Scan-independent slot arrays with parasitic wire arrays in astratified medium

The effect of a parasitic wire array on the scan admittance of a slot array has been investigated. Structures considered can consist of an infinite slot array and an arbitrary number of parasitic infinite arrays of piecewise linear wires, all arrays being embedded in a stratified medium. These include, as particular cases, phased arrays of Clavin elements. Expressing the fields from the arrays as plane waves, a procedure similar to the periodic moment method for infinite periodic structures is set up to obtain the scan admittance of the slot array. Scan admittances are presented for a slot array with monopole arrays in free space, and a slot array with a tilted dipole array in a stratified medium. Blind spots at which the incident energy is mainly reflected rather than transmitted were found. Results obtained indicate the possibility of using parasitic wire arrays for scan compensation of active slot arrays     

Scattering from finite by infinite arrays of slots in a thinconducting wedge

The radar scattering from a finite by infinite array of slots cut into a thin conducting wedge is considered. The wedge is formed by taking a thin ground plane and applying a bend to create a sharp edge which is parallel to the columns of slots in the infinite axis. Results are derived for thin linear slots whose major axes are either parallel or perpendicular to the edge. A hybrid moment method and geometrical theory of diffraction approach is used, with magnetic current expansion functions defined using Floquet's theorem on single columns of slots. Predictions generally agree with scattering measurements of finite by finite array physical models with monostatic patterns taken in a plane orthogonal to the sharp edge     

Analysis of an infinite periodic array of slot radiators withdielectric loading

An efficient numerical procedure for determining the radiation characteristics of an infinite periodic array of slots in a conducting screen is presented. The procedure employs a novel mixed-potential integral equation formulation and is solved by the method of moments. Subdomain-type basis functions are used to provide the flexibility to model arbitrarily shaped slots. Analysis is carried out to account for dielectric layers, ground planes, or cavities placed on either side of the slot. Series acceleration techniques are employed to reduce significantly the computation time required to sum the series representing the periodic Green's function. The numerical scheme developed is applied to obtain quantities such as the slot field distribution and input admittance as a function of the array scan angle. Where possible, numerical results obtained are compared with data available in the literature. Data for the half-space case are found to agree with those of A.Y. Grinev et al. (1978) except for the case of multilayer dielectric loading     

A novel expression for the mutual admittance of planar radiating elements

The mutual admittance between two identical planar radiating apertures can be expressed as the bidimensional Fourier transform of a function (defined in the wavenumbers plane), obtained by taking the inner product of the plane wave spectrum (representing the field radiated by the element) by another plane wave spectrum obtained from it by reversing the sense of propagation of each component wave. The asymptotic evaluation of the expression shows that (under certain limitations) the mutual admittance, for large spacing among the radiators, tends to be proportional to the power radiation pattern on the plane of the aperture. By using the formalism here introduced the "grating lobes series" for the driving point admittance of an element in an infinite periodic array can be simply derived from the "mutual admittances series." As a check of the theory the mutual admittance between rectangular slots, in different relative positions, has been numerically calculated.     

Transmission through a two-layer array of loaded slots

The mutual admittance method is used to calculate the transmission through a two layer array of slots. The slot arrays are thin and parallel. The plane wave illumination is at an arbitrary angle in either theE-plane orH-plane. The mutual admittance between two slot antennas, either in the same or different planes, is derived. In this derivation it is assumed that the slots are small enough so that when short-circuited at their terminals the electric field scattered from the slot is negligible. The evaluation of the mutual admittance sums is simplified by the extension to the slot case of certain impedance relationships established previously for a two-layer dipole array. For many applications the two-layer slot array is more desirable than a single-layer array since a wider passband and sharper skirts can be obtained with proper design. The analysis shows, however, that for high incidence angles the dip in the center of the passband may be deeper than for the similar two-layer dipole array.     

