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     

Near-field to near/far-field transformation for arbitrarynear-field geometry utilizing an equivalent electric current andMoM

Presented here is a method for computing near- and far-field patterns of an antenna from its near-field measurements taken over an arbitrarily shaped geometry. This method utilizes near-field data to determine an equivalent electric current source over a fictitious surface which encompasses the antenna. This electric current, once determined, can be used to ascertain the near and the far field. This method demonstrates the concept of analytic continuity, i.e., once the value of the electric field is known for one region in space, from a theoretical perspective, its value for any other region can be extrapolated. It is shown that the equivalent electric current produces the correct fields in the regions in front of the antenna regardless of the geometry over which the near-field measurements are made. In this approach, the measured data need not satisfy the Nyquist sampling criteria. An electric field integral equation is developed to relate the near field to the equivalent electric current. A moment method procedure is employed to solve the integral equation by transforming it into a matrix equation. A least-squares solution via singular value decomposition is used to solve the matrix equation. Computations with both synthetic and experimental data, where the near field of several antenna configurations are measured over various geometrical surfaces, illustrate the accuracy of this method     

基于曲面口径积分/几何光学的天线罩混合分析

提出了发射模式下，曲面口径积分／几何光学的混合分析方法。利用等效原理，将天线罩内表面上的反射场等效为面电流和面磁流，沿等效源所在曲面作口径积分，确定二次入射到罩壁上的入射场，经过局部平面的多层介质传输到天线罩外表面，在外表面上将一次传输场和二次反射场矢量叠加，对外表面切向场的表面积分得到天线带罩系统的远场方向图。该方法解决了发射模式下一次传输场和二次反射场的矢量叠加问题，计算精度高；仿真预测结果均为试验所证实。     

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     

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.     

全等效电流积分方程法分析微带天线

提出了一种分析微带天线的新方法——全等效电流积分方程法。根据等效原理，用等效表面电流表示金属导体影响，用等效体极化电流来取代介质结构影响，建立全等效电流积分方程，结合空域矩量法来求解整个微带结构的电流分布。采用该方法可以分析任意结构的微带天线，只需用最简单的自由空间格林函数而无须求解复杂的谱域或空域格林函数，避免了无穷积分或Sommerfeld积分，且在分析中精确考虑了有限尺寸金属接地板的影响。用该方法分析了矩形微带天线，计算结果与其它文献给出的结果一致，证实了该方法的有效性。     

Electromagnetic scattering from a chiral cylinder of arbitrarycross section

A simple moment solution is presented to the problem of electromagnetic scattering from a homogeneous chiral cylinder of arbitrary cross-section. The cylinder is assumed to be illuminated by either a TE or a TM wave. The surface equivalence principle is used to replace the cylinder by equivalent and magnetic-surface currents. These currents radiating in unbounded external medium produce the correct scattered field outside. When radiating in an unbounded chiral medium, they produce the correct total internal field. By enforcing the continuity of the tangential components of the total electric field on the surface of the cylinder, a set of coupled integral equations is obtained for the equivalent surface currents. Unlike a regular dielectric, the chiral scatterer produces both copolarized and cross-polarized scattered fields. Hence, both the electric and magnetic current each have a longitudinal and a circumferential component. These four components of the currents are obtained by using the method of moments (MoM) to solve the coupled set of integral equations. Pulses are used as expansion functions and point matching is used. The Green's dyads are used to develop explicit expressions for the electric field produced by two-dimensional surface currents radiating in an unbounded chiral medium. Some of the advantages and limitations of the method are discussed. The computed results include the internal field and the bistatic and monostatic echo widths. The results for a circular cylinder are in very good agreement with the exact eigenfunction solution     

Surface integral formulation for calculating conductor anddielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents     

Single integral equation for electromagnetic scattering bythree-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

A summary of the transmitting and receiving properties of antennas

An expression for the electric field radiated by an arbitrary current distribution is given, which leads to a straightforward characterization of an antenna by a complex vector called the equivalent length. All classical transmitting parameters-such as the radiated power density, power intensity, radiation resistance, directional gain, and gain-are simple functions of the equivalent length. The same is true for the receiving parameters: induced voltage, available power, equivalent surface, and antenna factor. Eliminating the equivalent length between the gain and an equivalent surface provides a simple, direct, and general proof of the fundamental relation for antennas     

Analysis of cavity-backed aperture antennas with a dielectricoverlay

A full-wave analysis of cavity-backed aperture antennas with a dielectric overlay is presented. The theoretical approach uses a closed-form dyadic Green's function in the spectral domain. The aperture equivalent magnetic currents are obtained using the surface equivalence theorem and an integral equation is obtained by matching the fields across the aperture. The moment method applied in spectral domain analysis is employed to solve the integral equation for the equivalent magnetic currents with proper combination of subdomain or entire domain expansion functions. Numerical results include the aperture field distribution and antenna parameters such as input impedance, bandwidth, and efficiency. A set of measurements data is compared with results based on the theoretical work     

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.     

