Showing papers in "IEEE Transactions on Antennas and Propagation in 1993"
TL;DR: In this article, the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented, where the general linear variation of the source is represented in terms of three linear basis functions, each one associated with a different vertex of the triangular domain.
Abstract: Formulas for the static and dynamic potentials due to linearly varying source distributions defined on a planar triangle are presented. The general linear variation of the source is represented in terms of three linear basis functions, each one associated with a different vertex of the triangular domain. The singular kernels considered are given by the 3-D Green's function and its gradient, both for the static and dynamic case. In the static case the evaluation of potentials is performed analytically and compact form results are given. In the dynamic case the results are given in a form suited for numerical integration. >
474 citations
TL;DR: An investigation into methods of modeling the radiation patterns of phased arrays that include the effects of radiative mutual coupling that accurately predicts the patterns of small and medium-size arrays of equally spaced elements is presented.
Abstract: Results from an investigation into methods of modeling the radiation patterns of phased arrays that include the effects of radiative mutual coupling are presented. The approaches are based on either the principle of pattern multiplication or the use of active element patterns. Theoretical derivations of the various active element pattern methods are presented. A new method, the hybrid active element pattern method, is introduced. It accurately predicts the patterns of small and medium-size arrays of equally spaced elements. Example arrays of center-fed dipoles are analyzed to verify and illustrate the representations. The results are general and can be applied to arrays of any type of element. The array patterns computed using both the classical pattern multiplication approach and the methods based on active element patterns are compared to those computed using accurate numerical codes based on the method of moments. >
376 citations
TL;DR: In this article, two variations of a novel feeding technique for a wideband circularly polarized aperture-coupled microstrip antenna are described, and experimental results are shown for each antenna, and results for the two designs are compared.
Abstract: Two variations of a novel feeding technique for a wideband circularly polarized aperture-coupled microstrip antenna are described. Prototype designs for wideband linearly polarized elements are first presented, and then used for circularly polarized designs. Techniques used for design of the feed network are detailed, for both series feed and parallel feed versions. Experimental results are shown for each antenna, and results for the two designs are compared. The impedance and axial ratio bandwidths for these antennas are among the best yet achieved for microstrip antenna elements. Several design variations are also discussed. >
376 citations
TL;DR: In this article, a wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the SCA.
Abstract: An approach which incorporates the theory of wavelet transforms in method-of-moments solutions for electromagnetic wave interaction problems is presented. The unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function, which is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer. The approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths. Using a Galerkin method and subsequently applying a threshold procedure, the moment-method matrix is rendered sparsely populated. The structure of the matrix reveals the localized scale-fitting distribution long before the matrix equation is solved. The performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double-slot aperture. >
313 citations
TL;DR: In this article, a comprehensive measurement program was conducted by Telesis Technologies Laboratory (TTL) in the San Francisco Bay area using three base station antenna heights of 3.2 m, 8.7 m, and 13.4 m and two frequencies at 900 MHz and 1900 MHz.
Abstract: To acquire a knowledge of radio propagation characteristics in the microcellular environments for personal communications services (PCS), a comprehensive measurement program was conducted by Telesis Technologies Laboratory (TTL) in the San Francisco Bay area using three base station antenna heights of 3.2 m, 8.7 m, and 13.4 m and two frequencies at 900 MHz and 1900 MHz. Five test settings were chosen in urban, suburban, and rural areas in order to study propagation in a variety of environments. This paper reports the LOS measurements in different environments, all of which show variations of signal strength with distance that have distinct near and far regions separated by a break point. It was also found that the location of the break point for different frequencies and antenna heights can be calculated based on first Fresnel zone clearance. The regression analysis reveals a slope that is less than two before the break point, while it is greater than two after the break point. This break distance can be used to define the size of microcell and to design for fast hand-off. Beyond the first Fresnel zone break distance the base station antenna height gain was observed to approximately follow the square power law of antenna height. >
303 citations
TL;DR: In this article, two variations of a circular microstrip patch design are presented which excite very little surface wave power and thus have smoother radiation patterns when mounted on finite-size ground planes, due to reduced surface wave diffraction.
