Mutual Coupling in Infinite Planar Arrays of Rectangular Waveguide Horns

The radiation admittance and effective power transmission coefficient are derived by a field matching method for arbitrary scan of an infinite array of open rectangular waveguides. Higher order waveguide modes, as well as higher order modes in the free space cell above the array, are included in the field matching problem. The convergence of the solution was studied, and the number of external free space and internal waveguide modes necessary for an adequate answer are given. Numerical results are obtained and compared with previous theory and with experiment for rectangular grids. Comparison is also made with experiment on a triangular grid which exhibited an anomalous notch in the element pattern. The experimental results in both cases seem to substantiate the theory, at least to the extent that could be expected from the small test arrays that were used for the measurements. The comparison indicates that the method of analysis includes all of the necessary features required for the study of mutual coupling effects in infinite arrays of rectangular waveguides having thick walls.     

Mutual coupling in finite coplanar rectangular waveguide arrays

Mutual admittance expressions are given for all possible combinations of mode coupling in an array of identical collinear rectangular waveguides opening into an infinite ground plane. Specific results are presented for the worst case of E-plane coupling between identical square waveguide to show that significant high-order mode excitation can occur. Some of these modes are a source of crosspolarisation, making mutual coupling important to the prediction of the crosspolar pattern of a rectangular waveguide array.     

Admittance analysis of nonuniformly spaced phased arrays of waveguide apertures in a ground plane

A general formulation for the analysis of a phased array of waveguide apertures in a common ground plane has been given for finite number of elements and nonuniform spacings based on network representation of the system. The analysis yields the radiation pattern, reflection coefficient, and aperture field in each waveguide. The pattern of an array of physically identical elements is expressed as superposition of patterns of infinite number of arrays. The formulation, when applied to single and two aperture cases, confirms the known results. It is then applied to investigate the properties of the element position modulated phased array of 15 rectangular waveguide apertures excited by uniform incident waves. Uniformly spaced arrays are also analyzed for comparison. The dominant mode and one higher order evanescent mode are included in the computations. The results show that the overall power reflection coefficient of the nonuniform array does not undergo any peaks over a wide scan range. It is concluded that the advantages of nonuniformly spaced arrays in suppressing grating lobes and eliminating blind spots are physically realizable.     

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.     

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 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     

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.     

波导阻抗带宽与缝隙导纳关系研究

本文从谐振阵等效网络出发,探索了缝隙波导谐振阵实现理想阻抗匹配的导纳特性,为波导谐振阵的超宽带设计提供了新思路.改进了波导并联缝隙的等效电路,首次实现缝隙导纳特性的单参数表征,创新提出了不同单元间距与单元数缝隙波导阵实现最大带宽的导纳特性分析方法,为波导缝隙阵带宽的优化设计提供了理论依据,建立了传统谐振阵非过载时的最大...     

Radiation characteristics of cavity backed aperture antennas infinite ground plane using the hybrid FEM/MoM technique and geometricaltheory of diffraction

A technique using the hybrid finite element method (FEM)/method of moments (MoM) and geometrical theory of diffraction (GTD) is presented to analyze the radiation characteristics of cavity fed aperture antennas in a finite ground plane. The cavity which excites the aperture is assumed to be fed by a cylindrical transmission line. The electromagnetic (EM) fields inside the cavity are obtained using finite element method (FEM). The EM fields and their normal derivatives required for FEM solution are obtained using: (1) the modal expansion in the feed region and (2) the MoM for the radiating aperture region (assuming an infinite ground plane). The finiteness of the ground plane is taken into account using GTD. The input admittance of open-ended circular, rectangular, and coaxial line radiating into free space through an infinite ground plane are computed and compared with earlier published results. Radiation characteristics of a coaxial cavity-fed circular aperture in a finite rectangular ground plane are verified with experimental results     

Analysis of an infinite phased array of dipole elements with RAMcoating on ground plane and covered with layered radome

An analysis of an infinite array of dipole elements over a radar absorbing material (RAM) coated ground plane and covered with a radome is presented. The radiation impedance of the dipole element is obtained when the array is in transmitting mode, and a scattering analysis is carried out when the array is excited by an incoming plane wave and the dipole elements are terminated in loads. The electric field Green's function in terms of Floquet mode expansion due to a periodic δ-function horizontal dipole source is derived to satisfy the layered boundary conditions. The method of moments is used to solve the current distribution on the dipole. Numerical calculation of the radiation impedance of a dipole array covered with a radome has been verified with results from waveguide simulator measurements. Numerical examples are given to show the effect of the RAM coated ground plane on the radiation impedance and the scattering characteristics     

Admittance of rectangular waveguide radiating from a conductingcylinder

Theory and experiment are compared for the admittance presented to a rectangular waveguide which terminates at an arbitrary angle in the surface of a conducting cylinder. Two methods are described for calculating the admittance: a single-mode approximation from the modal solution and an alternative asymptotic solution. Using these methods, the effect of aperture orientation on admittance, and the results obtained are compared with the experiment. The single-mode approximation is in good agreement with experimental results for the case when the input waveguide supports the TE₁₀ mode only. The accuracy of the approximate formula for waveguide admittance was also verified. The admittance is shown to be weakly dependent on aperture orientation for moderately large cylinders     

Generalized moment method analysis of planar reactively loadedrectangular waveguide arrays

