A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

New EBG solutions for mutual coupling reduction

Electromagnetic Band Gap (EBG) based on Frequency Selective Surfaces (FSS) [1] are one type of metamaterials [2] with electrical properties [3]. This EBG are used in mutual coupling reduction, back lobe radiation reduction, etc. In this work not only new shapes for the mushroom-type are presented, but also multilayered configurations were studied in order to reduce the patch size and the necessary number of elements.

Surface Impedance Characterization for Mutual Coupling Calculation of Patches on a Dielectric-Coated PEC Circular Cylinder

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green?s function between the original problem and the equivalent one with the IBC. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green?s functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.