Analytical solution for early-time transient radiation frompulse-excited parabolic reflector antennas

A closed-form analytical solution is developed for predicting the early-time transient electromagnetic fields which are generated by a perfectly conducting parabolic reflector antenna when it is illuminated by a transient step spherical wave due to an elemental Huygen's source located at the focus. This closed-form time-domain solution, which is valid both near and far from the reflector (and anywhere in the forward region) can be used via the convolution theorem to efficiently obtain the early-time transient fields generated by the same parabolic reflector antenna when it is illuminated by a realistic finite-energy pulse which emanates as a spherical wave from the focus. The transient solution is developed here by analytically inverting, in closed form, the corresponding frequency-domain solution in terms of a radiation integral that employs an asymptotic high-frequency geometrical optics (GO)-based approximation for the fields in the aperture. Numerical results are presented for the transient fields both near and far from the reflector. The fields on boresight exhibit an impulse-like behavior similar to that of the impulse radiating antenna (IRA) introduced by Baum et al. (1989, 1993)     

A physical optics based plane wave spectrum approach to theanalysis of finite planar antennas

An efficient physical optics based method of analysis of antennas over finite ground planes is presented. The far field radiated by the current on the finite ground plane is expressed as the convolution integral of the far field of the antenna above the infinite ground plane with the Fourier transform of the polygonal ground plane shape. The convolution integral is simplified by applying the sampling theorem     

Application of incremental length diffraction coefficients tocalculate the pattern effects of the rim and surface cracks of areflector antenna

Incremental length diffraction coefficients (ILDCs) for the half-plane are integrated around the rim of a paraboloid reflector antenna to obtain well-behaved far fields of the nonuniform current for all angles of observation. These far fields, when added to the physical optics far field, produce a more accurate total far field of the reflector. Excellent agreement with the far fields obtained from a method-of-moments solution to the electric field integral equation applied to a 20-wavelength-diameter reflector shows that the cross polarization, farther-out sidelobes, and fields near nulls of reflector antennas can be appreciably modified by the fields of the nonuniform currents. ILDCs are also used to investigate the effect of cracks on the surface of reflectors that can result from the imperfect fitting together of panels to form large reflectors. Three models of cracks are studied. Significant pattern effects are found, depending on the model and orientation of the cracks     

Planar near-field to far-field transformation using an array ofdipole probes

A method is presented for computing far-field antenna patterns from measured near-field data measured by an array of planar dipole probes. The method utilizes the near-field data to determine some equivalent magnetic current sources over a fictitious planar surface which encompasses the antenna. These currents are then used to find the far fields. The near-field measurement is carried out by terminating each dipole with 50 Ω load impedances and measuring the complex voltages across the loads. An electric field integral equation (EFIE) is developed to relate the measured complex voltages to the equivalent magnetic currents. The mutual coupling between the array of probes and the test antenna modeled by magnetic dipoles is taken into account. The method of moments with Galerkin's type solution procedure is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient-fast Fourier transformation (CG-FFT) method exploiting the block Toeplitz structure of the matrix. Numerical results are presented for several antenna configurations to show the validity of the method     

Planar near-field to far-field transformation using an equivalentmagnetic current approach

An alternative method is presented for computing far-field antenna patterns from near-field measurements. The method utilizes the near-field data to determine equivalent magnetic current sources over a fictitious planar surface that encompasses the antenna, and these currents are used to ascertain the far fields. Under certain approximations, the currents should produce the correct far fields in all regions in front of the antenna regardless of the geometry over which the near-field measurements are made. An electric field integral equation (EFIE) is developed to relate the near fields to the equivalent magnetic currents. The method of moments is used to transform the integral equation into a matrix one. The matrix equation is solved with the conjugate gradient method, and in the case of a rectangular matrix, a least-squares solution for the currents is found without explicitly computing the normal form of the equation. Near-field to far-field transformation for planar scanning may be efficiently performed under certain conditions. Numerical results are presented for several antenna configurations     

Full-wave analysis of radiated emission from arbitrarily shapedprinted circuit traces

A mixed (scalar and vector) potential surface integral equation formulation, developed for microstrip antennas, is employed in conjunction with the method of moments to predict the radiated emission from arbitrarily shaped printed circuit traces. Computed currents and radiated fields for a typical trace configuration in the form of a rectangular loop loaded by low- or high-impedance lumped loads indicate good agreement with transmission line theory and/or elementary loop antenna analysis, when the trace size is electrically small. Computed results are presented to highlight the radiation and coupling due to common-mode currents     

On the excitation of a circular loop antenna by travelling-and standing-wave current distributions

