Analysis and design of series-fed arrays of printed-dipolesproximity-coupled to a perpendicular microstripline

An analysis of a printed dipole element and a generalized configuration of a series-fed array of such elements, electromagnetically coupled to a covered microstripline running perpendicularly under it in a substrate-superstrate configuration, is presented. The solution is based on the principle of reciprocity and is formulated using a rigorous method of moments and full-wave spectral-domain Green's functions for multilayer dielectric substrates. The dipole excitation is characterized by an equivalent impedance, and can be controlled by suitably selecting the offset of the dipole from the feed line. Mutual coupling between dipoles is included. Using the results of the element analysis, a series-fed array prototype has been successfully designed, built, and tested in a standing-wave configuration; the design details are described, and measured performances are evaluated using the results of the array analysis. Mutual coupling effects are found to be not detrimental for this configuration, but can be severe for other nonstanding-wave configurations     

Mutual coupling between microstrip dipoles in multielement arrays

An analytical method for evaluating mutual coupling in multielement microstrip arrays is discussed. The elements of the array are strip dipoles covered by an overlayer and excited by microstrip lines embedded in the substrate. In addition, two different ways of excitation are considered to evaluate the effect of the feeding lines on the coupling between the dipoles. Throughout the analysis, the transmission line and dipole widths are taken to be a fraction of the free-space wavelength, so that the longitudinal current component is the dominant contributor to the characteristics of the array. Under this assumption, the transverse component of the current is neglected without introducing appreciable error. The current distribution along the longitudinal direction is evaluated by solving an appropriate integral equation using Galerkin's method with piecewise continuous sinusoidal functions. All possible interactions between the currents on the feeding transmission lines and dipoles are included. Using the computed current distribution, transmission-line theory is applied on the feeding microstrip lines to evaluate self- and mutual impedances as well as scattering coefficients at chosen reference planes     

Self and mutual admittances/impedances of two parallel nonstaggered dipoles driven by 2-wire lines

A new theoretical approach to the problem of two identical, parallel, nonstaggered dipole antennas, driven by 2-wire lines is presented. This contribution is an extension of earlier work dealing with the isolated dipole antenna driven by a 2-wire line. The present simple theory is limited to coupled dipoles, the distances of which are greater than one-tenth of a wavelength.     

E-plane scan performance of infinite arrays of dipolesprinted on protruding dielectric substrates: coplanar feed line andE-plane metallic wall effects

The effects of coplanar feed lines and of E-plane cavity walls on the performance of infinite arrays of dipoles printed on protruding dielectric substrates are investigated. In order to do so, two unit cell configurations are studied: (1) the dipole element fed by coplanar transmission lines and (2) the dipole element fed by coplanar transmission lines with finite-height metallic walls added parallel to the H-plane of the array. The element active impedances are calculated for these configurations, and they are compared with those obtained from arrays of dipoles without coplanar feed lines. Effects of the dielectric substrate permittivity and of its thickness on the array element active impedance are included. The results show that the arrays of dipoles with the coplanar feed lines exhibit feed-line-induced blindnesses which reduce considerably the scan volume of the array. It is also shown that these feed line effects are reduced for thicker or higher permittivity substrates, and that the insertion of electric walls is one possible avenue for eliminating these anomalies     

Analysis and design of a leaky-wave EMC dipole array

An analysis of an electromagnetically coupled (EMC) dipole array is presented, in which a microstrip line is coupled to an infinite periodic linear array of microstrip dipoles, arranged perpendicular to the line. The spectral-domain immittance method is used to obtain the periodic Green's function for the two-layered structure, and the method of moments with a Galerkin testing procedure is then used to enforce the electric field integral equation (EFIE) on the line and the dipole within a unit cell of the structure to obtain the determinantal equation for the unknown leaky-wave propagation constant. One of the interesting features of this analysis is the path of integration in the complex plane used to compute the moment method reactions, which must be partly on the improper sheet for the m=-1 space harmonic when it radiates in the forward direction. Measured radiation patterns for a 10-element EMC dipole array are presented and compared with the corresponding theoretical ones     

Difficulties in MoM analyses of resonant circular arrays of cylindrical dipoles

Previous studies have shown that a properly dimensioned, large circular array of cylindrical dipoles possesses very narrow resonances. Only one dipole is driven and the rest are parasitic. Those studies made use of the 'two-term theory'. In the present Letter, the Numerical Electromagnetics Code is applied to the aforementioned circular array. At some frequencies, meaningless results - large, negative driving-point conductances - are found. An attempt is made to explain why such results occur and to propose remedies when possible.     

