A new aperture admittance model for open-ended waveguides

A new model for the aperture admittance of open-ended waveguide structures radiating into a homogeneous, lossy dielectric is presented. The model is based on the physical and mathematical properties of the driving point admittance of passive, stable one-port networks. The model parameters, which depend upon the geometry of the waveguide and aperture, are determined from a relatively small number of computed admittances. This computed data is obtained by a full-wave moment method solution and, hence, includes the effects of radiation and energy storage in the near field and the evanescent waveguide modes. The accuracy of the numerical method is demonstrated by comparison with measured values. As an example, the model parameters are determined for the coaxial-line geometry. The accuracy of the model, for both the direct and inverse problem, is verified and a rigorous sensitivity and uncertainty analysis is performed. The new model has important applications in the field of dielectric spectroscopy     

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.     

Radiation from a flanged rectangular waveguide

The radiation from a rectangular waveguide with a perfectly conducting infinite flange is rigorously studied by using the method of the Kobayashi potential (KP). The fields in the waveguide and half-space are expanded in terms of the waveguide modes and the Weber-Schafheitlin discontinuous integrals, respectively. Continuity of the tangential aperture fields yields matrix equations for the expansion coefficients and the matrix elements consist of double infinite integrals and double infinite series of Bessel functions, which are calculated efficiently by applying the asymptotic approximation of the Bessel function. Numerical results are presented for various physical quantities, such as the aperture admittance, reflection coefficient of the incident wave, and magnitudes of higher-order mode waves, as well as the far-radiation pattern and aperture fields. To verify the validity of our method, the results are compared with other methods and excellent agreement is obtained.     

An integral equation analysis of an infinite array of rectangulardielectric waveguides

An integral equation analysis is applied to the study of the propagation characteristics of an infinite array of dielectric waveguides. The geometry under study is assumed to be rectangular. To find the Green's function of the structure, the Floquet theorem is applied such that the mutual coupling between dielectric waveguide elements is effectively included in the analysis. The effect of the coupling on the propagation characteristics of a dielectric waveguide is studied by varying the size of the Floquet cell. The validity of this analysis to simulate the case of an open dielectric waveguide is confirmed by a comparison with previous results, this in spite of the fact that radiation and leaky wave modes are not accounted for. The complex modes due to the periodicity of the structure are found and their properties are described. The analysis presented, with minor modification, can deal with the problems of dielectric image lines, or dielectric-loaded metallic waveguides     

Surface-wave behavior of a phased array analyzed by the grating-lobe series

A pictorial representation of the behavior of a phased array which supports a surface wave is obtained by using the grating-lobe series. The admittance crater for a slotted array, covered by a dielectric sheet, is derived and plotted showing several unusual properties. From the crater, the variation of array admittance with scan is also computed and a contour plot of reflection coefficient magnitude is presented on thesin thetaplane.     

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.     

多端口耦合问题的等效导纳矩阵

本文提出了一种处理多端口耦合问题的有效方法。在该问题中,各端口波导分别通过一耦合孔与耦合区进行耦合。利用矩量法,首先导出了多端口耦合问题的关于传输模和截止模的等效导纳矩阵的计算公式。在此基础上,考虑到截止模加载于端口波导的特性阻抗,经过适当的矩阵运算,得到仅仅关于传输模的等效导纳矩阵。用此方法计算了一个 H 面 T 形接头的等效导纳矩阵和等效电路参数,所得结果与文献[1]们的结果非要吻合。     

Numerico–Analytical Model of a Non-Planar Array of Horns

A non-planar array of strip horns is considered. A model of this structure is constructed in the form of a Floquet channel with smoothly varying parameters. The Floquet channel of an infinite array of coupled striplines is chosen as a reference waveguide. The scattering matrix of the Floquet channel in the quasi-periodic mode is found in the approximation of the theory of microwave transmission lines. Expressions are obtained for the elements of the scattering matrix in the mode of excitation of a single channel of a non-planar array. In this mode, the directional pattern of the radiation of the array into a planar waveguide is studied.     

