Optimal scale factors for Gaussian field expansions for a circular aperture

Gaussian field expansions for circular aperture antennas are reviewed, and a method for finding optimal scales in these expansions is given, paralleling the method for rectangular antennas presented in an earlier paper. This procedure is shown to lead to approximations structured in the sense that the number of lobes in the approximation corresponds to the number of terms retained in the expansion. An example is given of the development of a cosine distribution from the aperture, through the Fresnel region, to the far field.     

Calculation of the field radiated by horn-antennas using themode-matching method

Methods employed for evaluating fields radiated by horn antennas, like the aperture field method and the spherical wave expansion, have not taken into account the contribution by fields existing outside the horn aperture (e.g., along the outer walls of the horn). The use of the mode-matching technique for analyzing the transition from horn antenna to free space makes it possible to include in the analysis even those fields which exist outside (e.g., behind) the horn aperture when determining the far as well as the near field. Furthermore, the effects of the finite wall thickness and the discontinuity caused by the transition from waveguide to free space are also taken into account. A suitable development of the fields at the transition of the conical/corrugated horn to free space using the mode-matching technique is presented. Two different convergence diagrams, depending on the kind of modes excited in the horn antenna, are given. They show the results from extensive convergence investigations. With the help of these diagrams, a reliable evaluation of the fields radiated by horn antennas is guaranteed. Practical measurements of the fields radiated by horn antennas confirm the field distributions gained through analysis     

Equivalence of surface current and aperture field integrations for reflector antennas

The "extinction theorem" is used to prove that the fields of reflector antennas determined by integration of the current on the illuminated surface of the reflector are identical to the fields determined by aperture field integration with the Kottler-Franz formulas over any surfaceS_{a}that caps the reflector. As a corollary to this equivalence theorem, the fields predicted by integration of the physical optics (PO) surface currents and the Kottler-Franz integration of the geometrical optics (GO) aperture fields onS_{a}agree to within the locally plane-wave approximation inherent in PO and GO. Moreover, within the region of accuracy of the fields predicted by PO current or GO aperture field integration, the far fields predicted by the Kottler-Franz aperture integration are closely approximated by the far fields obtained from aperture integration of the tangential electric or magnetic field alone. In particular, discrepancies in symmetry between the far fields of offset reflector antennas obtained from PO current and GO aperture field integrations disappear when the aperture of integration is chosen to cap (or nearly cap) the reflector.     

Analytical form of EM fields radiated by circular aperture antennas of various current distributions

~~Analytical form of EM fields radiated by circular aperture antennas of various current distributions[1] Schelkunoff S. A., Advanced Antenna Theory, John Wiley &Sons, 1952. [2] E|liott R.S., Antenna Theory and Design, Prentice-Hall, Engie-wood Cliffs, N J, 1981. [3] R.W.P. King and G.S. Smith, Antennas in Matter: fundamen-tals, Theory and Applications, MIT Press, Cambirdge, MA,1981. [4] W.L. Stutzman and G.A. Thiele, Antenna Theory and Desigrn,John Wiley & S…     

口径天线在任意口径分布时的冲激响应

本文从夫累涅尔-基尔霍夫标量衍射场方程出发,证明了任意形状的并馈口径天线在任意口径幅度分布时的冲激响应和端馈矩形口径天线在任意口径幅度分布时的冲激响应都可以用口径幅度分布表达出来;而矩形口径天线在口径分布可分离时的冲激响应和圆形口径天线在口径分布圆对称时的冲激响应则为上述一般情况的特例。     

Complex rays for radiation from discretized aperture distributions

Many electromagnetic propagation problems require tracking of fields radiated by large actual or induced aperture distributions through complicated environments before reaching the observer. For a systematic approach to this problem area, it is desirable to represent the aperture field in terms of basis functions which are physically informative and well adapted to traversing the propagation path. At high frequencies, Ganssian beam-type basis functions meet these requirements. After referring to a rigorous aperture discretization scheme, various quasi-Gaussian basis field profiles are examined, with a special view toward expressing their radiation properties in terms of complex rays; complex ray tracing is promising for field tracking in complicated surroundings. By comparing reference solutions from numerical integration of radiation integrals with complex ray asymptotics, it is concluded that the true Gaussian has the most favorable attributes for matching aperture discretization, propagation requirements, and complex ray tracing. Thus, the analysis here may point the way toward systematic treatment of the above-noted class of propagation problems.     