Abstract: Two variations of a circular microstrip patch design are presented which excite very little surface wave power. Both of the designs are based on the principle that a ring of magnetic current in a substrate (which models the patches) will not excite the dominant TM/sub 0/ surface wave if the radius of the ring is a particular critical value. Numerical results for radiation efficiency and radiated field strength from a ring of magnetic current are shown to verify this basic design principle. The proposed patch designs are chosen to have a radius equal to this critical value, while maintaining resonance at the design frequency. The designs excite very little surface-wave power, and thus have smoother radiation patterns when mounted on finite-size ground planes, due to reduced surface-wave diffraction. They also have reduced mutual coupling, due to the reduced surface-wave excitation. Measured results for radiation patterns and field strength within the substrate are presented to verify the theoretical concepts. >
290 citations
TL;DR: The authors use range profiles as the feature vectors for data representation, and they establish a decision rule based on the matching scores to identify aerospace objects, and the results demonstrated can be used for comparison with other identification methods.
Abstract: The authors use range profiles as the feature vectors for data representation, and they establish a decision rule based on the matching scores to identify aerospace objects. Reasons for choosing range profiles as the feature vectors are explained, and criteria for determining aspect increments for building the database are proposed. Typical experimental examples of the matching scores and recognition rates are provided and discussed. The results demonstrated can be used for comparison with other identification methods. >
274 citations
TL;DR: This work has shown how input impedance, far-field radiation pattern, radiation efficiency, and the magnitude of the near field are affected by the presence of the human body.
Abstract: This work deals with the influence the presence of a person has on the performance of antennas for hand-held portable telephones. It is shown how input impedance, far-field radiation pattern, radiation efficiency, and the magnitude of the near field are affected by the presence of the human body. The investigations have been carried out by applying the finite-difference time-domain (FDTD) technique to a model of the telephone with a lambda /4 monopole antenna and a simple hand-head model of the operator. Results from this configuration are compared with results for the telephone box and antenna alone. Measurements have been performed to verify the results obtained by simulations. The results show that a shadow effect in the far-field pattern occurs in the direction of the person and that the radiation pattern, including polarization, changes considerably from the telephone with the antenna alone. The impedance results show a change in resonance frequency when the telephone is placed next to a person. Results for radiation efficiency show that close to half of the energy is absorbed by hand and head. On average a system loss of 3-4 dB should be included in a link budget, and there is considerable fading, even in a radio-anechoic chamber, when persons move around in a natural manner. >
261 citations
TL;DR: In this article, various standard antennas for measuring radio-frequency electric and magnetic fields are discussed and a theoretical analysis of each antenna's receiving characteristics is summarized and referenced; each type of antenna demonstrates a different compromise between broadband frequency response and sensitivity.
Abstract: Discusses various standard antennas for measuring radio-frequency electric and magnetic fields. A theoretical analysis of each antenna's receiving characteristics is summarized and referenced. The standard probes described are an electrically short dipole, a resistively-loaded dipole, a half-wave dipole, an electrically small loop, and a resistively-loaded loop. A single-turn loop designed for simultaneous measurement of the electric and magnetic components of near-fields and other complex electromagnetic environments is also described. Each type of antenna demonstrates a different compromise between broadband frequency response and sensitivity. >
260 citations
TL;DR: In this paper, it was shown that when polarization sensitive arrays consisting of crossed small loops and short dipoles are used, one can eliminate the requirement in the ESPRIT algorithm that sensors must occur in matched pairs.
Abstract: It is shown that when polarization-sensitive arrays consisting of crossed small loops and short dipoles are used, one can eliminate the requirement in the ESPRIT algorithm that sensors must occur in matched pairs. The dipoles and loops are sensitive to the polarizations of incident electromagnetic plane waves. The dipoles are sensitive to the incident electric field components, and the loops to magnetic field components of the incident waves. The invariance properties among the dipole and loop outputs of an arbitrary array of orthogonal loops and orthogonal dipoles are exploited to compute both the two-dimensional arrival angles and polarizations of incoming narrowband signals. It is shown that with dipoles and loops, vertical arrays are not necessary to obtain good direction estimates for signals from low angles. >
190 citations
TL;DR: In this paper, a hemispherical dielectric resonator antenna fed by a coaxial probe is studied both theoretically and experimentally, and the Green's function for the evaluation of the input impedance is derived rigorously and expressed in a form convenient for numerical computations.
