Analysis and element pattern design of periodic arrays of circular apertures on conducting cylinders

The analysis and the design of elements for a large array of circular apertures on a triangular grid is approached by modeling the antenna as an infinite structure rotationally symmetric and periodic along the cylinder axis. Because of this particular symmetry, every possible excitation is the superposition, with suitable weights, of a set of fundamental excitations having uniform magnitude and linear phase progression in the azimuthal direction and in the direction of the cylinder axis ("eigenexcitations"). Thus by invoking superposition, the electromagnetic analysis of the array is reduced to the solutions of the simpler boundary value problems pertinent to the set of eigenexcitations. This is done by expanding the field in normal modes in the region exterior to the cylinder and in the waveguides feeding the apertures, followed by a field matching at the cylinder surface (obtained approximately through Galerkin's method). The realized gain pattern of the radiators can be modified to a considerable extent by using an "element pattern shaping network" (in the radiator waveguides), serving the purpose of matching the array for a selected eigenexcitation. Criteria for the network design are given. A series of numerical examples illustrate the technique and shows that a "flat" element pattern can be thus obtained with a gain falloff with respect to the peak of less than 6 dB at 80 degrees, and an increase of 2 to 3 dB in the gain at 80 degrees with respect to that obtained for the same elements matched at broadside.     

Analysis of periodic arrays of waveguide apertures on conducting cylinders covered by dielectric

The analysis of infinite arrays of waveguide apertures on cylinders covered by a dielectric is approached by enforcing the continuity of the EM fields at the air-dielectric and at the dielectric-cylinder interfaces. The continuity of the EM fields at the first interface is enforced by representing the fields in the air and in the dielectric by an orthonormal set of modes LSE and LSM with respect to the radial direction. The matching of the fields at the second interface is performed by resorting to the "eigenexcitation" method [1]. The fields external to the cylinder are represented by a set of space harmonics matching the symmetry of the excitation of the array and the fields in the waveguides by a superposition of normal waveguide modes. The continuity of the fields is approximately enforced by using Galerkin's method. The rigorous analysis of these structures leads to rather involved expressions for the element driving point admittance and for the far fields. An approximate analysis is introduced to simplify the design of these structures for cylinders of large radius. Numerical examples illustrate the good approximation given by the simplified analysis. Numerical results are presented for the case of an array on a cylinder with radius approximately100lambda. The array element pattern shows the presence of resonance dips much more pronounced than the notches due to grating lobe phenomena.     

Mutual coupling analysis of a conformal array of elements on a cylindrical surface

The analysis of multiport antennas may be approached by resorting to the powerful concept of eigenexcitations of the structure. They may be defined as the eigenvectors of the admittance matrix, i.e., those sets of voltages and currents at the antenna terminals which are related simply by a proportionality factor (eigenvalue of the admittance matrix). Similarly, the eigenexcitations may be alternatively defined as the eigenvectors of the scattering matrix. The analysis for this special kind of excitation is sometimes relatively easy. The general case may then be treated by utilizing superposition principle. An array of infinitely long longitudinal slots equispaced on a conducting cylinder is analyzed in detail. The eigenvectors of the admittance and scattering matrices are easily found because of the symmetry of the structure. Expressions for the eigenvalues of these matrices, and for the radiation patterns due to the array eigenexcitations, are found in the form of infinite series rapidly convergent (even for cylinders of large radius). By using linearity an expression for the radiation pattern of the single excited element in the array environment (the main result of this paper) is then established. Expressions are also given for the coupling (or scattering) coefficients. A number of numerical examples with different cylinder radii are discussed in detail.     