Impulse responses of aperture antennas with arbitrary aperture distributions

On the basis of the equation of the Fresnel-Kirchhoff scalar diffraction field, it is shown that the impulse responses of parallel-fed aperture antennas of arbitrary configuration with arbitrary aperture amplitude distributions and those of end-fed rectangular aperture antennas with arbitrary aperture amplitude distributions can all be expressed by the aperture amplitude distributions, and that the impulse responses of rectangular aperture antennas with separable aperture distributions and those of circular aperture antennas with circularly symmetric distributions are special cases of the above general ones.     

Measurement Guideline of Fresnel‐Field Antenna Measurement Method

In this letter, a parametric analysis of the Fresnel‐field antenna measurement method is performed for a square aperture. As a result, the optimum number of Fresnel fields for one far‐field point is guided as M_opt=N_opt=D²/λR+5, where D is the antenna diameter, λ is the wavelength, and R is the distance between the source antenna and the antenna under test. For the aperture size 5 ≤ L_x/λ ≤ 20, the tolerable distances for gain errors of 0.5 dB and 0.2 dB can be guided as R_{0.5 dB} ≈ 1.2L_x/λ and R_{0.2 dB} ≈ 2.0L_x/λ, where L_x is the lateral length of the square aperture. The tolerable distances for 20 ≤ L_x/λ ≤ 200 are also proposed. This measurement guideline can be fully utilized when performing the Fresnel‐field antenna measurement method.     

面向远场计算的波谱射线方法

根据天线远区场对口径波谱的局部依赖特性,引入有效近场的概念,提出一种面向远场计算的波谱射线方法,该法采用波谱射线抽取的方法计算有效近场,通过近场空域积分计算远场,适合于具有雷达罩,透镜等近区散射体的天线远场计算。文中以带罩连续口径及阵列天线的远场方向计算为例,验证了方法的正确性和有效性。     

Effects of a dielectric coating on leaky-wave long-slot waveguideantennas

A theoretical and experimental study is made of the effects of a dielectric of arbitrary thickness, permittivity, and loss tangent upon the aperture field distributions and the far-field radiation pattern characteristics of long-slot leaky-wave antennas cut on the broadwall of a rectangular waveguide and mounted in an infinite ground plane. The relevant integral equations for determining the aperture fields are developed and then solved using the moment method. Expressions for the far-field radiation patterns and isolation responses are developed. Calculated and experimental results for several antennas are presented and discussed     

Reflector antenna fields--An exact aperture-like approach

A new computational approach is presented which allows fast analysis of radiation from large reflector antennas. For an aperture a Fourier transform (FT) relationship does exist between far-field and aperture distribution. Accordingly, the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe (Shannon-Whittaker theorem applied at Nyquist rate). The finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a FT. In order to overcome this difficulty a new pseudosampling expansion, which explicitly takes into account the extra factor, is developed. For parabolic reflector the sampling functions are related to the Fresnel integrals, and the far field can be exactly reconstructed in terms of aperture far-field samples, which can be computed using the fast Fourier transform (FFT). Numerical computations and error analysis show the excellent performance of the method, which can be generalized to deal with arbitrary reflector surfaces and near-field evaluation.     

Analysis of pyramidal horn antennas using moment methods

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The electric field integral equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the magnetic field integral equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large X-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distributions of two smaller X-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns     

二维天线的冲激响应

本文从夫累涅尔-基尔霍夫标量衍射场方程出发,导出了并馈和串馈矩形天线在口径分布可分离时的冲激响应,以及并馈和中心串馈圆形天线在口径分布圆对称时的冲激响应它们都可以用口径幅度分布表达出来。     

Analysis and synthesis of axial field patterns of focused apertures

It is shown that the axial field pattern of an aperture focused in the Fresnel region can be synthesized in the same manner as the angular pattern of an aperture in the Fraunhofer region. The aperture distribution which achieves a specified axial pattern is related to the aperture distribution of the specified pattern in the far field through a simple variable transformation. Therefore all analysis and synthesis techniques for far-field patterns can be applied to Fresnel region axial patterns of focused apertures.     

