Spectrum Of Two-dimensional Solutions Research Articles

Analysis and Uniform Design of a Single-Layer Slotted Waveguide Array Antenna with Baffles

This paper presents the formulation for the evaluation of external coupling in the alternating-phase feed single-layer slotted waveguide array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. A one-dimensional slot array is extracted from the array by assuming the periodicity in transversal direction and introducing the perfect electric conductors in the external region. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot pair which accelerate the iteration. Experiment at 25.3GHz demonstrates good uniformity of the aperture field distribution as well as the effects of the baffles. The directivity is 32.7dB which corresponds to the aperture efficiency 90.5% and the reflection is below -15.0dB over 1.3GHz.

Analysis and Design of a Reflection-Cancelling Transverse Slot-Pair Array with Grating-Lobe Suppressing Baffles

This paper presents the analysis and design of a reflection-cancelling transverse slot-pair array antenna with baffles by using the Spectrum of Two-Dimensional Solutions (S2DS) method. For the transverse slot array, the slot spacings with more than one free-space wavelength cause the grating-lobes. The baffles suppress the grating-lobes effectively. A one-dimensional slot array is extracted from the 2D array with in-phase excitation by assuming periodicity in the transversal direction. The uniform excitation over the finite array is synthesized iteratively to demonstrate the fast and accurate results by S2DS. A unit design model with the baffles is introduced to determine the initial parameters of the slot-pairs, which greatly accelerate the iterations process. Experiments at 25.3 GHz demonstrate the suppression of the grating lobes to the level less than -20.0 dB and also the good uniformity of the aperture field distribution.

Analysis of a Rectangular Waveguide, Edge Slot Array With Finite Wall Thickness

A method to analyze a one-dimensional array comprising tilted edge slots cut in the narrow wall of a rectangular waveguide is presented. The fields in the slots are calculated from a hybrid finite element-boundary integral (FE-BI) equation method. The boundary surface integrals on both the interior and exterior surface of the slots are computed from a spectrum of two-dimensional solutions (S2DS), which allows the influence of both the interior and exterior structure of the waveguide to be included rigorously. For initial array design, the mutual coupling between slots in the exterior region is treated approximately with an infinite array assumption modeled by two slots surrounded by periodic boundary walls with an imposed linear phase progression. A short, finite slot array is designed based on the infinite array assumption and fabricated. Results from full-wave analysis of the array and measurements are presented

On the odd-even property of functions for boundary currents over k/sub z/ in a spectrum of two-dimensional solutions

When a spectrum of two-dimensional (2-D) solutions (S2DS) is applied to calculate the far-field functions or impedances of three-dimensional (3-D) elements in the vicinity of two-dimensional (2-D) structures, in general, the calculations have to be performed for both positive and negative values of k/sub z/. This letter analyzes the odd-even property of functions for boundary currents over k/sub z/. Therefore, by using this odd-even property, the calculations of the far-field functions and impedances are only needed to be performed for positive values of k/sub z/, which reduces the computation cost by a factor of 2. A verification case is also presented.

A Fast Algorithm for Calculating the Radiation Pattern in the Longitudinal Plane of Antennas With Cylindrical Structure by Applying Asymptotic Waveform Evaluation in a Spectrum of Two-Dimensional Solutions

When dealing with electromagnetic problems of small three-dimensional (3-D) elements, such as dipole, microstrip patches and slots, in the vicinity of two-dimensional (2-D) structures, it is very efficient to find the radiation characteristics of the 3-D elements by using a spectrum of 2-D solutions (S2DS). Only one 2-D solution in the spectral domain is needed to obtain the radiation pattern in the transverse plane defined by /spl theta/=90/spl deg/. For the radiation in a longitudinal plane defined by a fixed azimuth angle /spl phi/, one 2-D problem has to be solved for each value of the polar angle /spl theta/. This paper presents a fast algorithm by which the radiation pattern in the longitudinal plane can be computed more efficiently. The algorithm applies the method of asymptotic waveform evaluation (AWE) in the 2-D spectral domain. For the cases shown in the paper, the algorithm needs only three 2-D solutions to determine the complete radiation pattern in the longitudinal plane.

A Fast Mode Analysis for Waveguides of Arbitrary Cross Section With Multiple Regions by Using a Spectrum of Two-Dimensional Solutions and Asymptotic Waveform Evaluation

A fast mode analysis for waveguides of arbitrary cross section with multiple regions is presented in this paper. The analysis is based on a spectrum of two-dimensional (2-D) solutions with application of asymptotic waveform evaluation, which requires only several 2-D solutions in searching for the propagation modes and calculating the field distribution of the modes in waveguides. The boundaries of waveguides can be modeled by perfect electric conductors, perfect magnetic conductors, dielectric materials, and asymptotic strip boundary conditions. By this modeling, one can also analyze the waveguides with the soft and hard surfaces. The method is excitation dependent, which provides a tool to analyze the response of different modes to different excitations. No existence of spurious modes is experienced by using this method. The verification and comparison of the numerical results with analytical, published data, and measurements are also presented in this paper.

Mutual coupling in aperture-coupled patches on cylindrical reflectors calculated using a spectrum of two-dimensional solutions

The mutual coupling between groundplane slots in aperture-coupled patch antennas on cylindrical structures is calculated using a moment method in the Fourier domain. By separating the three-dimensional (3D) problem into a spectrum of two-dimensional (2D) problems an efficient calculation of the admittance is possible. To increase the accuracy in the mutual admittance calculation, an asymptotic extraction technique is used. Several cases of antenna geometry are investigated and comparison is made to measurements. The method used allows for efficient and accurate analysis of dual polarized aperture-coupled patches placed on general cylindrical structures, as in the case of base-station antenna arrays for mobile communications.

