Real axis integration of Sommerfeld integrals: Source and observation points in air
Abstract
Change of variables and subtraction of asymptotic terms are used to aid in the integration of Sommerfeld integrands along the real axis. The change of variables smooths oscillations which would otherwise become densely packed at the associated branch point. Subtraction of asymptotic terms is used to speed up the truncation process of an otherwise infinite integration interval. Interest is restricted to practical earth parameters and frequencies above 2 MHz. Comparison with a complex contour technique shows the present method to be particularly well suited for the analysis of a vertical, thinwire antenna in the presence of a lossy earth.
 Publication:

Radio Science
 Pub Date:
 April 1983
 DOI:
 10.1029/RS018i002p00175
 Bibcode:
 1983RaSc...18..175J
 Keywords:

 Antenna Radiation Patterns;
 Atmospheric Scattering;
 Ground Effect (Communications);
 Numerical Integration;
 Sommerfeld Approximation;
 Asymptotic Methods;
 Bessel Functions;
 Computer Programs;
 Electric Dipoles;
 Integral Transformations;
 Points (Mathematics);
 Communications and Radar