E‐plane radiation pattern analysis of rectangular horn antennas with V‐shaped corrugations by UTD‐PO formulation

Abstract

[1] A new method for the calculation of the radiation pattern of corrugated E-plane rectangular horn antennas based on a hybrid uniform theory of diffraction-physical optics (UTD-PO) formulation is presented. The method, which allows for the analysis of horns in which V-shaped corrugations have been considered, has been validated with numerical data obtained through the application of both an electric field integral equation (EFIE) solved by the method of moments (MoM) and the finite element method (FEM)-based full-wave electromagnetic analysis software, HFSS. In this sense, the proposed solution is mathematically less complex and computationally more efficient than existing techniques.Citation: Rodríguez, J.-V., F. Quesada-Pereira, L. Juan-Llácer, E. Verdú-Rodríguez, J.-M. Molina-García-Pardo, and A. Álvarez-Melcón (2012), E-plane radiation pattern analysis of rectangular horn antennas with V-shaped corrugations by UTD-PO formulation, Radio Sci., 47, RS3011,

UTD-PO Radiation Pattern Analysis of Rectangular Horn Antennas With Cylindrical Corrugations

“…2, a total of 1044 basis functions have been used (which ensures, at least, one basis function every or more), and the reaction integrals have been evaluated by the application of a maximum fifth order Gauss-Legendre quadrature rule. For the sake of comparison, the radiation pattern of the equivalent non-corrugated horn is also shown in the plot, calculated with both the above-mentioned EFIE technique (with 479 basis functions in this case) and the UTD method presented in [12]. Moreover, the pattern of a horn with the same structure parameters as that under study in which the cylindrical corrugations have been replaced by analogous rectangular corrugations of width and the same has also been calculated with the EFIE technique (with 1531 basis functions in this case) and is also included in Fig.…”

“…As was demonstrated in [16], [12], the analysis of the E-plane radiation pattern of a non-corrugated E-plane rectangular horn can be obtained by a ray-based UTD approach. The technique is based on the evaluation of the total field existing at the point where the emitting source (a magnetic current line) is located, with the assumption that a plane wave is impinging over the horn (applying reciprocity).…”

“…which is the term that represents the field of both the contributions and , and is a reflection coefficient for hard/vertical polarization for positive incidence over the cylinders: (4) where is the so-called transition function, which is defined in terms of a Fresnel integral, is the Fock scattering function for hard polarization [18], and (5) where (6) and (7) Moreover, , which is the relative amplitude of the incident plane wave, is the wave number, and and form the first cylinder over which the formulation presented in [17] for the evaluation of the multiple diffraction of a plane wave by a series of cylinders is applied-assuming a positive incidence angle (lit region), which implies the calculation of both and .-Furthermore, the second term of (2) can be calculated as (8) where , is the above-mentioned reflection coefficient for hard/vertical polarization given by (4), where in this case (9) and (10) and and are assumed to be the same point, with (11) where is the diffraction coefficient for an edge given in [19], is the length of the faces of the horn, is the half-angle of the aperture of the horn, and (12) In this case, in order to evaluate , one first diffraction at the edge of the end of the lower arm of the horn is considered, ( and are approximated by the same point, as occurs in the case of a non-corrugated horn), therefore obtaining the field existing over the subsequent cylinder . Then, the remaining multiple-cylinder diffraction is calculated by considering a grazing incidence over the cylinders, since the direct ray was already considered in (3), where the smaller angle of incidence makes the effect of the multiple diffraction much more relevant than that arising at the array of corrugations of the lower arm of the horn, where the angle of incidence is greater (13) with (14) where is the diffraction coefficient for hard/vertical polarization for negative incidence over the cylinders (shadow region): (15) with (16) where (17) and…”

“…Certainly, in such cases, rectangles are not easily machined due to the fact that the manufacturing processes can destroy the previous tooth as the next gap is being cut. In this sense, the employment of triangular (V-shaped) corrugations has been considered in some works [11], [12], but the presence of wedges could still lead to fabrication problems. Therefore, the utilization of alternative shapes such as cylindrical corrugations not only could solve the above-mentioned issues but, besides, improve the performance of the horn antenna as compared to the case where wedge-shaped corrugations are employed, due to the greater losses existing in the rays which are multiply diffracted along the arms of the corrugated horn in the former in comparison to the latter.…”