Calculation of self‐impedance and radiation efficiency of a dipole near a lossy cylinder with arbitrary cross section by using the moment method and a spectrum of two‐dimensional solutions

AbstractWe present a computation method for the self‐impedance and radiation efficiency of a dipole near a lossy dielectric cylinder with arbitrary cross section by using a spectrum of two‐dimensional (2‐D) solutions. The 2‐D solutions for the spectral Green's functions of the cylinder as well as the 3‐D solution for the current on the dipole are found by the method of moments (MoM). The 2‐D MoM approach makes use of the algorithm G2DMULT (Green's function of 2‐D multiregion structures). The geometry of a dipole near a lossy circular dielectric cylinder is, in a parallel work, used to validate a reverberation chamber for measuring the radiation efficiency and self‐impedance of small antennas. Therefore, the results in the present paper could be verified against results from other numerical programs and from measurements in both an anechoic chamber and a reverberation chamber. © 2002 John Wiley & Sons, Inc. Microwave Opt Technol Lett 32: 108–112, 2002.

Analysis of an untilted wire-excited slot in the narrow wall of a rectangular waveguide by including the actual external structure

The admittance of an untilted slot in the narrow wall of a rectangular waveguide is calculated by including the actual external structure. The slot is excited by two tilted thin wires inside the waveguide. The slot is also allowed to extend into the two broad walls of the waveguide to make it sufficiently long for resonance to occur. The external slot admittance is evaluated by using a spectrum of two-dimensional solutions, a method which can handle the arbitrary cross section of the external structure, The analysis predicts that if both the slot and the wires are tuned to resonance, the transmission coefficient gets constant phase over a wide-frequency band. The results also show that resonance can be obtained for any slot length by adjusting the wire length, and this relation between the lengths is presented. The distance between the slot and the wires needed to maximize the radiated power is also shown; some results are confirmed by measurements.

Analysis of nearly cylindrical antennas and scattering problems using a spectrum of two-dimensional solutions

This paper presents a powerful method for analysing antennas which can be considered principally two-dimensional (2-D) or cylindrical, except for some three-dimensional (3-D) physical or equivalent sources, e.g., dipoles or slots. It is shown by Fourier transform techniques that such antennas can be analyzed as 2-D problems with harmonic longitudinal field variation. The radiation pattern can often be determined directly from a finite set of such 2-D solutions, each one obtained by any method, e.g., the moment method. The mutual interaction between the cylindrical scatterer and the sources must be calculated to determine the exact current distribution on the sources and their impedances or admittances. This is facilitated by performing an inverse Fourier transform of an infinite spectrum of the numerical 2-D solutions followed by a moment method solution in the spatial domain to satisfy the boundary conditions on the 3-D equivalent sources themselves. The inverse Fourier transform is simplified by the use of asymptote extraction. The method is in itself a hybrid technique as one method is used to solve the harmonic 2-D problem, and the other to solve for the source currents.

Calculation of external aperture admittance and radiation pattern of a narrow slot cut across an edge of a sectoral cylinder in terms of a spectrum of two-dimensional solutions

A slotted triangular cylinder is a candidate for a base station antenna in mobile communications. This paper presents an analysis of the external aperture admittance and the radiation pattern of a transverse narrow slot cut across one of the wedges of a sectoral cylinder, the cross section of which approximates the actual triangular shape. Thereby, the external region can be described in terms of two canonical shapes, for which the dyadic Green's functions are obtained analytically. The aperture admittance of the slot is expressed in terms of the integrals of magnetic current over the slot aperture and the infinitely extended interface of the canonical regions. These integrals are evaluated in the spacial and spectral domains, respectively. This hybrid analysis provides good convergence of the results. The dependence of the 3-dB beamwidth and the front to back ratio of the transverse radiation pattern from the slot upon the size and the sector angle of the cylinder are also presented. >

Admittance of an isolated waveguide-fed slot radiating between baffles using a spectrum of two-dimensional solutions

An efficient method of computing resonant length and admittance characteristics of an isolated broad-wall shunt slot radiating between baffles of finite height is presented. The outer three-dimensional (3D) field problem associated with this geometry is reduced to a two-dimensional (2D) one via a Fourier transformation with respect to the longitudinal z direction. For each value of the longitudinal wave number k/sub z/ an integral equation is solved for the E field in the mouth of the plates using the method of moments. This procedure is repeated for several discrete values of k/sub z/, to obtain a spectrum of 2D solutions which are then inverse-transformed to construct the 3D solution in the spatial domain for the exterior baffle region and the half space. The slot aperture field is determined by the conventional moment method solution to the integral equation that enforces the continuity of the H field across the slot. Scattering properties of the slot are then deduced. Numerical results for the resonant length and resonant conductance are presented. Computer results are found to be in good agreement with experimentally measured data. >

Transverse radiation pattern of a slotted waveguide array radiating between finite height baffles in terms of a spectrum of two-dimensional solutions

In arrays of waveguide fed slots, the periodicity of the slots causes grating lobes off the principal planes, referred to as second-order beams. To suppress these lobes, parallel plates baffles) on both sides of the array can be used. In this paper, a linear array of longitudinal slots radiating between such baffles of finite height is analysed. The three-dimensional (3D) field problem is reduced to a two-dimensional (2D) problem via a Fourier transform. An integral equation for the 2D problem is developed and solved. The 3D radiation pattern, including the effect of a finite ground plane outside the baffles, is calculated from the 2D solutions. Results for various baffle dimensions, showing the attenuation of second-order beams, are presented and computed solution has been verified by measurements.