Efficient Analysis of Phased Arrays of Microstrip Patches Using a Hybrid Generalized Forward Backward Method/Green's Function Technique With a DFT Based Acceleration Algorithm

A hybrid method based on the combination of generalized forward backward method (GFBM) and Green's function for the grounded dielectric slab together with the acceleration of the combination via a discrete Fourier transform (DFT) based algorithm is developed for the efficient and accurate analysis of electromagnetic radiation/scattering from electrically large, irregularly contoured two-dimensional arrays consisting of finite number of probe-fed microstrip patches. In this method, unknown current coefficients corresponding to a single patch are first solved by a conventional Galerkin type hybrid method of moments (MoM)/Green's function technique that uses the grounded dielectric slab's Green's function. Because the current distribution on the microstrip patch can be expanded using an arbitrary number of subsectional basis functions, the patch can have any shape. The solution for the array currents is then found through GFBM, where it sweeps the current computation element by element. The computational complexity of this method, which is originally ( being the total number of unknowns) for each iteration, is reduced to using a DFT based acceleration algorithm making use of the fact that array elements are identical and the array is periodic. Numerical results in the form of array current distribution are given for various sized arrays of probe-fed microstrip patches with elliptical and/or circular boundaries, and are compared with the conventional MoM results to illustrate the efficiency and accuracy of the method.     

General relations for a phased array of printed antennas derived from infinite current sheets

Simple and general relations characterizing the behavior of infinite phased arrays of printed antenna elements are derived from a model based on infinite current sheets. The Green's function of an electric current source on a grounded dielectric slab is used in various limiting forms to treat arrays in free space, arrays above a ground plane, arrays on a semi-infinite substrate, and arrays on a grounded dielectric slab. Current sheets are selected, using the orthogonality properties of the Floquet modes of the infinite array Green's function, to excite only a few specific low-order Floquet modes. Results from this idealized model, in the form of reflection coefficient magnitudes and input resistance, are compared with rigorous moment method solutions for specific elements (dipoles and microstrip patches). It is shown how the dominant scanning characteristics of a printed phased array, such as reflection coefficient and input resistance trends, scan blindnesses, and grating lobe effects, are dictated more by factors such as element spacing and substrate parameters than by the particular element type itself.     

Analysis of finite arrays of axially directed printed dipoles on electrically large circular cylinders

Various arrays consisting of finite number of printed dipoles on electrically large dielectric coated circular cylinders are investigated using a hybrid method of moments/Green's function technique in the spatial domain. This is basically an "element by element" approach in which the mutual coupling between dipoles through space as well as surface waves is incorporated. The efficiency of the method comes from the computation of the Green's function, where three types of spatial domain Green's function representations are used interchangeably, based on their computational efficiency and regions where they remain accurate. Numerical results are presented in the form of array current distributions, active reflection coefficient and far-field pattern to indicate the efficiency and accuracy of the method. Furthermore, these results are compared with similar results obtained from finite arrays of printed dipoles on grounded planar dielectric slabs. It is shown that planar approximations, except for small separations, can not be used due to the mutual coupling between the array elements. Consequently, basic performance metrics of printed dipole arrays on coated cylinders show significant discrepancies when compared to their planar counterparts.     

Analysis of infinite arrays of microstrip-fed dipoles printed onprotruding dielectric substrates and covered with a dielectric radome

A method for analyzing infinite arrays of antennas printed on both sides of substrates protruding from a ground plane and covered with a dielectric radome is described. Using the equivalence principle, the array unit cell is decomposed into homogeneous regions where the fields are expressed as Floquet summations, and an inhomogeneous cavity region where the fields can be found by a combination of the method of moments and modal analysis. The approach is rigorous in the sense that the combined effects of the radiating element and feed geometry printed on opposite sides of a protruding substrate are taken into account. The method is quite general, capable of modeling any antenna elements with substrate currents that are perpendicular and/or parallel to the ground plane. In addition, both the radiating and scattering/receiving modes of operation are treated in the analysis. The method is used to calculate the active element impedance of an infinite array of dipoles transmission line-coupled to microstrip feeds. Examples of numerical results are presented for various scan conditions and the effects of a near-field dielectric radome are demonstrated     

Scattering of TE-polarized EM wave by discontinuity in groundeddielectric layer

The two-dimensional problem of EM wave interaction with a dielectric discontinuity in an infinite grounded dielectric layer is studied. An electric field integral equation (EFIE) for TE illumination has been derived based on the Green's function for the electric field produced by induced polarization currents in the discontinuity region. Impressed electric fields consist of either plane waves incident from space above the dielectric layer or surface waves supported by that layer. Method of Moments (MoM) numerical solutions for the induced electric field in the discontinuity region are implemented. The amplitudes of surface waves excited by excess discontinuity-region polarization currents are calculated, as well as the pattern of the scattered field and the associated scattering width. It is observed that the excitation of a surface-wave mode reduces the back scattered radiation for TE-polarized plane wave incidence. The accuracy of the theory is verified by comparison of numerical results with those of existing studies     

