Real axis integration of Sommerfeld integrals: Source and observation points in air

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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, thin‐wire antenna in the presence of a lossy earth.