Simple procedure to evaluate singularity free expressions for radiation patterns of an antenna with rectilinear symmetry

Abstract

An efficient, simple technique is demonstrated here to find a singularity free analytic solution for the far-field radiation patterns of an antenna with rectilinear symmetry. Closed form singularity free expressions are given for the rectangular slot antenna, rectangular microstrip antenna, rectangular dielectric resonator antenna, equilateral triangular microstrip antenna (ETMA) and TMAs. Theoretical results are verified with measured data as found in the published literature. It is found that one can easily avoid singularities and complex mathematical calculations for the far-field radiation patterns by applying this novel technique. This procedure is also applied here to evaluate certain types of complex integrals which are essential to evaluate conductor loss and stored energy within a cavity, waveguide and antenna. Typical results are shown for ETMA where 18 numbers of integrals are replaced by a single integration. Theoretical results are verified by numerical integration using the inbuilt function of MATLAB^®. Therefore, it is concluded that this novel technique can efficiently be utilized (i) to give singularity free expressions for the far-field radiation patterns (ii) to reduce unnecessary, time consuming mathematical processing (iii) to provide a much more efficient analysis than these offered by the commercial numerical simulator.

Acknowledgments

Authors wish to thank Indo-Tunisian Programme of Co-operation in Science and Technology sanctioned by DST (India) and MHESR (Tunisia) for helpful discussion during this work.