Abstract: A hemispherical dielectric resonator antenna fed by a coaxial probe is studied both theoretically and experimentally. The Green's function for the evaluation of the input impedance is derived rigorously and expressed in a form convenient for numerical computations. The method of moments is used to obtain the probe current from which the input impedance of the DR antenna is calculated. Both delta gap and magnetic frill source models are considered. Moreover, the results using a reduced kernel as well as the exact kernel are presented. Both entire basis (EB) and piecewise sinusoidal (PWS) expansion modes are used and the results are compared. The effects of the probe length, feed position, and dielectric constant on the input impedance are discussed. Finally, the theoretical radiation patterns for the first three resonant modes (TE/sub 111/, TM/sub 101/, and TE/sub 221/) of the DR antenna are presented. >
TL;DR: In this paper, the exact radiation pattern is compared with the leaky wave pattern for a specific case to demonstrate the role of leaky waves in determining the total pattern, and simple asymptotic formulas for the propagation and attenuation constants are derived.
Abstract: Previous work has demonstrated that very narrow beam radiation patterns can be obtained from a simple source embedded within multiple dielectric layers of appropriate thicknesses above a ground plane. The configuration consists of dielectric layers having permittivities epsilon /sub 1/ and epsilon /sub 2/ stacked in an alternating arrangement, with epsilon /sub 2/> epsilon /sub 1/. This narrow-beam effect can be attributed to weakly attenuated leaky waves that exist on the structure. Simple asymptotic formulas for the propagation and attenuation constants are derived. The formulas show how the beamwidth varies with the number of layers and the material constants. The exact radiation pattern is compared with the leaky-wave pattern for a specific case to demonstrate the role of the leaky waves in determining the total pattern. >
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TL;DR: In this article, a radiation element, designated as a curl antenna, is proposed for a circularly polarized antenna, and the radiation characteristics of the curl are numerically analyzed; the gain is approximately 8.4 dB and the 3-dB axial ratio criterion is 6.7%.
Abstract: A radiation element, designated as a curl antenna, is proposed for a circularly polarized antenna. The radiation characteristics of the curl are numerically analyzed. The gain is approximately 8.4 dB, and the 3-dB axial ratio criterion is 6.7%. Two aspects of curl array antennas are also presented: a decoupling factor between two curls and a circular array antenna consisting of 168 curls. Calculations show how the decoupling factor depends on the relative rotation angle of the two curls. The 168-curl array antenna shows a high aperture efficiency of 95%. >
TL;DR: In this paper, a double-strip grating leaky-wave antenna consisting of two strips per unit cell is analyzed, and an approximate design rule is discussed to achieve the minimum possible variation in attenuation as the beam is scanned through broadside.
Abstract: A double-strip grating leaky-wave antenna consisting of two strips per unit cell is analyzed. The stopband behavior exhibited at broadside scan in the single-strip grating antenna is characteristic of all periodic leaky-wave antennas having a single strip per unit cell, and results in a drastic increase in the attenuation rate of the leaky wave as the beam is scanned to broadside. By nearly eliminating this stopband behavior, the double-strip leaky-wave antenna can scan from backward end fire to forward end fire without any large frequency regions of high attenuation. An approximate design rule for the double-strip antenna is discussed, and results are presented to show how the antenna may be further optimized to achieve the minimum possible variation in attenuation as the beam is scanned through broadside. Although the stopband behavior is never completely eliminated with the addition of the extra strip, the optimum design shows an almost negligible region of rapidly varying attenuation near broadside. >
TL;DR: This paper presents a new and original approach for computing the high-frequency radar cross section (RCS) of complex radar targets in real time with a 3-D graphics workstation using a hybrid graphic-electromagnetic computing (GRECO) approach.