Analysis of waveguide antenna arrays with protruding dielectricelements

The two-dimensional problem of radiation of TE and TM waves from a waveguide array with protruding smooth dielectric elements of arbitrary shape is considered, and solution algorithms are suggested. The algorithms are based on applying the method of auxiliary sources for the representation of electromagnetic fields outside and inside the protrusions in combination with the method of integral equations for the electric field at the waveguide aperture. The point matching of the field tangential components on the protrusion-to-free-space boundary and at the waveguide aperture is used to reduce the problem to a system of linear algebraic equations for the amplitudes of the auxiliary filamentary currents and of the waveguide aperture electric field, which is assumed to be piecewise constant. The amplitudes obtained from the solution of the system are used for computing the array reflection coefficient and element pattern, which are shown in some cases to be significantly dependent on the protrusion shape. Examples of arrays with flat-topped element patterns resulting from array geometry numerical optimization are also presented     

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.     

一种双极化液晶阵列天线设计与方向图综合方法

针对极化相控阵雷达应用背景,提出了一种基于电磁调控液晶的二维方向图可重构双正交极化阵列天线设计方法.该阵列天线设计由两种极化方式的亚波长超表面天线线阵交替排列构成,线阵上的单元均有两种工作状态,且每个单元都可以独立控制.该天线在一个方向维度上利用液晶超材料结构的电磁调控能力采用全息方向图综合方法实现了两个极化方式的独立调控,另一个方向维度上采用外部移相器对两个极化方式进行分别调控,创新地在两个方向维度上分别实现了正交极化信号的同时方向图重构,并确保了正交极化在二维方向图重构的一致性和良好的隔离度.仿真结果表明在法线两个正交极化的主瓣电平差小于0.01 dB,波束指向角为-40°时两个正交极化的的主瓣电平差小于0.02 dB.文章提出的双极化液晶阵列天线设计和方向图综合方法具有正交极化一致性好、结构简单等特点,并具有低功耗、低损耗、低成本制造、轻薄等优点,为小型全极化相控阵雷达精确信号制导应用提供了一个新颖的设计方案.     

An approach to analysis of waveguide arrays with shaped dielectricinserts and protrusions

The classical moment method solution of the waveguide-array problem is extended to allow for generally shaped dielectric matching inserts in the waveguide-to-free-space transition region. The aperture electric field is represented in terms of waveguide modes. To account for the presence of the matching inserts, the aperture fields are numerically propagated through the dielectric regions. Novel matching configurations, which extend the scanning range of waveguide elements or can be used to shape the element pattern in limited-scan applications, are proposed and analyzed     

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.     

Pattern Synthesis and Polarization Optimization of a Conical Array

A feasible method for synthesizing millimeter-wave conical array and optimizing low cross-polarization is proposed.Starting from the far-field superposition principle,an efficient approach including element mutual coupling and mounted platform effects is used to calculate the far-field patterns.A coordinate transform is applied to create polarization quantities,and a general process for the element polarized pattern transformation is performed.Corresponding numerical example is given and the desired sidelobe level and low cross-polarization are optimized.The numerical results indicate the proposed method is valid.     

New Results in Dielectric-Loaded Resonators

Analysis of cylindrical dielectric-loaded resonators is reviewed. The fields within the dielectric-loaded region are postulated as the superposition of hybrid, TE, or TM modes of the infinite dielectric-loaded waveguide, while the fields in the end regions of the resonators are described by the superposition of the normal modes of a homogeneously filled waveguide. Numerical results are presented which reveal that accurate representation of the fields in the resonant structure generally require several modes. Hence, the resonant modes cannot be correlated directly with single waveguide modes. A new method for mode identification is proposed. For a wide range of parameters, the resonant frequencies, mode charts, field expansion coefficients, field intensity, and distributions are presented. Excellent agreement of the mode charts with resonant frequency measurement results are obtained.     

Arrays of horizontally polarized loop-fed slotted cylinder antennas

Measured center element gain patterns, voltage standing-wave ratio (VSWR), and mutual coupling for passively terminated arrays of horizontally polarized loop-fed slotted cylinder antennas over a ground plane are given. A seven-element hexagonal array is investigated in detail. The element gain pattern is shown to have a null at broadside with omnidirectional coverage along a constant cone angle from broadside. Maximum gain occurs close to50degfrom broadside which provides for wide-angle phased array scanning capability. The antennas are also configured in a linear array geometry, to investigate mutual coupling effects on the element gain pattern as the number of elements is varied. The element gain pattern is shown to converge for a relatively few number of elements and there is no indication of undesired blind spots.     

