Spherical Mode Expansion Research Articles

Fourier Synthesis of Linear Arrays Based on the Generalized Scattering Matrix and Spherical Modes

This paper presents a novel, simple pattern synthesis procedure for linear equispaced arrays which can be characterized by a generalized scattering matrix (GSM) and whose radiated field can be expressed as a weighted sum of shifted spherical waves. It can be viewed as an extension of the classic design techniques of the Fourier series (FS) method or the Woodward-Lawson frequency sampling method, to the case in which the individual antenna elements' patterns and all interelement couplings are taken into account. The design procedure, which yields the excitations needed to achieve the desired pattern, is based on either the FS or the discrete Fourier transform (DFT) of the spherical mode expansion of the array radiated field, as well as on various properties associated to the FS or DFT coefficients. In this work, to compute the GSM of the array and the spherical mode expansion of the field, a validated hybrid full-wave methodology, based on the finite element method and rotation and translation properties of spherical waves, is used. Numerical results of different synthesized array patterns are presented for different arrays made up of dielectric resonator antennas and cavity-backed microstrip circular patches.

Linear programming from generalised scattering matrix analysis of array for minimum sidelobe level and prescribed nulls

A pattern synthesis technique for arbitrary planar arrays which are characterised in terms of a generalised scattering matrix and whose radiated field is expressed as a spherical mode expansion is introduced. The procedure yields the complex-valued excitations to achieve a minimum-maximum sidelobe level given a specified pointing direction and mainlobe width, as well as prescribed field nulls. All inter-element coupling effects coming from complex radiating structures used as array elements are inherently taken into account. Numerical results are presented for arrays of dielectric resonator antennas.

Multiobjective Optimization of Real and Coupled Antenna Array Excitations via Primal-Dual, Interior Point Filter Method From Spherical Mode Expansions

A novel method for the multiobjective optimization of arbitrary planar array excitations is presented. The optimization problem formulation, which inherently takes into account every array element pattern as well as all interelement couplings, is based on matrix-valued functions which are computed from the generalized-scattering-matrix characterization of an array and spherical mode expansions of its radiated field. It allows the maximization of the directive gain subject to a maximum sidelobe level, a maximum crosspolar level and a minimum aperture illumination efficiency, the setting of null-pointing directions and the dynamic range control. To solve the resulting non-linear optimization problem, we have developed a primal-dual interior point method specifically adapted to the presented formulation, which makes use of novel filtering techniques. Numerical examples of arrays of microstrip patches and dielectric resonator antennas covering a wide variety of requirements on these parameters are presented.

Mutual Coupling Compensation in Arrays Using a Spherical Wave Expansion of the Radiated Field

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This letter presents a flexible method to compensate the interelement mutual coupling (MC) effects that may degrade the field pattern of an array of real and coupled antennas. A closed-expression for a mutual coupling compensation matrix (MCCM) is derived. The MCCM is used to compensate the presence of the real individual elements' patterns and the interelement MC effects for any excitations obtained with an isotropic-based pattern synthesis method. The MCCM is calculated from the generalized scattering matrix (GSM) of an antenna array and the spherical mode expansion (SME) of its radiated field. For a given array, this MCCM has to be calculated only once since it only depends on the radiating and scattering characteristics of the antenna elements as well as on their location in the array. Conditions regarding null field pattern directions can also be reinforced in the MCCM. To compute the GSM of the array and the SME of the radiated field, a validated full-wave hybrid and modular methodology is used. Numerical results of synthesized patterns where the MC effects have been compensated are presented for arrays made up of dielectric resonator antennas. </para>

Comparative Design and Analysis of Luneburg and Half Maxwell Fish-Eye Lens Antennas

The design and performances is described of half Maxwell fish-eye (HMFE) and Luneburg lens antennas. Techniques to estimate the gradient index lens weights are first proposed and compared to measurements. Thanks to an analytical method based on spherical modal expansion, the radiation performances of Luneburg and HMFE lens antennas are then quantified and compared. The effects of the shell number, the lens diameter and the air gaps on the lens antenna directivity are investigated. Finally, a minmax optimized 9-shell 60 mm-diameter HMFE lens antenna is characterized at both 77 GHz and 110 GHz for on- and off- axis configurations to show its frequency behavior, focalization and beam scanning properties.