Analysis of a cylindrical antenna containing an aperture coupledload

In this paper we present the basis for the analysis of shielded tuning networks coupled to wire antenna elements. The structure analyzed comprises three conducting cylindrical tubes that form an aperture-fed circular coaxial waveguide. Two methods are presented for formulating and solving integral equations for the structure. The first method is based on the mixed potential electric field integral equation enforced on the three cylindrical tubes, and the second is based on aperture theory. An end correction capacitance is used to adjust the reflection coefficient in the eigenmode expressions of the aperture method. The data obtained by the two methods are in close agreement. Differences in actual currents and equivalent currents obtained from solutions are discussed and reconciled     

Calculation and experimental validation of induced currents on coupled wires in an arbitrary shaped cavity

An efficient numerical technique is presented for the calculation of induced electric currents on coupled wires and multiconductor bundles placed in an arbitrary shaped cavity and excited by an external incident plane wave. The method is based upon the finite-difference time-domain (FD-TD) formulation. The concept of equivalent radius is used to replace wire bundles with single wires in the FD-TD model. Then, the radius of the equivalent wire is accounted by a modified FD-TD time-stepping expression (based on a Faraday's law contour-path formulation) for the looping magnetic fields adjacent to the wire. FD-TD computed fields at a virtual surface fully enclosing the equivalent wire are then obtained, permitting calculation of the currents on the wires of the original bundle using a standard electric field integral equation (EFIE). Substantial analytical and experimental validations are reported for both time-harmonic and broad-band excitations of wires in free space and in a high-Qmetal cavity.     

The effects of a nearby biological body on the parameters of asmall hand-held transmitter operating in the HF band (3 MHz-30 MHz)

The effects of a nearby biological body on the efficiency and radiation patterns of a small hand-held radio operating in the HF band are determined by computer modelling. The close proximity of the radio operator's body results in the scattered field from the body reradiating and perturbing the known free-space current distribution on the antenna to some extent. However, due to the extremely small electrical size of the radiating system, this body-to-radio coupling is assumed to be minimal and henceforth neglected. Thus, a direct moment method is used to solve a volumetric electric field integral equation with the near field of the radio used as the excitation field. Once the equivalent volumetric currents are determined, the efficiency and radiation patterns are found using these currents and the unperturbed free space current of the radio antenna     

Rigorous Analysis of Rectangular Dielectric Resonator Antenna With a Finite Ground Plane

A probe-fed rectangular dielectric resonator antenna (RDRA) placed on a finite ground plane is numerically investigated using method of moments (MoM). The whole structure of the antenna is exactly modeled in our simulation. The feed probe, coaxial cable and ground plane are modeled as surface electric currents, while the dielectric resonator (DR) and the internal dielectric of coaxial cable is modeled as volume polarization currents. Each of the objects is treated as a set of combined field integral equations. The associated couplings are then formulated with sets of integral equations. The coupled integral equations are solved using MoM in spatial domain. The effects of ground plane size, air gap between dielectric resonator and ground plane, probe length, and position on the radiation performance of the antenna including resonant frequency, input impedance, radiation patterns, and bandwidth are investigated. The results obtained for the antenna parameters based on the MoM investigation shows that there is a close agreement with those obtained by measurement. Moreover it is shown that the MoM results are more accurate than other simulation results using software package such as High Frequency Structure Simulator (HFSS).      

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme     

Equivalent source analysis of curved edge tapered slot-line antennas

An equivalent source model for the analysis of curved edge tapered slot-line antenna is developed, which employs effective filamentary currents along the conductor edges of the slot, but forces the electric field produced by the currents to satisfy the boundary condition on the whole conductor surface. This idea is implemented by method of moments with collocation technique, and applied to analyze a tapered slot-line antenna with arbitrarily curved edge.     

2-D validation of a formulation for the analysis of 3-D bodies thatare periodic in one direction and finite sized in the others

A numerical scheme to analyze three-dimensional bodies that are periodic in one direction (z) and finite sized in the other ones (x, y) is presented. The geometry and material composition of the body can be arbitrary. A new formulation using the conjugate gradient-fast Fourier transform method (CG-FFT) has been developed. The formulation is based on the discretization and resolution of the electric field integral equation (EFIE) in both the real and spectral domains and leads to an efficient and accurate numerical procedure. Results are presented for RCS, equivalent currents and fields inside 3-D periodic structures (infinitely long cylinders with arbitrary shape and material composition). These results are compared with analytical solutions and the agreement is found to be good