Space-domain method of moments solution for a strip on a dielectricslab

This paper presents a space-domain method of moments (MoM) solution to the problem of a strip dipole on a dielectric slab. The solution involves the use of a special junction basis function which models the nearly singular polarization currents in the vicinity of the strip/dielectric junction     

Tailoring the AMC and EBG characteristics of periodic metallic arrays printed on grounded dielectric substrate

The artificial magnetic conductor (AMC) and electromagnetic band gap (EBG) characteristics of planar periodic metallic arrays printed on grounded dielectric substrate are investigated. The currents induced on the arrays are presented for the first time and their study reveals two distinct resonance phenomena associated with these surfaces. A new technique is presented to tailor the spectral position of the AMC operation and the EBG. Square patch arrays with fixed element size and variable periodicities are employed as working examples to demonstrate the dependence of the spectral AMC and EBG characteristics on array parameters. It is revealed that as the array periodicity is increased, the AMC frequency is increased, while the EBG frequency is reduced. This is shown to occur due to the different nature of the resonance phenomena and the associated underlying physical mechanisms that produce the two effects. The effect of substrate thickness is also investigated. Full wave method of moments (MoM) has been employed for the derivation of the reflection characteristics, the currents and the dispersion relations. A uniplanar array with simultaneous AMC and EBG operation is demonstrated theoretically and experimentally.     

Infinite phased arrays of cavity-backed patches

An analysis of the radiation properties of infinite phased arrays of probe-fed circular microstrip patches backed by circular cavities using a rigorous Green's function/Galerkin's method is presented. The effect of substrate thickness on both scan volume and bandwidth performance is considered. Results are compared to those of infinite arrays of conventional probe-fed circular patch antennas     

A hybrid SBR/MoM technique for analysis of scattering from smallprotrusions on a large conducting body

A hybrid technique combining the shooting-and-bouncing-ray (SBR) method and the method-of-moments (MoM) is presented for analyzing scattering by large conducting bodies having small protrusions. In this technique, the MoM with an approximate Green's function is used to characterize the small protrusions, yielding an admittance matrix, which, when multiplied with the incident field on the protrusions, yields the currents induced on the protrusions. The incident field in the presence of the large bodies is calculated using the SBR method. The field radiated by the currents on the protrusions is also calculated using the SBR method with the aid of reciprocity. Furthermore, an iterative approach is developed, which can reduce the error introduced by the use of the approximate Green's function, Numerical results are given to demonstrate the accuracy and capability of the hybrid technique     

Radiation and scattering analysis of infinite arrays of endfireslot antennas with a ground plane

A Green's function moment-method analysis of infinite arrays of endfire slot antennas is described that includes the constant width slot antenna (CWSA) and the linearly tapered slot antenna (LTSA), with a ground plane. The method utilizes an application of equivalence at a plane in front of the array which facilitates the extension of this analysis to antennas printed on protruding dielectric sheets and/or the addition of a radome. Numerical calculations are compared with waveguide simulator experiments for CWSA and LTSA arrays as well as several less complex problem. Relevant numerical considerations and convergence issues are also discussed     

Efficient analysis of input impedance and mutual coupling of microstrip antennas mounted on large coated cylinders

An efficient and accurate hybrid method, based on the combination of the method of moments (MoM) with a special Green's function in the space domain is presented to analyze antennas and array elements conformal to electrically large material coated circular cylinders. The efficiency and accuracy of the method depend strongly on the computation of the Green's function, which is the kernel of the integral equation that is solved via MoM for the unknown equivalent currents representing only the antenna elements. Three types of space-domain Green's function representations are used, each accurate and computationally efficient in a given region of space. Consequently, a computationally optimized analysis tool for conformal microstrip antennas is obtained. Input impedance of various microstrip antennas and mutual coupling between two identical antennas are calculated and compared with published results to assess the accuracy of this hybrid method.     

A coupled surface-volume integral equation approach for thecalculation of electromagnetic scattering from composite metallic andmaterial targets

A coupled surface-volume integral equation approach is presented fur the calculation of electromagnetic scattering from conducting objects coated with materials. Free-space Green's function is used in the formulation of both integral equations. In the method of moments (MoM) solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. General roof-top basis functions are used to expand the surface and volume currents, respectively. This approach is applicable to inhomogeneous material coating, and, because of the use of free-space Green's function, it can be easily accelerated using fast solvers such as the multilevel fast multipole algorithm     

On the Scattering of Electromagnetic Waves by Periodic Rough Dielectric Surfaces: A BOA Solution

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.      

