Transmission Matrix Formulation Research Articles

On the Reduction of Transmission Complexity in MIMO-WCDMA Frequency-Selective Fading Orientations via Eigenvalue Analysis

In this paper, a novel transmission strategy for Mutliple Input Multiple Output Wideband Code Division Multiple Access (MIMO-WCDMA) orientations operating in frequency-selective fading environments is investigated, in terms of overall algorithmic complexity reduction. To this end, Principal Component Analysis (PCA) is employed on the received data matrix, in order to define the significant terms that are taken into account during transmission matrix formulation. According to the presented results, feedback information of only the primary eigenvector of the corresponding covariance matrix of the received data matrix is required, in order to maintain the mean Bit Error Rate (BER) at acceptable levels. In particular, a complexity reduction of up to 10% can be achieved, when comparing BER values derived by the selection of all components of the received covariance matrix during transmission matrix formulation, and the corresponding BER when selecting half of the components. This reduction is maintained to 10%, when considering a realistic four-element antenna design; however, in this case mean BER inaccuracy is further reduced to 1%.

Modelling cascaded cylindrical metasurfaces using sheet impedances and a transmission matrix formulation

Metasurfaces that manipulate electromagnetic waves have gained significant attention in recent years. The focus has primarily been on planar devices, while many applications require curved surfaces. In this study, the authors propose an analysis approach for cylindrical cascaded (multilayer) metasurfaces. The approach combines the concept of sheet impedance in the spectral domain with a new transmission matrix formulation that is applicable to stratified, canonical curved geometries. Approximate formulas for the sheet impedance of common planar, metallic patterns are also adapted to curved geometries. The reported analysis approach allows one to determine the optimal spectral-domain, azimuthal dependence of a sheet impedance, as well as the best geometrical elements to obtain the required azimuthal variation. The results are verified through several cylindrical metsurface examples.

Calculated magnetic and transport properties of Fe/Nacl/Fe (0 0 1) magnetic tunnel junction

The electronic structure and magnetic properties of Fe/NaCl/Fe (0 0 1) magnetic tunnel junction have been studied by means of a first-principles Green's function technique based on the tight-binding linear muffin-tin orbital method in the atomic sphere approximation. The results show the formation of sharp Fe/NaCl interfaces and the enhancement of the interface iron magnetic moment ( M Fe=2.96 μ B). The spin-dependent transport properties in current-perpendicular-to-plane configuration were calculated by means of the transmission matrix formulation of Kubo–Landauer formalism. The main contribution to the conductance in the ferromagnetic state is given by minority-spin electrons. The tunneling magnetoresistance rapidly increases with increasing NaCl barrier width.

Perpendicular-current giant magnetoresistance of M∕Cu∕M (001) junctions (M=Fe, Co, or Ni): An ab initio study

The electronic structure and magnetic properties of semi-infinite Cu(001)∕M∕Cu∕M∕semi-infinite Cu (001) multilayer systems with M=Fe, Co, or Ni have been studied by means of a first-principle Green’s function technique based on the tight-binding linear muffin-tin orbital method. The results show that at the M∕Cu (M=Fe or Co) interfaces there is a net charge transfer from iron and cobalt atoms to the neighboring paramagnetic copper atoms and an enhancement of the iron magnetic moment while at the Ni∕Cu interface, the nickel magnetic moment is reduced compared with its bulk value. This behavior is explained in terms of the relative positions of the Fermi levels of the magnetic material and copper. The conductance is determined in the ballistic limit, in the current-perpendicular-to-the-plane geometry by means of transmission matrix formulation of Kubo-Landauer formalism. It is shown that the oscillations of the giant magnetoresistance ratio are mainly the result of the oscillations of the minority-spin conductance.

Aspects of magnetotunnelling drawn fromab-initio-type calculations

Tunnelling between two semi-in®nite ferromagnetic electrodes separated by vacuum is studied theoretically on an ab-initio level by using the fully relativistic spin-polarized screened Korringa±Kohn±Rostoker and the spin-polarized nonrelativistic tight-binding linear muA n-tin orbital method. The Kubo± Greenwood equation is employed to calculate the non-local conductivity and layer-resolved sheet resistances; the transmission matrix formulation in turn is used to evaluate the conductance. We show that the dependence of sheet resistance on the imaginary part of the Fermi energy allows us to distinguish between the tunnelling and conductive regimes of electron transport. Our numerical studies of the system bcc Fe(100)/vacuum/bcc Fe(100) show quite dramatic variations in the electrostatic potential in the vacuum region and a gradual development of the tunnelling barrier with increasing thickness of the vacuum barrier. Varying the Madelung potential in the interior of the vacuum barrier allowed us to simulate spacers made of semiconducting or insulating material and to discuss the conditions for the presence of a magnetoresistance in such multilayers. As far as the thickness of the vacuum barrier is concerned the results obtained with the transmission matrix approach for fcc Co(001)/vacuum/ fcc Co(001) show a similar tendency to those obtained within the Kubo± Greenwood equation for bcc Fe(100)/vacuum/bcc Fe(100); asymptotically, that is with increasing thickness of the vacuum barrier, the magnetoresistance tends to zero.