Abstract: This paper presents a new and original approach for computing the high-frequency radar cross section (RCS) of complex radar targets in real time with a 3-D graphics workstation. The aircraft is modeled with I-DEAS solid modeling software using a parametric surface approach. High-frequency RCS is obtained through physical optics (PO), method of equivalent currents (MEC), physical theory of diffraction (PTD), and impedance boundary condition (IBC). This method is based on a new and original implementation of high-frequency techniques which the authors have called graphical electromagnetic computing (GRECO). A graphical processing approach of an image of the target at the workstation screen is used to identify the surfaces of the target visible from the radar viewpoint and obtain the unit normal at each point. High-frequency approximations to RCS prediction are then easily computed from the knowledge of the unit normal at the illuminated surfaces of the target. The image of the target at the workstation screen (to be processed by GRECO) can be potentially obtained in real time from the I-DEAS geometric model using the 3-D graphics hardware accelerator of the workstation. Therefore, CPU time for RCS prediction is spent only on the electromagnetic part of the computation, while the more time-consuming geometric model manipulations are left to the graphics hardware. This hybrid graphic-electromagnetic computing (GRECO) results in real-time RCS prediction for complex radar targets. >
TL;DR: In this paper, the authors derived the necessary extension to the FDTD equations to accommodate nondiagonal tensors and obtained excellent agreement between FDTD and exact analytic results for a one-dimensional anisotropic scatterer.
Abstract: The popularity of the finite-difference time-domain (FDTD) method stems from the fact that it is not limited to a specific geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However, researchers have limited their investigation to materials that are either isotropic or that have diagonal permittivity, conductivity, and permeability tensors. The authors derive the necessary extension to the FDTD equations to accommodate nondiagonal tensors. Excellent agreement between FDTD and exact analytic results is obtained for a one-dimensional anisotropic scatterer. >
TL;DR: In this paper, an algorithm is developed that estimates the optimal distribution of antenna elements in a minimum redundancy linear array, which is used to synthesize effective antenna apertures much larger than the physical aperture.
Abstract: An algorithm is developed that estimates the optimal distribution of antenna elements in a minimum redundancy linear array. These distributions are used in thinned array interferometric imagers to synthesize effective antenna apertures much larger than the physical aperture. The optimal selection of antenna locations is extremely time consuming when large numbers of antennas are involved. This algorithm uses a numerical implementation of the annealing process to guide a random search for the optimal array configuration. Highly thinned low-redundancy arrays are computed for up to 30 array elements. These arrays are equivalent to the optimal solutions that are known for up to 11 elements. The arrays computed for 12-30 elements have the fewest redundancies reported to date. >
TL;DR: The impedance matrix localization (IML) method was introduced as a modification to standard moment method calculations to ease the limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems as mentioned in this paper.
Abstract: Moment method calculations have the well-known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems. The impedance matrix localization (IML) method was introduced as a modification to standard moment method calculations to ease these limitations. It utilizes a matrix transformation which effectively changes the basis (testing) functions into ones resembling traveling waves. An improved method that uses an orthogonal transformation to generate standing-wave-like basis functions is presented here. Remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers. Furthermore, the correspondence of the large elements in this matrix to geometrical theory of diffraction (GTD) terms is strengthened, as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements. >
TL;DR: In this paper, a four-element lumped-parameter equivalent circuit, consisting of a resistance, an inductance, and two capacitances, was found to represent the feed-point impedance of a dipole antenna.
Abstract: A four-element lumped-parameter equivalent circuit, consisting of a resistance, an inductance, and two capacitances, has been found to represent the feed-point impedance of a dipole antenna. The values of these elements are related only to the physical dimensions of the antenna, not the frequency of operation. Empirical formulas are given for all the elements. The equivalent circuit gives negligible errors in radiation resistance and reactance for dipole half-lengths less than 0.1 lambda , rising to 1% for resistance and 6% for reactance at 0.25 lambda . It can be readily used in standard computer software packages such as SPICE, PSPICE, and MICROCAP. >
TL;DR: In this article, an edge-based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions, where the mesh is placed a small fraction of a wavelength away from the scatterer.
