Abstract
The time-domain step response of a transmission line (TL) with a dielectric insulator having a frequency-dependent conductance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G(\omega)</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\propto \omega^{m} (m < 1)</tex> is analyzed. It is shown that for the case <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m \simeq 0.8</tex> , which describes many kinds of dielectric materials, the arctan-function represents an excellent approximation to the exact step-response function as given by Nahman [5] in the form of an integral. Based on the arctan approximation, a simple method for correlating the frequency-domain attenuation with the step-response rise time is presented. Experimental data on attenuation versus frequency and on corresponding step-response curves illustrate the application of the theoretical results.
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