A combined modal expansion and moment method is applied for analyzing finite planar arrays of rectangular waveguides in an infinite ground plane including reactively loaded waveguide elements. The analysis, which is based on the moment method for solving the aperture problem, in combination with the modal analysis for the reactively loaded waveguide cavities or feeding waveguides, extends the network formulation of single apertures to multiple waveguide arrays including reactively loaded elements. Two orthogonally polarized sets of basic functions are utilized to model the expansion into the complete set of eigenmodes is used to formulate the waveguide cavity problem. The theory is applied to a finite planar array of arbitrarily spaced rectangular waveguides, where reactive loads are realized by placing sliding electrical conductors at specified distances in each of the unfed waveguides. Numerical design examples show that beamforming, beamsteering, and the improvement of the crosspolarization behavior is possible by a suitable choice of the geometrical parameters. The theory is verified by results available from the literature as well as newly performed experimental measurements     

Attenuation Due to Ohmic Losses in Periodic Dipole and Slot Arrays

The analysis of the attenuation due to ohmic losses in periodic linear arrays of metallic cylinders, ribbons, and slots in a metallic ground plane is presented. Calculations indicate that the loss per unit length of the ribbon and cylinder arrays is comparable to that of a standard rectangular waveguide operated in the TE/sub 10/ mode. With a proper choice of parameters, the loss per unit length of the slot array can be brought to within a factor of 2 of that of rectangular waveguides.     

Aperture performance of a double-ridge rectangular waveguide in a phased array

Despite its widely recognized broad-band characteristics, the potential of a double-ridge rectangular waveguide as a phased array element has not been systematically explored. An additional benefit in using this waveguide is its reduced size which permits realization of a compact array lattice for wide angle scanning applications. A number of treatments of ridge waveguide propagation characteristics appear in the literature [1] -[5], but an analysis of the performance of a double-ridge waveguide phased array element has only recently been published [6], [7]. The results presented are based on [6], but they include additional material. The unmatched aperture performance of a rectangular ridge-guide in a number of wide-band phased arrays with quarter-hemispherical coverage, and a single narrow-bandH-plane scan design are examined. A parametric study and comparison of the unmatched aperture performance of a ridged-guide element with that of a rectangular waveguide reflects the capabilities of the double ridged-guide wide-band element in a large phased array. Such parametric study reveals to the designer the active admittance of the unmatched radiating element and leads in a systematic manner to a choice of the ridge-guide geometry and array lattice, to be followed by the determination of a suitable matching structure. This approach contrasts that of [7], which concentrates on demonstrating the feasibility of broad-band matching of a particular dual ridged-element.     

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     

Analysis of an infinite phased array of aperture coupled microstrippatches

An analysis of an infinite array of aperture-coupled microstrip patch antennas is described; this type of element is well suited to integrated phased-array applications, offering several advantages over other array configurations. The solution uses the spectral-domain moment-method approach, and combines features of a previous solution of infinite arrays of probe-fed patches and a reciprocity analysis of single-aperture-coupled microstrip element. The theoretical analysis is described and data are presented for the active input impedance of several arrays. Experimental data from a waveguide simulator confirm the theory     

Transmission from a Rectangular Waveguide into Half Space through a Rectangular Aperture (Computer Program Descriptions)

The program calculates the admittance seen by the waveguide, the tangential electric field in the aperture, and the radiation gain patterns for a rectangular waveguide feeding a rectangular aperture in a perfectly conducting plane of infinite extent.     

Phased arrays of probe-fed stacked microstrip patches

This paper presents calculated and measured results for infinite phased arrays of probe-fed stacked rectangular and circular microstrip patches. A numerical model is described that is based on a rigorous Green's function/Galerkin solution. In this solution, the connection of one or more vertical probe feeds to each patch is accurately modeled using a special attachment mode basis function, which is derived from the corresponding cavity model solution. Numerical results for both linearly and circularly polarized arrays are obtained. Measured results from a waveguide simulator are also presented and used to validate the numerical model     

Analysis of untilted edge slots excited by tilted wires

An untilted narrow wall slot, cut between a pair of tilted strips inside a rectangular waveguide, has been analyzed. The combination is excited internally by a TE₁₀ mode and the slot radiates externally. This slot/tilted-strips element behaves like a shunt admittance on an equivalent transmission line. This feature can be utilized to design arrays of such slots. Coupled integral equations are derived and solved, using the method of moments, to obtain the slot aperture E-field and the internal forward and backward scattering. Numerical and experimental results are presented to validate the method and to discover the range of useful dimensions for this composite element     

Phased array antenna analysis with the hybrid finite element method

A new analysis technique for infinite phased array antennas was developed and demonstrated. It consists of the finite element method (FEM) in combination with integral equation radiation conditions and a novel periodic boundary condition for 3-D FEM grids. Accurate modeling of rectangular, circular and circular-coaxial feeds is accomplished by enforcing continuity between the FEM solution and several waveguide modes across an aperture in the array's ground plane. The radiation condition above the array is enforced by a periodic integral equation in the form of a Floquet mode summation, thus reducing the solution to that of a single array unit cell. The periodic boundary condition at unit cell side walls is enforced through a matrix transformation. That mathematically “folds” opposing side walls onto each other with a phase shift appropriate to the array lattice and scan angle. The unit cell electric field is expanded in vector finite elements. Galerkin's method is used to cast the problem as a matrix equation, which is solved by the conjugate gradient method. A general-purpose computer code was developed and validated for cases of open-ended waveguides, microstrip patches, clad monopoles and printed flared notches, showing that the analysis method is accurate and versatile