Linear array of woodpile EBG sectoral horn antennas

A technique is described for creating linear array antennas that conform to the natural stacking sequence of the woodpile electromagnetic bandgap (EBG) material. Each element in the linear array consists of a woodpile EBG sectoral horn antenna. The electromagnetic confinement mechanism within each horn antenna relies wholly on the 3-D EBG of the woodpile material. The array element has a typical sectoral horn pattern with a directional beam in one principal plane and a broader beam in the other. The bandwidth of the sectoral horn is almost equal to that of the defect EBG waveguide. Measured and theoretical results for radiation patterns, impedance bandwidth and gain of a sectoral horn antenna made from alumina are described, and theoretical results for a design made from silicon are presented. It is shown that the layer-by-layer nature of the woodpile EBG material enables sectoral horn antennas to be easily stacked together in the E-plane to create linear arrays. Analysis of the mutual coupling as a function of element separation and its effect on reflection coefficient are presented for a two-element linear array in silicon. Theoretical analyses for fixed and scanned beam linear arrays of silicon woodpile EBG sectoral horns are described and finite-difference time-domain results are compared with array theory. The fixed beam arrays are designed for high directivity while the scanned beam array enables wide angle beam steering through the use of parasitic array elements.     

Performance of an array of circular waveguides with strip-loadeddielectric hard walls

An infinite planar periodic antenna array of radiating open-ended circular waveguides is considered. The conducting waveguide walls are covered with dielectric layers loaded with longitudinal conducting strips for providing the hard wall boundary condition. Analysis of the array is carried out by the mode-matching method. The waveguide modes involved in the method are calculated by using the asymptotic strip boundary condition. It is shown that they are split into an independent subsystem of TE modes for the whole cross section and two independent subsystems of TM modes: one is for the central region and another is for the layer region. The calculations show that the operation of the hard waveguides in an array with small element spacing is similar to that of the multimode smooth wall waveguides completely filled with dielectric. For large diameters and element spacing, the hard waveguides have significant advantages over the smooth ones. It is shown that unlike an individual hard waveguide, the aperture efficiency of such a waveguide in the array has a nonmonotonic dependence on the waveguide radius. The results characterizing the behavior of the aperture efficiency and cross-polarization level in a frequency band as well as the contribution of certain waveguide modes in the reflected power are presented and discussed. The examples of the element patterns corresponding to minimal cross polarization are also given     

Shaping of flat-topped element patterns in an array of slow-wavestrip structures excited by parallel-plate waveguides

A two-dimensional (2-D) model of a corrugated-rod antenna array in the form of an infinite periodic array of finite slow-wave strip structures arranged above the apertures of two-or three-mode parallel-plate waveguides excited by TEM modes is analyzed. The formulated problem is solved by the method of matching the waveguide and Floquet modes on the waveguide apertures in combination with the Galerkin method for calculation of the currents on the strips. The geometrical parameters of the strip structures are optimized for shaping the flat-topped element patterns. It is shown that high quality of the flat-topped patterns in the element spacing range from 0.65 to 1.3 of wavelength is achieved if the excitation of the optimized structures is performed using the second and third reflected waveguide modes returned back to the apertures with the corresponding optimum phases. The presented examples also show that the shape of the obtained patterns keeps well at least in a 10% frequency band     

A hybrid projection method for analysis of waveguide arrays with protruding dielectric elements: 2D problems

A method is proposed for the analysis of an array of parallel-plate waveguides with protruding longitudinally inhomogeneous dielectric elements. The method consists in expansion of the transverse electric (for the case of E polarization) or magnetic (for the case of H polarization) field in the domain containing the dielectric elements in terms of transverse functions of the Floquet channel. This expansion contains unknown variable coefficients. Projection of the Helmholtz equation for the aforementioned fields onto the transverse functions and application of a 1D finite-element method along the longitudinal coordinate in combination with projective matching of the fields in the waveguide apertures and at the boundary with free space reduces the problem to solution of a system of linear algebraic equations. The results of calculation of the reflection coefficient and the radiation pattern of an array element are presented. These results characterize both the efficiency of the proposed method and the possibility of formation of sector element patterns in the studied arrays.     