Ab initiotheory of perpendicular magnetotransport in metallic multilayers

The current-perpendicular-to-plane ~CPP! magnetotransport of a metallic sample sandwiched by two ideal leads is described at an ab initio level. The so-called ‘‘active’’ part of the system is either a trilayer consisting of two magnetic slabs of finite thickness separated by a nonmagnetic spacer or a multilayer formed by alternating magnetic and nonmagnetic layers. We use a transmission matrix formulation of the conductance based on surface Green’s functions as formulated by means of the tight-binding linear muffin-tin orbital method. The formalism is extended to the case of lateral supercells with random arrangements of atoms of two types, which in turn allows to deal with specular and diffusive scattering on equal footing, and which is applicable also to the case of noncollinear alignments of the magnetization in the layers. Applications refer to fcc-based Co/Cu/Co~001! trilayers and multilayers, considering in detail the effect of substitutional alloying in the spacer and in the magnetic layers, as well as interdiffusion at the interfaces.

AB-INITIO THEORY OF THE CPP-MAGNETOCONDUCTANCE*)

The current-perpendicular-to-plane (CPP) magnetoconductance of a trilayer consisting of a spacer sandwiched between two ideal leads is described on anab initio level. We employ the transmission matrix formulation of the conductance within the framework of the spin-polarized surface Green function technique as formulated in terms of the tight-binding linear muffin-tin orbital method. The formalism is extended to the case of lateral supercells in each layer with random arrangements of atoms which allows to treat both the ballistic and diffusive transports on equal footing. The application is made to fcc-based Co/Cu/Co(001) trilayers.

Analysis of multilayered meander line polarizer

In this paper, we present an analysis of a multilayered meander line polarizer. Using waveguide modal fields and Galerkin's method of moments, the equivalent susceptance of a meander line screen is determined. The equivalent susceptance includes the effect of the dielectric layers that are present in the close vicinity of the meander line plane. The transmission matrix formulation then is invoked to find the transmission and reflection behavior of a multilayered meander line structure. Numerical results for equivalent susceptance, return loss, and axial ratio are found to compare well with the measured data. Performance characteristics of multilayered meander line polarizers are studied, and the results are presented. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 442–454, 1997.

An Improved Transmission Matrix Formulation of Cascaded Discontinuities and its Application to E-Plane Circuits

We study the effect of the relative convergence problem on the transmission matrix formulation of cascaded discontinuities. A numerically efficient modified formulation satisfying the edge condition is presented. Application is in the analysis of waveguiding structures in which a number of conductors are placed on various interfaces. Numerical results are presented for double-ridged waveguides and finlines. Applications to E-plane filters are also discussed.

Vibration Analysis of Rotor Blades with Pendulum Absorbers

A comprehensive vibration analysis of rotor blades with spherical pendulum absorbers is presented. These absorbers are mounted on the blade to attenuate the loads that pass through the rotor shaft at a frequency that is an integer multiple of the blade passage frequency. The spherical pendulum absorber is considered here because such an absorber may be more versatile in controlling the out-of-plane, in-plane, and pitching vibratory loads. A transmission matrix formulation is given to determine the natural vibrational characteristics and a direct transmission matrix method is given to determine the forced response of the rotor blades with pendulum absorbers. The pendulum absorber alters significantly the initial blade frequencies that are adjacent to the uncoupled frequencies of the pendulum. In the case of spherical pendulum, two natural modes of vibration are injected between the displaced initial modes of the blade. The pendulum hinge offsets significantly affect the torsional frequencies of the blade. The effect of root collective pitch, in the normal range, on the natural frequencies is small. With the use of a spherical pendulum, it is possible to achieve significant reductions in all five root forces of the blade simultaneously. If the pendulum is tuned such that its uncoupled natural frequency coincides with the excitation frequency, the pendulum introduces constrained deflections at its point of connection with the blade; this may not help in attenuating the root forces of the blade but may actually amplify them.

On a Derivation of the Transmission Matrices for the Longitudinal, Torsional, and Bending Vibrations of Families of Tapered Rods

The transmission-matrix representation of structural elements finds useful application in the description of multielement systems. Many practical systems use tapered elements for which at present transmission matrices are not readily available. The present paper discusses a particularly useful approach to the derivation of transmission matrices for tapered rods. The transmission-matrix formulation is demonstrated to represent a particularly important fundamental set of the general solution to the governing differential equation. When viewed in this way, the coefficients of the matrix are shown to possess certain properties with respect to each other and the eigenvalue problem. Transmission matrices are derived from known general solutions for certain functional forms of taper and presented in tabular form.