Presented here is an exact formulation of the electric and magnetic (EM) fields radiated by a circular loop antenna, assuming both travelling- and standing-wave current distributions. By using a differential current element positioned in an azimuthal direction as the starting point, the paper systematically develops the EM fields radiated by the circular loop via a vector potential theory. This approach leads to a general integral representation for the radiation characteristics of the loop antenna where we completely evaluate the resulting expressions, when the excitations of the loop assume travelling- and standing-wave distribution forms. In addition, this paper briefly examines a method to generate approximately such current distributions by coupling the loop to a two- or four-wire transmission line. Furthermore, the paper discusses a graphical representation of the current distribution plotted as a function of frequency or loop size. From the field expressions determined, we derive generalized closed-form results for some important design parameters for the loop antenna. These parameters include the radial component of the Poynting vector, the total power radiated by the loop, the directivity, the radiation resistance, and the effective area and height of the antenna. When we specialize to the important case of uniform current excitation, the exact values of the parameters deduced from the general expressions, are summarized and exhibited in a comprehensive table. This table facilitates the computations of these important physical parameters. Further analysis involving small argument and asymptotic approximations in the residts for the travelling-wave current excitation leads to closed-form expressions in terms of tabulated functions. Numerical results presented, include the fields radiated by the loop when the standing-wave current excitation admits a Fourier series representation. The present approach via potential theory reveals that the fields can be calculated in any arbitrary direction : this is consistent with a previous observation of Knudsen (1951, 1953) who employed a different approach.     

Analysis of a four parallel wire antenna system by the spatialFourier transform method

The electromagnetic fields and currents associated with an infinite four parallel wire transmission line are analyzed through the use of the spatial Fourier transform method. The near and far electromagnetic fields and currents that are associated with frill and gap voltage excitations are analyzed by the Fourier transform method. Possible VHF compact range applications of a four parallel wire antenna system are discussed, including the possibility of simulating an off-axis EM plane wave by the appropriate adjustment of the exciting voltage phase on each of the four parallel wires. Comparisons of Fourier transform method solutions with method-of-moments solutions and finite-difference-time-domain solutions are made for an infinite four parallel wire antenna system     

Time-domain fields exterior to a two-dimensional FDTD space

A transformation algorithm for the near-zone and far-zone fields exterior to a two-dimensional (2-D) finite-difference time-domain (FDTD) field lattice has been developed entirely in the time domain. The fields are found from a surface integration of the convolution of the time derivative of equivalent currents and charges along a contour that encloses the scatterer or radiator of interest. The kernel of the convolution integral has a square-root singularity for which an efficient numerical integration rule is presented. Using this technique, a very accurate solution is obtained; however, convolution integrals are computationally expensive with or without singularities. As an alternative, a rapidly convergent approximate series expansion for the convolution integral is presented, which can be used both in the near and far zone. Results using the new 2-D transform are compared with analytical expressions for the fields generated by a modulated Gaussian pulse for TE and TM line sources. In addition, the 2-D transform solution for the near-zone fields scattered from an open-ended cavity for a TE incident modulated Gaussian pulse plane wave is compared against a full-grid FDTD solution for accuracy and efficiency. The 2-D transform far-zone fields are compared against an alternative technique, which uses a double Fourier transform to perform the convolution in the frequency domain     

Far-field predictions from near-field measurements using an exactintegral equation solution

This paper presents a new approach to derive far-field data needed in antenna and EMI/EMC testing from near-field measurements. An exact integral equation solution to the wave propagation problem is used to transform the near-field data to the far field. The method requires near-field measurements on two closed surfaces enclosing all sources and inhomogeneities. The approach is validated with numerical simulation of measurements of fields radiated from a known antenna     

基于天线方向图与近场SBR的海面舰船复合散射研究

针对弹目交互场景中近场电磁散射仿真问题,提出了一种基于近场弹跳射线(shooting and bouncing ray,SBR)法并考虑天线方向图影响的海面舰船复合散射计算模型.根据天线方向图和海面舰船一体化几何模型,给出满足物理光学远场计算条件的面元所接收到的电场强度,通过SBR法得出所有面元的散射场,最后由矢量叠加...     

用矢量球面波理论和互易原理分析伦伯透镜天线

伦伯透镜是一种球形分层介质天线,考虑到数值计算的复杂性,本文提出用矢量球面波理论和互易原理相结合,分析其性能。该方法首先用矢量球面波理论计算平面波入射到多层介质球的散射场,在此基础上,用互易原理将散射场转变成天线的远区辐射场。基于这种方法,本文着重研究了伦伯透镜天线的焦区场和远区场特性,包括透镜分层总数以及层与层之间存在的空气间隙对实际应用可能造成的影响。最后,对卫星通信中伦伯透镜天线多波束应用的可行性给出了分析结果。     

Theoretical and measured electric field distributions within anannular phased array: Consideration of source antennas

A detailed calculation of sources and electric fields associated with a prototype annular phased array for clinical hyperthermia is presented. Two antenna current distributions are used as field sources. One is based on a linear dipole model. The second models the thin strip antenna elements in detail, and the current is derived using the theory of a microstrip transmission line. These currents are then used to calculate the magnetic vector potential and the electric field. To verify the theoretical simulations, the magnitude of the electric field is measured under the same conditions as those used in the theoretical simulations. The comparison between measured and calculated fields demonstrates better convergence of theory and experiment when the antenna sources are modeled in detail. Thus, the use of these results for an improved incident-scatter model that will allow more general calculations of E fields in inhomogeneous media with irregular geometries is anticipated     