Admittance calculation of a slot in the shield of a multiconductortransmission line

The admittance calculation for a narrow slot in the conducting shield of a multiconductor transmission line (MTL) is presented. An approximate calculation is given for the admittance seen looking into a slot in the shield of a multiconductor transmission line when a uniform magnetic current is placed over the slot. The calculation presented is approximate in that only the transmission line mode is used in the calculation. All higher-order waveguide modes are neglected. This allows the magnetic current to be replaced by a point voltage source at the slot location. The admittance calculation then corresponds to calculating the driving point admittance of a point voltage source located in the shield of an MTL     

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     

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.     

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.     

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     

Waveguide excited microstrip patch antenna-theory and experiment

An arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally. The metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate. The substrate (and superstrate, if present) consists of one or more planar, homogeneous layers, which may exhibit uniaxial anisotropy. The analysis is based on the space domain integral equation approach. More specifically, the Green's functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field. The layered medium Green's function is expressed in terms of Sommerfeld-type integrals and the waveguide Green's function in terms of Floquet series, which are both accelerated to reduce the computational effort. The coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains. The dominant mode reflection coefficient in the waveguide and the far-field radiation patterns are then found from the computed aperture field and patch current distributions. The radar cross section (RCS) of a plane-wave excited structure is obtained in a like manner. Sample numerical results are presented and are found to be in good agreement with measurements and with published data     

Mutual coupling in a slotted phased array, infinite inE-plane and finite in H-plane

The mutual admittance matrix is computed for a planar phased array of thin slots with assumed single-mode cosinusoidal aperture electric field. The array is of infinite extent in the E-plane and of finite extent in the H-plane. The H-plane excitation is arbitrary and the array is phase scanned in the E-plane. Resultant active row-port admittances and H-plane aperture distribution are in agreement with large strictly finite array calculations and with a Floquet mode infinite array model, for the example case of uniform H-plane excitation     

Design criteria for linearly polarized waveguide arrays

The influence of the waveguide aperture size on the admittance variation with scan angle of a waveguide phased array is presented. It is shown that certain size waveguide apertures can cause zero radiation directions. Design criteria which yield the maximum waveguide size to minimize or eliminate this condition are derived.     

The grating-lobe series for the impedance variation in a planar phased-array antenna

In an infinite planar array of elements with periodic spacing, the element active impedance varies with phasing for beam steering. This impedance variation may be expressed as the sum of a double Fourier series. This series is identified with the periodic grating-lobe pattern on the "sin thetaplane" which is also the plane of two-dimensional phasing coordinates. An "impedance crater," with contours peculiar to the kind of element, is placed on every grating-lobe center. The inside of the central crater, which coincides with the unit circle of real space on this plane, determines the resistance variation with scan angle of the main lobe. The central crater and the skirts of the surrounding craters overlap in this circle; their sum determines the accompanying reactance variation. All craters together form the "grating-lobe series," which gives a picture of the entire impedance variation with scan angle. In a simple example, the reactance variation associated with half-wave spacing of the elements is found to be nearly equal to the resistance variation associated with the kind of element.     

X 波段加膜片式单脊波导裂缝天线的研究

等效导纳值是波导宽边纵缝天线的关键设计参数。为克服传统波导裂缝天线副瓣偏高、设计效率低下等问题,本文提出了一种单脊波导裂缝天线的改进设计方法,在传统波导裂缝阵列天线设计的基础上,利用等效导纳值对天线等效电路的影响,在裂缝单元下增加金属膜片,通过改变金属膜片的高度,优化裂缝等效导纳值,使得每个裂缝口径场分布更加接近于理论设计值,并在设计过程中使用牛顿迭代法提取导纳进一步缩短设计时间。通过设计实例表明:应用此方法设计单脊波导裂缝天线能够有效抑制副瓣电平,天线方位面副瓣电平可达到-30 dB 以下;在满足主要指标要求的前提下,设计效率显著提升。     

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