Analysis of mutual coupling between a finite phased array ofdipoles and its feed network

The mutual coupling effects between a finite phased array of dipoles and its feed network are analyzed. The feed network is typically a corporate feed consisting of split-tee power dividers cascading to form a certain power distribution over the aperture. A simple iterative approach is used to solve the interaction between elements and feed. The radiation of a finite dipole array are first found for a given voltage excitation. These radiation impedances are then used as loads for the feed network, and the n+1 port network problem is analyzed. Due to the interaction between the feed network and dipoles, the antenna parameters such as mismatch, antenna pattern, and gain are all affected. These effects can be determined from the analysis of the network representation. Numerical results for a typical phased array with a corporate feed show that the resultant VSWR of the feed pattern degradation is due to the mutual coupling effects     

A quasi-periodic design procedure for a traveling-wave array ofdipoles

A simple iterative design procedure is given for a traveling-wave array of dipole elements fed in a shunt configuration by a meandering transmission line. The design procedure is based on a quasi-periodic analysis of the loaded line, which assumes a Bloch wave propagation on the structure. A design procedure is formulated for the cases of constant attenuation and tapered attenuation on the line. A ten-element array of vertical monopoles fed by a meandering stripline is used to illustrate the design technique. Results show that the design procedure based on power into the dipoles gives good agreement with one based on actual dipole currents if a certain assumption is used. It is important, however, to account for mutual coupling in the design procedure in order to obtain accurate patterns, especially for low sidelobe designs     

Antenna synthesis and optimization using weighted Inagaki modes

Inagaki modes represent a new modal formalism for problems of radiation and scattering from arbitrary discrete and continuous structures. These modes can be generalized to be orthogonal over any sector of the sphere at infinity, as well as the source region itself. Theory and application of these modes to problems of pattern synthesis and array optimization, including constraints, are presented. Examples are given for a line source, an array of printed dipoles, and a dipole array in free space.     

Antenna Modeling Based on a Multiple Spherical Wave Expansion Method: Application to an Antenna Array

A method to derive an equivalent radiation source for planar antennas is presented. This method is based on spherical near-field (NF) data (measured or computed) to ascertain an equivalent set of infinitesimal dipoles placed over the main antenna aperture. These produce the same antenna radiation field, both inside and outside the minimum sphere enclosing the antenna. A spherical wave expansion (SWE) of the NF data is written in terms of infinitesimal dipoles using a transition matrix. This matrix expresses the linear relations between the transmission coefficients of the antenna and the transmission coefficients of each dipole. The antenna a priori information are used to set the spatial distribution of the equivalent dipoles. The translational and rotational addition theorems are exploited to derive the transmission coefficients of the dipoles. Once the excitation of each dipole is known, the field at any aspect angle and distance from the antenna is rapidly calculated. Computations with EM simulation data of an antenna array illustrate the reliability of the method.      

Frequency- and time-domain Green's functions for a phasedsemi-infinite periodic line array of dipoles

We extend a previous prototype study of Felsen and Capolino (see ibid. vol.48, p.921-931, June 2000) of frequency-domain (FD) and time-domain (TD) Green's functions for an infinite periodic phased line array of dipoles to account for the effects of truncation, as modeled by a semi-infinite array. These canonical problems are to be used eventually for the systematic analysis and synthesis of actual rectangular TD plane phased arrays. In the presentation, we rely on the analytic results and phenomenologies pertaining to the infinite array, which are reviewed. Major emphasis is then placed on the modifications introduced by the truncation. Finite Poisson summation is used to convert the individual dipole radiations into collective truncated wavefields, the FD and TD Floquet waves (FW). In the TD, exact closed-form solutions are obtained, and are examined asymptotically to extract FD and TD periodicity-matched conical truncated FW fields (both propagating and nonpropagating), corresponding tip-diffracted periodicity-matched spherical waves, and uniform transition functions connecting both across the FD and TD-FW truncation boundaries. These new effects can again be incorporated in a FW-modulated geometrical theory of diffraction. A numerical example of radiation from a finite phased TD dipole array with band-limited excitation demonstrates the accuracy and efficiency of the FW-(diffracted field) asymptotic algorithm when compared with an element-by-element summation reference solution     