Full-Wave Analysis of Microstrip Open-End and Gap Discontinuities

A solution is presented for the characteristics of microstrip open-end and gap discontinuities on an infinite dielectric substrate. The exact Green's function of the grounded dielectric slab is used in a moment method procedure, so surface waves as well as space-wave radiation are included. The electric currents on the line are expanded in terms of longitudinal subsectional piecewise sinusoidal modes near the discontinuity, with entire domain traveling-wave modes used to represent incident, reflected, and, for the gap, transmitted waves away from the discontinuity. Results are given for the end admittance of an open-ended line, and the end conductance is compared with measurements. Results are also given for the reflection coefficient magnitude and surface-wave power generation of an open-ended line on substrates with various dielectric constants. Loss to surface and space waves is calculated for a representative gap discontinuity.     

Scattering from a finite array of microstrip patches

A full-wave solution to the problem of plane wave scattering by a finite array of rectangular microstrip patches printed on a grounded dielectric slab is presented. The electric field integral equation is solved using the spectral-domain Green's function/moment method approach. Derivations for the elements of the impedance and voltage matrices are presented. An efficient massively parallel computer implementation of the moment method solution is described. Computed radar cross section (RCS) data for microstrip patch antenna arrays are presented as a function of incident signal frequency and angle of incidence     

TM and TE scattering by a dielectric/ferrite cylinder in the presence of a half-plane

An integral equation solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by an isotropic dielectric/ferrite material cylinder in the presence of a perfectly conducting half-plane is presented. The technique is termed a method of moments (MM)/Green's function solution since the method of moments is used to determine the electric and magnetic polarization currents representing the material cylinder, while the presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations. Numerical results are presented for the echo width, material cylinder interior fields, and the surface impedance of a material slab on the surface of a half-plane.     

Theory and experiment of circularly polarized dielectric resonator antenna with a parasitic patch

The use of a single parasitic patch for circular polarization (CP) excitation of the dielectric resonator antenna (DRA) is investigated. For demonstration, the technique is applied to the conformal-strip fed hemispherical DRA, excited at the fundamental TE/sub 111/ mode. Using the Green's function approach, the integral equations for the conformal-strip and parasitic-patch currents are formulated by matching the appropriate boundary conditions. The equations are then solved using the method of moments (MoM). In using the MoM, both the rigorous and simplified current expansions are used for the parasitic patch, and their results are compared with each other. In each case, the impedance integrals are evaluated by virtue of newly obtained recurrence formulas and direct analytical integration. Hence, the results can be calculated very efficiently without the need for any numerical integration, which greatly facilitates the numerical implementation. The input impedance, axial ratio, and radiation patterns of the CP DRA are calculated, and the results are in good agreement with measurements.     

Broad-band fragmented aperture phased array element design using genetic algorithms

In this paper, a synthesis procedure to design thin broad-band fragmented aperture array elements is described. The arrays are assumed to be infinite periodic and the elements consist of a conducting pattern etched on a dielectric backed by a groundplane. A genetic algorithm (GA) is used to design the conducting pattern, relative permittivity, and thickness of the dielectric substrate with respect to array scan and bandwidth performance. The fitness function in the GA is evaluated using a finite-difference time-domain code with periodic boundary conditions. For a substrate thicker than about 0.1 /spl lambda//sub L/ (/spl lambda//sub L/= wavelength at the lowest frequency in the frequency band investigated), it was found that a bandwidth of at least one octave can be obtained for arrays scanned within 45/spl deg/ from broadside.     

Numerical modeling of dielectric-resonator antennas in a complexenvironment using the method of moments

Aperture coupled dielectric resonator antennas (DRAs) that reside above a layered background are analyzed using the method of moments (MoM). Dyadic Green's functions for the layered medium are derived in a simple and effective manner and the Rao-Wilton-Glisson (RWG) function is used to expand both electric and magnetic currents. A transmission-line technique is used to compute the antenna-input impedance. Numerical results obtained for both hemispheric and rectangular DRAB agree well with published measurement results     

Scan blindness phenomenon in conformal finite phased arrays of printed dipoles

Scan blindness phenomenon for finite phased arrays of printed dipoles on material coated, electrically large circular cylinders is investigated. Effects on the scan blindness mechanism of several array and supporting structure parameters, including curvature effects, are observed and discussed. A full-wave solution, based on a hybrid method of moments/Green's function technique in the spatial domain, is used to achieve the aforementioned goals. Numerical results show that the curvature affects the surface waves and hence the mutual coupling between array elements. As a result, the array current distribution of arrays mounted on coated cylinders are considerably different compared to similar arrays on planar platforms. Therefore, finite phased arrays of printed dipoles on coated cylinders show different behavior in terms of scan blindness phenomenon compared to their planar counterparts. Furthermore, this phenomenon is completely different for axially and circumferentially oriented printed dipoles on coated cylinders suggesting that particular element types might be important for cylindrical arrays.