Abstract: An edge-based finite element formulation with vector absorbing boundary conditions is presented for scattering by composite structures having boundaries satisfying impedance and/or transition conditions. Remarkably accurate results are obtained by placing the mesh a small fraction of a wavelength away from the scatterer. >
TL;DR: In this paper, a cylindrical monopole antenna with a continuous resistive loading is considered as a radiator for temporally short, broad-bandwidth pulses, and the electromagnetic field in the space surrounding the antenna is determined as a function of time.
Abstract: The cylindrical monopole antenna with a continuous resistive loading is considered as a radiator for temporally short, broad-bandwidth pulses. Specifically, the variation of the resistance used along the monopole is one proposed by Wu and King (1965). This antenna is analyzed by the finite-difference-time-domain (FDTD) method utilizing a new, efficient technique for handling the thin-walled, conducting tube that forms the resistance. The electromagnetic field in the space surrounding the antenna is determined as a function of time, and quantities useful for describing the performance of the antenna are then calculated from these results. Graphical displays of the results are used to give new insight into the physical processes for transient radiation form this antenna. An experimental model is constructed using a discretized version of the Wu-King profile formed from a set of precision, high-frequency resistors. Measurements of both the reflected voltage in the feed line and the time-varying radiated field are in excellent agreement with the theoretical calculations. >
TL;DR: In this paper, a uniform rectangular array of crossed dipoles is used to find 2D angles of wave arrival and wave polarizations using a 2D moving-window smoothing method.
Abstract: The authors study the problem of finding two-dimensional (2-D) angles of wave arrival and wave polarizations using a uniform rectangular array of crossed dipoles. The method presented effectively exploits the redundancy in this array via 2-D moving-window smoothing to handle coherent sources and to achieve optimum noise sensitivity. The method combines the computational advantages of the MUSIC and matrix pencil approaches. The method is shown in simulation to be nearly optimum compared with the Cramer-Rao bound. >
TL;DR: In this paper, a general method is presented to treat the instabilities which are frequently observed in the electromagnetic transient solutions using the marching-on-in-time method, which is applied to apply an finite impulse response (FIR) filter with a constant group delay during the course of marching in time.
Abstract: A general method is presented to treat the instabilities which are frequently observed in the electromagnetic transient solutions using the marching-on-in-time method. The basic idea is to apply an finite impulse response (FIR) filter with a constant group delay during the course of marching-in-time. An electric field integral equation (EFIE) formulation for perfectly conducting bodies is used as a vessel to demonstrate the method. Sample numerical results are presented and discussed. The computed results, while showing good agreement with the data obtained from other methods, present great stability improvement. >
TL;DR: In this article, a comparison is made between several different methods that have recently been proposed for efficiently modeling electrically thin material sheets in the finite-difference-time-domain (FDTD) method.
Abstract: A comparison is made between several different methods that have recently been proposed for efficiently modeling electrically thin material sheets in the finite-difference-time-domain (FDTD) method. The test problems used in the comparison are parallel-plate waveguides loaded with electrically thin dielectric (lossless) and conducting sheets for which exact solutions are available. The accuracy of the methods is illustrated by comparison with analytical results for model problems that have exact solutions. >
TL;DR: In this paper, an antenna made of a dielectric disk with a high permittivity mounted on top of a grounded substrate of low permittivities is analyzed, and a numerical procedure based on surface integral equations, derived from the equivalence principle, is used to compute the natural resonant frequencies for the HEM/sub 11/ mode from which the radiation Q factor of the antenna is obtained.
Abstract: An antenna made of a dielectric disk with a high permittivity mounted on top of a grounded dielectric substrate of low permittivity is analyzed. A numerical procedure based on surface integral equations, derived from the equivalence principle, is used to compute the natural resonant frequencies for the HEM/sub 11/ mode from which the radiation Q factor of the antenna is obtained. Then the radiation pattern of the antenna, operating at the resonant frequency evaluated previously, is computed with an electric dipole excitation located within the dielectric substrate under the dielectric disk. The effect of various parameters on the radiation characteristics of the antenna is studied, and presented in the form of diagrams. The low values of the radiation Q, combined with the high values of the dielectric Q and conductor Q, indicate that this antenna promises to be more efficient then the microstrip antenna. >
TL;DR: In this article, a frequency and short-pulse (SP) time-domain (TD) study of two-dimensional plane wave scattering from a finite periodic array of thin, flat, coplanar perfectly conducting strips is presented.