On the relations between the excitation fronts propagating in theheart and the equivalent dipoles

The equivalent dipoles of cardiac electrical activity are determined either by minimizing the square deviation between the measured potential distribution and that generated by the dipoles or by comparing them through their multiple expansion coefficients. The two methods, called the direct and indirect method, respectively, are applied to the potential distribution obtained from a three-dimensional heart model composed of about 50000 unit cells, and the dipole locations thus obtained are compared to the mean location of the excitation fronts. When there is a single excitation front with simple shape, the equivalent dipole location obtained from the single-moving-dipole approximation coincides with the mean location of the excitation front. The coincidence is better with the direct method, but it needs longer calculation time than with the indirect method. For 25-30 ms after the onset of the ventricular depolarization, the excitation fronts have complicated shapes, and the deviations of the equivalent dipole locations from their mean locations become large even if the two-moving-dipole approximation is used     

Reflection properties of periodic surfaces of loaded dipoles

Two-dimensional periodic arrays of dipoles or slots act as reflecting or transmitting surfaces, respectively, which have bandpass filter characteristics. The resonant frequency and the bandwidth may be controlled by varying the length, spacing, and load impedance of the dipoles (slots). A theoretical and experimental investigation of the scattering by a two-dimensional array of loaded dipoles is described. The scattering through the resonance region shows that a unit reflection coefficient is achieved. The effect of grating-lobe radiation is included. The scattering properties as a function of the angle of incidence are given for both loaded and unloaded dipoles. The loaded dipole array described in this paper produces a narrower bandwidth than the array of unloaded dipoles, and the resonant frequency is much less dependent on the angle of incidence. The resonant frequency of the array as well as the bandwidth depends strongly on the resonant frequency of the dipole element as would be expected; however, it is also substantially influenced by the interelement spacing and the angle of incidence.     

Dipole separability in a neuromagnetic source analysis

By studying the ability of a one-dipole model to explain the magnetic field actually resulting from two dipoles, minimum requirements for a successful separation of two dipoles were explored. Two dipoles in different depths generally require a much higher signal-to-noise ratio (SNR) than two dipoles in the same depth. For the latter condition, the dipole distance as well as the angles between the moments and the line connecting the dipole locations (connecting line) were systematically varied. A perpendicular orientation of the two dipoles turned out to be the most favorable condition: the minimum distance required for a separation of two dipoles was more than four times smaller than for a configuration with both moments oriented parallel to the connecting line. Separability of parallel dipoles was moderately enhanced if both moments assumed an orientation perpendicular to the connecting line. The separability of two antiparallel dipoles is not limited by concurrence with a one-dipole model, but by the low signal amplitudes resulting from a mutual cancelation of the fields arising from the two dipoles, and by concurrence with a quadrupole model. The results are presented so that quantitative conclusions about dipole separability can be derived for arbitrary SNR's. The study does not generally disprove the common belief that magnetoencephalography has a relatively poor spatial resolution, but it qualifies this view by suggesting that under favorable conditions two sources with a distance of only 1 cm may be resolvable     

Comment on "Incompleteness of the periodic moment method":correction

It was previously shown by the author (see ibid., vol. 29, no. 14, p.1245-6, 1993) that the periodic moment method (PMM) predicts the correct impedance between a dipole in a planar array of dipoles with rectangular lattice, and a single dipole in a parallel plane, when the single dipole is also parallel to the array dipoles. Also it was asserted that when the single dipole was inclined the PMM results were incorrect; a correct formula for perpendicular dipoles was presented. S. Schneider of the USAF Wright Laboratories has shown how a correct formulation for the parallel plane PMM case can be obtained, and that a coding error of a missing factor of 2 was made by the author for the limiting case of |α|=1. Now the calculated results agree with those the author calculated using the Richmond piecewise sinusoidal code     

Coupling Reduction Between Dipole Antenna Elements by Using a Planar Meta-Surface

The mutual coupling between dipole antenna array elements using a planar meta-surface as superstrate is experimentally investigated. The meta-surface is based on grids of short metal strips and continuous wires. A comparison between the mutual coupling when the dipoles are radiating in free space and in presence of the superstrate is presented. On average, between 3 to 14 dB reduction of the mutual coupling is achieved when the superstrate is used. The effect of the mutual coupling on the radiation performance of the array is studied by spherical near-field measurements of the radiation pattern when one driven dipole is fed and the others are matched with 50 $Omega$ loads. The back-projected field on the aperture and on the E-plane is shown.      