Optimal Radiated Waveforms From an Arbitrary UWB Antenna

Solutions are presented for the optimal electric field waveforms radiated by an arbitrary ultrawideband (UWB) antenna. Optimization criteria include maximization of the electric field amplitude at a particular time and location, or maximization of energy density over a specified time interval at a particular location. Assuming bandpass signals, constraints are placed on the total radiated energy, the Q of the antenna, and the size of the antenna. The solution is developed using a spherical mode expansion of the fields radiated by an arbitrary antenna enclosed by a spherical mathematical surface, and optimized using variational methods. A closed-form result is obtained for the case of amplitude maximization, while an integral equation must be solved numerically for the case of energy maximization in a time interval. An interesting result from these solutions is that the shapes of the optimal radiated field waveforms are largely independent of the size of the antenna. The solutions also indicate that the antenna characteristics that provide optimum field amplitude or energy in the transient case are identical to those associated with maximum gain in the CW case.

Computation of antenna pattern correlation and MIMO performance by means of surface current distribution and\\ spherical wave theory

Abstract. In order to satisfy the stringent demand for an accurate prediction of MIMO channel capacity and diversity performance in wireless communications, more effective and suitable models that account for real antenna radiation behavior have to be taken into account. One of the main challenges is the accurate modeling of antenna correlation that is directly related to the amount of channel capacity or diversity gain which might be achieved in multi element antenna configurations. Therefore spherical wave theory in electromagnetics is a well known technique to express antenna far fields by means of a compact field expansion with a reduced number of unknowns that was recently applied to derive an analytical approach in the computation of antenna pattern correlation. In this paper we present a novel and efficient computational technique to determine antenna pattern correlation based on the evaluation of the surface current distribution by means of a spherical mode expansion.

A CAD-Oriented Method to Analyze and Design Radiating Structures Based on Bodies of Revolution by Using Finite Elements and Generalized Scattering Matrix

In this work, an efficient analysis of radiating structures based on bodies of revolution is dealt with. The procedure is a hybrid method based on a segmentation of the structure into two-dimensional regions, finite elements and a spherical computation domain surrounding the antenna, defining a boundary or port where a spherical mode expansion of the fields is used. A reduced order model is computed for a fast frequency sweep. To validate this method, some structures based on bodies of revolution as a rod dielectric antenna, conical dielectric-loaded horns, profiled horns and a monopole-dielectric resonator antenna are studied and results are compared with those demonstrated by other authors. The design of a smooth-walled horn by means of the optimization of the profile is also carried out.

Analytical spherical-mode-based compensation of mutual coupling in uniform circular arrays for direction-of-arrival estimation

An analytical circuit model with a limited number of parameters is presented to describe mutual coupling in uniform circular arrays. The model, which is based on a spherical-mode expansion, provides physical insight into the frequency dependence and the dependence on azimuth and elevation angle of the coupling between antenna elements. It is shown that the number of circuit elements, required to describe the open-circuit voltages and the mutual impedances at the different antenna ports, depends on the overall size of the array and not on the spacing between the antenna elements. Based on this observation, an analytical technique is described to derive a coupling matrix representing the mutual coupling effects. Relying on the phase-mode-based circuit elements, dedicated eigenstructure techniques are developed for direction-of-arrival (DOA) estimation with uniform circular arrays. By considering several synthetic reference scenarios, it is shown that even in the presence of severe mutual coupling, root-MUSIC combined with a limited number of phase-mode components gives very robust DOA estimations for the azimuth angle, when all signals are incident on the array from a fixed elevation angle.

Generalized-scattering-matrix analysis of a class of finite arrays of coupled antennas by using 3-D FEM and spherical mode expansion

A rigorous method for characterizing, in terms of a multimode scattering matrix, a finite array of antennas where each antenna can be described by means of spherical waves is presented in this paper. The procedure provides the impedance, coupling and radiating characteristics of the arrays and comprises two steps. First, the generalized scattering matrix (GSM) of each single antenna is numerically calculated over a wide band of frequencies. For this purpose we use a previously-developed methodology that combines the domain segmentation technique, the three-dimensional finite element method (3D-FEM), spherical mode expansion and a reduced order model obtained using a symmetric matrix Pade/spl acute/-Via-Lanczos (SyMPVL) algorithm. Second, the overall GSM of the finite array is calculated starting from the GSM of each antenna and using rotation and translation of spherical waves. A closed-form expression for the overall GSM is given and different examples are shown in order to validate the proposed method.

