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Real axis integration of Sommerfeld integrals: Source and observation points in air
Author(s) -
Johnson W. A.,
Dudley D. G.
Publication year - 1983
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs018i002p00175
Subject(s) - methods of contour integration , subtraction , mathematical analysis , point (geometry) , truncation (statistics) , lossy compression , interval (graph theory) , mathematics , antenna (radio) , numerical integration , geometry , computer science , telecommunications , combinatorics , statistics , arithmetic
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, thin‐wire antenna in the presence of a lossy earth.