__Keywords:__linear antenna array of slot elements integral equation field diffraction on antenna case surface and dielectric radom phase synthesis cosecant radiation pattern

M. W. Indenbom

This article covers methods for computation of the transmitting MMDS antennas with horizontal polarization presented in the first part of paper. Each of the antenna types is a printed stripline linear array of slot radiators located inside the cylindrical dielectric radom.
For phase synthesis cosecant shape of radiation pattern in the vertical plane, the method of geometrical optics was applied. It is shown how controlling the parameters of amplitude distribution and synthesizing phase distribution, one can effectively control a pattern shape. The required pattern shape is obtained with asymmetric amplitude taper with a moderate amplitude level on the edge of antenna.
To calculate the radiation pattern in the azimuth plane, an integral equation of the second kind is obtained for the surface density of the induced electric current in a conducting or impedance case antenna surface. The task is reduced to two-dimensions by replacing the linear array slot elements with infinite length slot. The distribution of the electric field in slot was taken to be uniform. To account for the influence of a thin dielectric substrate, on the inner side of which the foil layer with slot elements is located, a concept of surface impedance, corresponding to the surface TH-wave with a large value of permittivity substrate, was employed. The influence of cylindrical dielectric radom was described by the representation of electromagnetic waves as a series of cylindrical (Bessel) functions.
Integral equation was solved numerically with the method of moments with basis functions in the form of δ-functions and weight functions in the form of rectangular finite elements. The computation program was realized in Mathematical interpretative editor MathCAD.
The results of the calculation of the azimuth pattern of the three types of radiators forming a circular (omni), cardioid and directional azimuth pattern, are compared with measurement results. It is shown for which types of radiators the calculation results obtained with impedance boundary conditions are in the better agreement with an experiment than the calculation results obtained with boundary conditions for perfectly conducting surfaces. Using the developed mathematical model, a constructive synthesis of screens is carried out to obtain the desired shape and width of the antennas pattern

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