Calculated and Measured Absorption Cross Sections of Lossy Objects in Reverberation Chamber

Reverberation chambers can be used to measure radiation efficiency of small antennas when these are located close to lossy objects. The lossy objects represent a heavy loading of the chamber. This loading is characterized by the mean absorption cross section of the lossy objects. This paper describes how this mean absorption cross section can be calculated from the scattered far field of an object by using the forward scattering theorem, or from a more laborious near-field evaluation. Results for lossy spheres and cylinders are calculated by using three different codes, based on spherical mode expansion, finite difference time domain techniques, and moment methods, respectively. The results for the cylinder are compared with measured levels in a reverberation chamber.

Radiation Q of electrically large loop antennas with nonuniform currents

AbstractAn analysis of the radiation Q of electrically large loop antennas is presented and its characteristics are discussed. The methodology involves the spherical mode expansion for the fields outside the loop. It is found that higher‐order modes need to be considered for a realistic estimate of the radiation Q of large loops. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 377–380, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10467

Radial field retrieval in spherical scanning for current reconstruction and NF-FF transformation

A near-field to far-field (NF-FF) transformation is addressed for the case of spherical scanning using equivalent magnetic currents (EMCs) and matrix methods. It is based on the decoupling of the field components and the iterative retrieval of the radial component of the electric field. The technique is applied for far-field calculation as well as for the estimation of the current distribution of the antenna under test (AUT) using spherical near-field facilities. Results from measured near-field data of several antennas are presented and compared to those of the analytical solution via a spherical wave mode expansion method.

Analysis of cavity-backed microstrip antennas by a 3-D finite element/segmentation method and a matrix Lanczos-Pade algorithm (SFELP)

A methodology that combines the domain segmentation technique, the three-dimensional finite-element method (3-D FEM), and a symmetric matrix Lanczos-Pade algorithm, is used for the fast frequency-sweep analysis of cavity-backed microstrip antennas by using a spherical mode expansion on the radiation boundary. Results for a circular patch antenna validate the proposed method.

Analysis of radiating axisymmetric structures using a 2-d finite-element and spherical mode expansion

Analysis of radiating axisymmetric structures using a 2-d finite-element and spherical mode expansion

Analysis of radiating axisymmetric structures using a 2‐d finite‐element and spherical mode expansion

Analysis of radiating axisymmetric structures using a 2‐d finite‐element and spherical mode expansion

Highly efficient technique for solving radiation and scattering problems

A method based on vector spherical mode expansion (VSME) for solving radiation and scattering problems is developed. Combined with numerical methods such as MoM or FDTD, three dimensional electric and magnetic current sources are theoretically analysed according to image theory and equivalence principles. The electric and magnetic VSME coefficients introduced are written in terms of the electric and magnetic current densities with space sinusoidal and Legendre functions. By using these coefficients and the correct choice of the co-ordinates, the electromagnetic fields can be constructed with a minimum number of modes.

Radiation pattern analysis of arbitrary wire antennas using spherical mode expansions with vector coefficients

A spherical mode expansion with Cartesian vector coefficients is presented for the study of the radiation patterns of arbitrary wire antennas. Coefficients are obtained by using a spherical harmonic series for the free space Green's function in conjunction with the current distribution obtained with the method of moments. Transverse components of the far field are ultimately obtained yielding a compact pattern representation suitable for rapid retrieval and display. The length of the expansion is shown to be related to the precision specified for the pattern; i.e., more precision requires more terms. A useful truncation criterion is proposed and verified by comparing results obtained for several typical wire antennas. >

Mutual admittance between circular apertures on a large conducting sphere

Explicit expressions for the self admittance and the mutual admittance Yij between two arbitrarily polarized circular apertures are presented. The aperture field distribution is that of TE11 circular waveguide mode. The analysis makes use of a spherical mode expansion and of the addition theorem for tesseral harmonics. Numerical results show Yij as a function of angular separation θ. The E‐plane coupling exhibits asymptotic (large θ) behavior consistent with the lowest “hard” surface ray order results. The slope of the H‐plane coupling for large values of θ does not correspond to the lowest‐order “soft” surface ray attenuation, but rather to that of the lowest‐order “hard” ray. This behavior is explained.

Radiation pattern of a corrugated conical horn in terms of Laguerre-Gaussian functions

Many papers can be found on radiation properties of corrugated feeds. The radiated field is described either by means of the Kirchhoff-Huyghens formula, or with a spherical mode expansion. In both cases, especially where the horn is long, the computation may be important. In this letter we present a third method founded on a Laguerre-Gaussian expansion in cylindrical coordinates.