Abstract
Transient pulses for electromagnetic compatibility problems, such as the high-altitude electromagnetic pulse and ultrawideband pulses, are often described by a double-exponential pulse. Such a pulse shape is specified physically by the three characteristic parameters rise time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</i> , pulsewidth <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fwhm</sub> (full-width at half-maximum), and maximum amplitude <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> . The mathematical description is a double-exponential function with the parameters α, β, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . In practice, it is often necessary to transform the two groups of parameters into each other. This paper shows a novel relationship between the physical parameters <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fwhm</sub> on the one hand and the mathematical parameters α and β on the other. It is shown that the least-squares method in combination with the Nelder-Mead simplex algorithm is appropriate to determine an approximate closed-form formula between these parameters. Therefore, the extensive analysis of double-exponential pulses is possible in a considerably shorter computation time. The overall approximation error is less than 3.8%.
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