A generalized approach to the analysis of infinite planar array antennas

In this paper a generalized expression for the complex power radiated by an element in an infinite planar array antenna is derived. Since this power formula applies to a large class of phased array antennas where the aperture field distribution can be completely specified (in normal mode form), it proves to be a powerful, unifying principle. The utility of this approach is illustrated by the simplicity with which previously known results can be derived; e.g., an infinite array of slots in a ground plane and an infinite array of flat dipoles with or without a ground plane. Further demonstrations of the usefulness of the power formula are provided by the systematic and straightforward solutions of the less-well-known problems of infinite arrays of crossed-dipole pairs and infinite arrays of open-ended rectangular waveguides. The waveguide array solution is particularly interesting because it reduces to a set of equations which are identical to those one would use to characterize an N-port network on an admittance basis (N is the number of waveguide modes). Since the power formula is derived for a parallelogram element Lattice, the resultant solution for a specific type of element is in its most general form. Expressions for the scan-dependent, dominant mode radiation admittance and the element gain function for a multimode rectangular waveguide radiator are also derived. In addition, various aspects of the waveguide array solution are investigated in the light of previous studies of infinite arrays.     

The design of large waveguide arrays of shunt slots

It is shown that the method of moments (MM) solution can determine the active admittance of each slot in a finite array and that the infinite array model is quite accurate for the design of large waveguide arrays of shunt slots. Active admittances computed by an infinite array model agree favorably with that of slots in sufficiently large finite arrays. Measured results verify the MM solution, thereby validating the infinite array model accuracy     

Modal analysis of periodic planar phased arrays of apertures

A general method is established for the evaluation of the driving point admittance of a radiating aperture, fed by a waveguide of the same cross section as the aperture, in an infinite periodic planar phased array. The array may have an arbitrary element lattice and it may be covered by a dielectric layer. The coefficients of the waveguide modal expansion and of the Floquet series representing the electromagnetic field in the waveguide and in the radiation half-space, respectively, are determined by approximately enforcing the boundary conditions in the array plane through an application of Galerkin's method. By eliminating from the set of equations thus obtained the complex amplitudes of the waveguide modes and of the Floquet harmonics, the driving point admittance can be expressed as the ratio of two determinants of order N and N-1 (N being the number of the waveguide modes utilized), whose elements contain truncated bidimensional series, structurally similar to the well-known grating-lobe series. The expression allows relatively simple numerical computations if the Fourier transforms of the waveguide vector mode functions are known in closed form (as they are for rectangular or circular elements). The variation of the power reflection loss with scan angle has been numerically calculated for various array configurations. The results are in some cases substantially different from those predicted through the conventional grating-lobe series technique, which is based on the assumption of one-mode elements.     

The determination of active array impedance with multielement waveguide simulators

The basic principles behind a multielement waveguide simulator are presented for the case of general symmetric elements in a rectangular or triangular spaced infinite array. The techniques are applicable to any polarization and are valid for array spacings which allow grating lobes in real space. It is shown that a single simulator containingN times Melements can be used to measure the reflection coefficient for the infinite array atN times Mscan angles. The measurement involves the determination of theN times Mtransmission coefficients between one element and each of the other elements in the simulator when the simulator waveguide is terminated in a matched load. It is shown that theN times Mreflection coefficients so obtained are actually the eigenvalues of the scattering matrix of the network formed by theN times Minput ports to the simulator. An interpolation scheme is presented which allows the infinite array impedance to be approximated over a large range of scan angles by means of an expansion in terms of the eigenvalues of the simulator. The physical significance of the interpolation is discussed, and experimental results for a 25-element simulator utilizing stripline slots are presented.     

Theoretical considerations in the optimization of surface waves on a planar structure

The problem of optimum excitation of surface waves on a grounded dielectric slab by means of slots in the ground plane is considered. By adopting a two-dimensional (2-D) model, analysis lead to closed forms for the power launched as surface waves and power leaked as radiation. Input admittance of a single slot source and mutual admittance between two slots are derived and utilized to design a three element Yagi array of slots to achieve a prescribed ratio of forward to backward surface wave power. As a development of the 2-D model, we allow finite extent of slot excitation by assuming a Gaussian E-field distribution across the slot. The effect of the Gaussian width on the excited surface wave power is studied. The analysis is relevant to the study of surface waves on printed circuits. Specifically, it applies to the implementation of power combiners based on quasioptical slab beam that have been recently introduced in the literature for use in the millimeter wave band.     