High frequency approximations to the physical optics scatteringintegral

Discusses two high frequency (HF) approximations to the physical optics (PO) scattering integral for the far field radar backscatter from a general curved edged reflecting surface viewed at arbitary aspect. The PO scattering integral is first approximated as the sum of a specular effect and an edge effect, where the latter is represented explicitly as a certain line integral evaluated over the boundary edge of the reflector. A closed form result is then obtained by applying the method of stationary phase to the line integral. With the exception of singularities that can occur at caustics, or when the specular point falls on the boundary edge, these HF approximations are found to work reasonably well for smooth surfaces whose Gaussian curvatures have constant sign (positive or negative, but never zero)     

Improvement of prompt response from impulse radiating antennas by aperture trimming

Reflector impulse radiating antennas (IRA) traditionally have been constructed by terminating a self-reciprocal, transverse electromagnetic (TEM) transmission-line feed structure into a paraboloidal reflector. The section of the paraboloid used is usually circular in cross-section, with the outer boundary coinciding with the circle of symmetry of the TEM feed. The reflector converts the spherical TEM mode on the feed line into an approximate plane wave in the near field by geometric optics. The prompt radiated electric field in the direction of focus is given in the physical optics approximation in terms of the integral of the electric field of the TEM mode over the aperture plane inside the reflector boundary. Balanced feed structures have TEM modes that provide both positive and negative contributions to this integral in the aperture plane. Determination of the contour where the principal component of the electric field in the TEM mode is zero identifies portions of the aperture that contribute destructively to the integral. These portions are removed, thereby increasing the prompt radiated field without altering the feed structure or the applied voltage waveform. Furthermore, decreasing the size of the TEM feed relative to the aperture size, followed by appropriate aperture trimming, allows an even greater increase in radiated field. Results are presented that predict an increase in prompt radiated fields for all electrode configurations. Improvements are largest for electrode angles that are large (with respect to the vertical). The trends predicted by the numerical results are verified by an experiment conducted on a time-domain antenna range.     

Near fields of the constant current thin circular loop antenna ofarbitrary radius

Assuming a known (constant) current distribution on the thin circular loop antenna of arbitrary radius in free space, an exact integration of the vector potential is performed without recourse to approximations. The only restrictions on the solution variables are that the observation point distance must be greater than the loop radius and that the polar angle must run between 0 and π. The resulting vector potential infinite series solution possesses a real part composed of linear combinations of complete elliptic integrals of the first and second kind and an imaginary part composed of elementary functions. Thus, it is possible to obtain an exact solution which is valid everywhere that r>a and 0⩽&thetas;⩽π. The electromagnetic field components of the constant current circular loop antenna are then determined by direct series differentiation. These solutions are valid in the near and induction fields, converging rapidly there, and are also valid in the far field, although many terms of the series are needed for convergence     

On an algorithm for analysis of the radiation patterns of dual reflector and segmented reflector antennas

Large reflector antennas, from cost and weight considerations, appear to be the best configurations for achieving the very large apertures needed for antennas mounted on orbiting spacecraft. Radiation pattern calculations for such antennas are, in general, quite costly both in terms of computer time and the considerable memory required to perform the large surface integrations. The method presented here treats the large aperture as a set of small subapertures for which the radiation fields are computed separately, stored and then added with due regard to phase to yield the radiation pattern of the large reflector. Numerical methods developed to provide the illumination of each subaperture to avoid overlap of the aperture fields of adjacent subapertures and to simplify the surface integrations are discussed. The algorithm is straightforward and has considerable intuitive appeal. The methods of geometrical optics (GO) are used to calculate the aperture plane tangential field components; and electric vector potential is then used to compute the antenna radiation fields. The algorithm includes a set of options for different reflector surfaces. If high accuracy of the far sidelobe levels is required, a subroutine accounting for edge diffraction should be added to the algorithm given here. Calculations made with this algorithm are compared with calculations made by other methods and with measured patterns.     

A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application

As a generalization of the fractional Fourier transform (FRFT), the linear canonical transform (LCT) plays an important role in many fields of optics and signal processing. Many properties for this transform are already known, but the correlation theorem, similar to the version of the Fourier transform (FT), is still to be determined. In this paper, firstly, we introduce a new convolution structure for the LCT, which is expressed by a one dimensional integral and easy to implement in filter design. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, based on the new convolution structure, the correlation theorem is derived, which is also a one dimensional integral expression. Last, as an application, utilizing the new convolution theorem, we investigate the sampling theorem for the band limited signal in the LCT domain. In particular, the formulas of uniform sampling and low pass reconstruction are obtained.     

Evaluation of reflected fields at caustic regions using a set of GO equivalent line currents

A set of equivalent electric and magnetic line currents is derived which supplements the geometrical optics (GO) solution in the far zone whenever one of the surface principal radii becomes very large. These hypothetical currents lie along the specular line of the surface and are shown to produce the same result as the stationary phase contribution of the physical optics integral. An example of a systematic application of such equivalent currents for the computation of the scattered field from a complex structure is also demonstrated.