Approximate 3D model of electromagnetic modes in waveguide cross-shaped junctions with dielectric filling

Athree-dimensional electrodynamic model of hybrid electromagnetic modes in a waveguide junction of cylindrical and rectangular waveguides with dielectric filling of a cylindrical waveguide is proposed in this study. To solve the vector problem, the mode matching technique (MMT) is applied with the separation of the common waveguide junction region and the representation of the field in this region in the form of superposition of the fields of the partial eigenwaves of waveguides. Classification of eigenmodes is carried out: intrinsic resonances of junction based on transcendental modes and resonances of a waveguide-dielectric type. The investigated structure can be used for measuring the electrical parameters of dielectric samples of both cylindrical and rectangular cross-section shape. Since the spectral characteristics of the junction are determined mainly by the size of the central coupling region of the waveguides and the electrical parameters of the dielectric in the junction, the measurements are of a local nature.     

表面波放电狭缝天线辐射电磁场的三维数值分析

针对平板型表面波放电等离子体源,建立了表面波放电狭缝天线辐射电磁波模型,对狭缝天线辐射电磁场分布进行了三维数值计算,并与表面波电磁场进行对比分析,讨论了平板型表面波放电机理。结果表明:整个狭缝天线阵激发的电磁场是每个狭缝天线激发电磁场的线性叠加;狭缝天线阵直接激发的电磁场强度在临近波导壁面处很大,并且随着空间距离的增大迅速衰减;狭缝天线阵直接激发和表面波的电场均远大于各自的磁场,分析电、磁场对带电粒子的力作用时可以忽略磁场力的作用;表面波电磁场远大于狭缝天线阵直接辐射的电磁场,强电磁场范围也远大于狭缝天线阵直接激发的强电磁场范围,等离子体有增强电磁场强度、扩大强电磁场范围的作用。     

A finite element analysis on electromagnetic waves in rectangular dielectric chirowaveguide

A finite element algorithm on eigenvalue problem of the dielectric waveguide with chiral material is presented. The chiral material is defined by the constitution relations which make the electromagnetic coupling between the electric and magnetic fields by means of the chirality admittance. The chiral material has potential applications in the areas of infrared and mm-wave band. For different chirality admittance, the computation is developed for different structure of waveguides which are difficult for analytical calculation. From the eigenvalues and the eigenvectors, the dispersion curves, the modes and the field patterns are obtained. The maximum value of dispersion curves is obvious greater than that without chiral material. The main points of the results of finite element calculation are consistent with those of analytical approach.     

Circular cylindrical waveguide filled with uniaxial anisotropicmedia electromagnetic fields and dyadic Green's functions

Electromagnetic fields in a circular cylindrical conducting waveguide filled with uniaxial anisotropic media are formulated in this paper by using Fourier transformations. These fields are obtained as a superposition of the TE (or ordinary) and TM (or extraordinary) modes satisfying, respectively, different characteristic equations. Lastly, the dyadic Green's function is derived using the Ohm-Rayleigh method and represented by vector wave functions expansion     

Hybrid modes in a dielectric lined conical waveguide

The letter presents a new conical structure which can support the spherical hybrid modes associated with a corrugated conical waveguide. The analysis closely follows that of hybrid modes in a corrugated conical waveguide. It is found that, to obtain hybrid modes in a dielectric lined conical waveguide, it is necessary to taper the dielectric constant of the lining.