Abstract: A frequency and short-pulse (SP) time-domain (TD) study of two-dimensional plane wave scattering from a finite periodic array of thin, flat, coplanar perfectly conducting strips is presented. Rigorous analytical-numerical reference solutions are established by spatial spectral wave number decomposition and the method of moments (MOM), followed by frequency inversion. The analytical portion is approximated so as to yield via high-frequency asymptotics, for a sufficiently large number of strips, a hybrid ray-Floquet-mode-MOM algorithm that not only explains the phenomena in physical terms but is also numerically efficient and reasonably accurate when compared with the reference solution. Of special interest are the TD Floquet modes with their space-time-dependent frequencies and wave numbers. By superposition, they can synthesize the highly resolved pulse train return under SP conditions. Attention is given also to direct SP-TD synthesis, and to processing options for SP-TD data. >
TL;DR: In this paper, the wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets, which consists of both small-scale natural resonances and large-scale scattering center information.
Abstract: The wavelet analysis technique is applied to analyze the frequency-domain electromagnetic backscattered signal from finite-size targets. Since the frequency-domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such multiscale signals. Wavelet analysis examples of backscattered data from an open-ended waveguide cavity and a plasma cylinder are presented. Compared with the conventional short-time Fourier transform, the wavelet transform provides a more efficient representation of both the early-time scattering center data and the late-time resonances. The different scattering mechanisms are clearly resolved in the time-frequency representation. >
TL;DR: In this article, the conical monopole antenna with a section of continuous resistive loading is considered as a radiator for temporally short, broad-bandwidth pulses, and the geometrical details of the coaxial feed and the resistive load are varied to optimize this structure for pulse radiation.
Abstract: The conical monopole antenna with a section of continuous resistive loading is considered as a radiator for temporally short, broad-bandwidth pulses. The geometrical details of the coaxial feed and the resistive loading are varied to optimize this structure for pulse radiation. Compared with the perfectly conducting cone, the optimized resistive cone radiates a better reproduction of the pulse excitation with no loss in amplitude, and has internal reflections that are much smaller in amplitude. Graphical displays of the field surrounding the antenna are used to give insight into the physical processes for transient radiation from this antenna. Experimental models were constructed to verify the optimization and demonstrate the practicality of the design. Measurements of both the reflected voltage in the feed line and the time-varying radiated field are in excellent agreement with the theoretical calculations. >
TL;DR: In this article, the effects of the beamforming network on the overall noise figure of a multichannel active array antenna were studied and the dependence of the noise figure on various losses, and the difference between a resistive and non-resistive taper in the combining network.
Abstract: A figure of merit, G/T, for a multichannel active array antenna was derived, and the effects of the beamforming network on the overall noise figure of the system were studied. Also examined are the dependence of the noise figure on various losses, and the difference between a resistive and nonresistive taper in the combining network. When the amplifier gain is sufficiently large, the losses following the LNA can usually be ignored. For a photonic array with lossy time shift elements, however, the downstream losses become significant. Also, if resistive tapering is employed, not only the array gain but also the noise figure will be degraded by the collective effect of the feed network. >
TL;DR: It is shown that the method, even if developed for the analysis of large arrays, is able to handle small arrays and the results obtained are good even for single patches.
Abstract: A method for the analysis of large phased arrays of microstrip patches is presented. It is based on an infinite array approach where the edge effects are taken into account through the convolution with a proper window function. In the first step, a rigorous Green's function corresponding to a finite array of elementary sources is derived. This Green's function is then used to analyze the finite phased array of microstrip patches. Results are shown for the active impedance and element patterns of several arrays, and compared with measurements or, in the case of small arrays, with results obtained by a rigorous element-by-element approach. It is shown that the method, even if developed for the analysis of large arrays, is able to handle small arrays. Indeed, the results obtained are good even for single patches. Although the method has been developed for the microstrip phased array case, the results are general and are valid for any phased array with a rectangular grid. >