Fundamental study of direct current resistance effect on transmission line characteristics

Abstract

High-speed transmission line characteristics have been analyzed from the point view of many parameter's effects in huge amount of papers. As far as maintaining geometric (dimensional) similarity of transmission line configurations, i.e., shrink or expansion of cross-sectional dimension, characteristics of transmission lines are not affected by their configurations based on electromagnetism from Maxwell's equations. However, direct current resistance (DCR) and skin depth surface/bulk ratio (SBR) of metal conductor in constant transmission length are changed even if geometric similarity is maintained. There have been seen no previous studies performed from this stand point. Therefore, as a fundamental study we examined on characteristics of transmission lines with geometric similarity by focusing on the effect of DCR and SBR. Time domain reflectometry (TDR) profiles, clock pulse rise/fall times (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> /t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> ), and eye-patterns were measured on the transmission line samples with different dimensions (line width and thickness) while maintaining geometric similarity. Experimental results suggest that the surface electron behavior would be related with DCR and SBR on the characteristics of transmission lines despite experimental accuracy is still not enough. These phenomena should more care for recent printed circuit boards over 10 Gbps/pin preferably toward 20 Gbps/pin.