Efficiency as a measure of size of a phased-array antenna

This communication addresses the problem of estimating the minimum size a phased-array antenna must have in order that analyses based on simple infinite-array models yield meaningful results. The measure of array size proposed herein is an efficiency parameter defined for an infinite array with truncated excitations. Numerical results are presented for arrays of slots and dipoles, showing the rate of convergence of the efficiency parameter for various spacings and scan angles. The conclusions deduced from this analysis as to the minimum array size are in substantial agreement with exact computations dealing with finite arrays published in the literature.     

The Coupling of Electromagnetic Waves Through Long Slots

The problem of a plane wave incident upon one or more long, parallel slots in an infinite plane screen is treated by the method of moments. A Galerkin's solution with triangular expansion and weighting functions is used. The complete solution for aperture fields, transmission coefficients, near and far fields is formulated and programmed. Arbitrary polarization and arbitrary angles of incidence are treated. Where comparison is possible, there is good agreement with classical results. Wide slots, and multiple slots, which cannot be treated by classical methods, are readily handled by the method of moments procedure. Two separate computer programs have been prepared for a) single slot and b) double slots. The theory is outlined; the computer program is described briefly, and representative examples are given.     

Surface waves and anomalous wave radiation nulls on phased arrays of TEM waveguides with fences

This paper describes the behavior of an infinite array of parallel plane waveguides in a conducting ground plane with metallic fences perpendicular to the ground plane and spaced halfway between each pair of radiators. The study is mainly concerned with anomalous wave nulls and their relation to endfire surface-wave radiation, and in addition some data is presented to demonstrate the scan matching properties of the fence geometry. An interesting new development in open periodic structure theory is reported and is shown to apply to both surface waves and anomalous waves. Certain restrictions on the phase distributions of the aperture fields and fence currents are revealed and their origin outlined briefly. These restrictions are introduced to further emphasize relationships between surface and anomalous waves. In addition to these basic relationships, a numerical study of the scanning properties of waveguide-fence arrays is presented which has indicated that structures of this type can reduce impedance variation during scan and can be especially useful when it is desirable to scan very near to, or in the limited scan case, beyond the point at which a grating lobe moves into real space.     

Properties of a phased array of rectangular waveguides with thin walls

The radiation impedance of an infinite array of open rectangular waveguides has been calculated by a function-theoretic method forHplane and quasi-Eplane beam scanning directions. The mutual coupling between columns has also been obtained. The amplitudes of the coupling coefficients decay asymptotically asr^{-3/2}while the phase difference between successive coupling coefficients approaches that to be expected from free space wave propagation. This asymptotic behavior is independent of waveguide dimensions for both planes of scan. It is similar to the asymptotic behavior of a line-source-excited wave propagating over a lossy surface. This suggests that the interface between an array and free space may in general be treated as such a surface. The coupling coefficients are used to determine the properties of an array, which has a finite number of active elements surrounded by an infinite passive array. Also, the edge effect due to the finiteness of an array is evaluated.     

Radiation from periodic structures excited by an aperiodic source

In the past, periodic structures have been extensively studied for guided waves along the surface, or for plane wave excitation. However, very little has been reported concerning the problem of exciting periodic structures by a localized source. The essential difficulty of this problem is due to the aperiodic nature of the source. This paper presents a study of a two-dimensional periodic structure excited by a magnetic line source. The structure consists of a grounded dielectric slab covered by a periodically slotted conducting plane. From the continuity of the fields in the slots, an infinite system of integral equations for the aperture fields is derived. Under the assumption of narrow slots, these equations are converted into a single integral equation by the use of the sampling technique, and the solution is expressed in an inverse Fourier transform. The integrand is then converted into a form of space harmonics which contains an infinite number of poles and branch points. The relationship between these singularities and thek-betadiagram is clearly demonstrated. The radiation pattern is calculated and compared with experimental data. The Wood anomalies associated with leaky waves and the Rayleigh wavelength, and in particular, the relationship between the behavior of the field near the Rayleigh wavelength and the lateral waves are discusssed.     