Focused Microstrip Array Antenna Using a Dolph-Chebyshev Near-Field Design

A new concept in designing large array antennas to focus the microwave power in the radiation near-field region is presented. A small focused array antenna using microstrip patch elements to achieve the desired sidelobes levels in the Fresnel region based on Dolph-Chebyshev design is implemented. This array is built to verify the concept, and then the measured and computed near fields are compared to verify the accuracy of the design. Larger arrays are designed by using the knowledge of the mutual admittances between the elements of smaller arrays. Several computed examples are presented in order to show some properties of focusing arrays. It is shown that the maximum intensity of the electric field along the axial direction is displaced from the focal point towards the antenna aperture. This displacement decreases as the aperture size increases.      

On an algorithm for analysis of the radiation patterns of dual reflector and segmented reflector antennas

Large reflector antennas, from cost and weight considerations, appear to be the best configurations for achieving the very large apertures needed for antennas mounted on orbiting spacecraft. Radiation pattern calculations for such antennas are, in general, quite costly both in terms of computer time and the considerable memory required to perform the large surface integrations. The method presented here treats the large aperture as a set of small subapertures for which the radiation fields are computed separately, stored and then added with due regard to phase to yield the radiation pattern of the large reflector. Numerical methods developed to provide the illumination of each subaperture to avoid overlap of the aperture fields of adjacent subapertures and to simplify the surface integrations are discussed. The algorithm is straightforward and has considerable intuitive appeal. The methods of geometrical optics (GO) are used to calculate the aperture plane tangential field components; and electric vector potential is then used to compute the antenna radiation fields. The algorithm includes a set of options for different reflector surfaces. If high accuracy of the far sidelobe levels is required, a subroutine accounting for edge diffraction should be added to the algorithm given here. Calculations made with this algorithm are compared with calculations made by other methods and with measured patterns.     

Impulse responses of two-dimensional antennas

On the basis of the equation of the Fresnel-Kirchhoff scalar diffraction field, the impulse responses of parallel-fed and series-fed rectangular antennas with separable aperture distributions and the impulse responses of parallel-fed and center-series-fed circular antennas with circularly symmetric distributions are derived—all of them can be expressed in the aperture amplitude distributions.     

A scattering matrix-based beamformer for wide-angle scanning in hybrid antennas

This paper presents a new approach to beamforming in hybrid antennas. Using a scattering matrix model for the hybrid antenna system, a bidirectional transformation is developed that relates the signals at the hybrid system feed to the signals that would be present in a planar array at the location of the reflector aperture. For example, the received fields at the feed of a hybrid antenna system may be transformed into the fields at the reflector aperture, and these reflector aperture fields may then be processed as if they were received by a planar or linear array. Similarly, the desired field or current distribution across the reflector aperture when transmitting may be transformed into the required field or current distribution at the hybrid system feed. This method allows standard linear or planar array analysis and synthesis techniques to be used with the hybrid system. Examples are provided for transmit and receive weight synthesis.     

Fresnel region power density levels from Earth station antennas

A method for predicting power density levels near transmitting parabolic Earth station antennas is described. The Fresnel region analysis applies to circular aperture antennas with an appropriate aperture amplitude distribution, and can be used to predict power densities along the antenna boresight or at off-boresight angles     

Equivalent current excitation for an aperture antenna embedded in an arbitrarily shaped impedance surface

It is demonstrated, via the equivalence principle, that if the aperture fields are known, one can explicitly obtain the equivalent current excitation required for modeling an aperture in an arbitrarily shaped impedance surface, when the aperture surface is closed, by replacing it with an impedance surface. It is also demonstrated that the impedance condition over the antenna body and the closed aperture can be nonuniform and anisotropic and that different choices are possible for the value of the surface impedance of the surface that closes the aperture. It is expected that the procedures described will be most useful in approximately modeling aperture antennas embedded in nonplanar impedance surfaces where the aperture electric field is known.