Beam reconfiguration of linear array of parallel dipole antennas through switching with real excitation voltage distribution

In this paper, authors propose a method based on the modified particle swarm optimization (PSO) for beam reconfiguration of linear array of mutually coupled parallel half-wavelength dipole antennas with real excitation voltage amplitude distribution. Two different beam pairs are generated, one pencil/pencil beam pair and another pencil/flat-top beam pair in the horizontal plane. One beam is changed to another through switching while sharing a common amplitude distribution. Two examples are presented, one without ground plane and another in presence of ground plane. Dipoles are connected to its feed network through a switch, so that it can be turned on or off, depending on the switch position. Beam reconfiguration is achieved by suitably turning the array elements on or off using same voltage excitation distribution. Modified PSO is used to compute the excitation voltages as well as the switching configuration for each pattern having a prefixed side lobe level. The current in the driven and parasitic elements is determined via induced EMF method considering the current distribution on each dipole to be sinusoidal. Proposed method efficiently synthesizes dual-beam switching the power pattern from pencil to pencil and pencil to flat-top having same or different side lobe levels using common excitation voltages. It calculates the maximum variation of the active impedance of driven elements and the power losses when the radiation patterns switch from one beam to another. The paper calculates the array directivity as the distances between antenna array and the ground pane varies. Three other state-of-the-art metaheuristics like differential evolution, gravitational search algorithm, artificial bee colony algorithm are also employed for achieving a comparative evaluation.     

Optimization of radio communication in media with three layers

The electromagnetic radiation of an electric dipole in a medium with three layers is examined using dyadic Green's functions. The far zone field for problems of this nature is primarily determined from the lateral wave. It is shown that the excitation of this wave may be reinforced through a dipole inclination and an optimum position may be determined. The radio losses for typical forests were calculated for vertical and horizontal dipoles and for dipoles with an optimum inclination. The theoretical results are in good agreement with the available experimental data.     

输入阻抗相近的不等长振子阵

从线天线电流分布与输入阻抗关系的基本原理出发,结合矩量法等数值计算方法,综合出产生给定方向图的平行偶极子天线阵。阵列中各单元的长度不同,而它们的输入阻抗趋于一致。     

Multiple dipole modeling and localization from spatio-temporal MEGdata

An array of biomagnetometers may be used to measure the spatio-temporal neuromagnetic field or magnetoencephalogram (MEG) produced by neural activity in the brain. A popular model for the neural activity produced in response to a given sensory stimulus is a set of current dipoles, where each dipole represents the primary current associated with the combined activation of a large number of neurons located in a small volume of the brain. An important problem in the interpretation of MEG data from evoked response experiments is the localization of these neural current dipoles. We present here a linear algebraic framework for three common spatio-temporal dipole models: i) unconstrained dipoles, ii) dipoles with a fixed location, and iii) dipoles with a fixed orientation and location. In all cases, we assume that the location, orientation, and magnitude of the dipoles are unknown. With a common model, we show how the parameter estimation problem may be decomposed into the estimation of the time invariant parameters using nonlinear least-squares minimization, followed by linear estimation of the associated time varying parameters. A subspace formulation is presented and used to derive a suboptimal least-squares subspace scanning method. The resulting algorithm is a special case of the well-known MUltiple SIgnal Classification (MUSIC) method, in which the solution (multiple dipole locations) is found by scanning potential locations using a simple one dipole model. Principal components analysis (PCA) dipole fitting has also been used to individually fit single dipoles in a multiple dipole problem. Analysis is presented here to show why PCA dipole fitting will fail in general, whereas the subspace method presented here will generally succeed. Numerically efficient means of calculating the cost functions are presented, and problems of model order selection and missing moments are discussed. Results from a simulation and a somatosensory experiment are presented.