Equivalent circuit formulation for an array of phased waveguide apertures

An expression for the radiation admittance of an infinite planar array of rectangular waveguide apertures is formulated and a technique for finding the complete equivalent circuit of the waveguide to space junction is given. The formulation includes multiple layers of dielectric above the array ground plane and waveguide elements which are center loaded with dielectric. Experimental verification of the radiation admittance formulation and the equivalent circuit concepts is given.     

A hybrid moment method solution for TEz scattering fromlarge planar slot arrays

This paper develops a hybrid moment method (MM) based numerical model for electromagnetic scattering from large finite-by-infinite planar slot arrays. The model incorporates the novel concept of a physical basis function (PBF) to reduce dramatically the number of required unknowns. The model can represent a finite number of slot columns with slots oriented along the infinite axis, surrounded by an arbitrary number of coplanar dielectric slabs. Each slot column can be loaded with a complex impedance to tailor the array's edge currents. An individual slot column is represented by equivalent magnetic scattering currents on an unbroken perfectly conducting plane. Floquet theory reduces the currents to a single reference element. In the array's central portion, where the edge perturbations are negligible, the slot column reference elements are combined into a single basis function. Thus, one PBF can represent an arbitrarily large number of slot columns. A newly developed one-sided Poisson sum formula is used to calculate the mutual coupling between the PBF and the slot columns in the presence of a stratified dielectric media. The array scanning method (ASM) gives the mutual coupling between the individual slot columns. The hybrid method is validated using both numerical and experimental reference data. The results demonstrate the method's accuracy as well as its ability to handle array problems too large for traditional MM solutions     

The interpolation of general active array impedance from multielement simulators

The multielement waveguide simulator gives the active reflection coefficient of an infinite array at a discrete number of scan angles. A general method to estimate the active reflection coefficient at in between angles is presented. The method expands any array excitation into a series using the orthogonal set of waveguide modes of the simulator. The portion of the simulator reflections which is proportional to the applied excitation is extracted. An estimate of the accuracy of the interpolation is also derived in terms of the form of the power reflected from the simulator. The technique is demonstrated on a 30- element simulator and comparisons are made with calculations for an infinite array composed of open-ended circular waveguides.     

Monte Carlo法在平板裂缝天线辐射缝导纳误差分析中的应用

采用MonteCarlo法分析了平板裂缝天线辐射缝的导纳误差。建立辐射缝导纳误差的概率模型,将波导和裂缝的结构参数误差看作在某误差范围内服从正态分布的随机变量。对这些变量进行抽样计算,得到各个结构参数误差对谐振频率和谐振电导的影响,其中缝隙长度和偏置的误差对谐振电导和谐振频率的影响较大,波导窄边和壁厚误差产生的影响较小。根据计算结果调整各结构参数的误差范围,使它们对谐振频率和谐振电导的影响程度接近,在此基础上分析了同时存在这些误差项时对谐振频率和谐振电导的影响,由此提出满足导纳提取精度要求的加工误差指标。最后用Ansoft HFSS软件仿真验证了该方法的正确性。     

Cross polarization losses in periodic arrays of loaded slots

A periodic array of apertures in a conducting plane can act as a bandpass filter. With proper design the structure will be transparent at its resonant frequency but will have a transmission coefficient below unity at all other frequencies. These periodic surfaces are useful as radomes and in dual frequency antenna feeds. The resonant frequency of such an array may vary with incidence angle. This variation is undesirable for most applications, and can be greatly reduced by reactively loading the slots with the Babinet equivalent of a short circuited two-wire transmission line. It has been found, however, that singly loaded slot arrays have transmission loss due to cross polarized radiation when scanned in theH-plane (perpendicular polarization). It is shown that this cross polarized radiation may be eliminated by using symmetrical loaded slots, which have the further advantage of transmitting waves of arbitrary polarization. In conjunction with this investigation, the modal matching method, previously applied to arrays of rectangular and circular slots, has been extended to the more complicated loaded slot shapes. Both the single loaded and 4-legged symmetrically loaded slots are treated, and good agreement with measured data is obtained.