Effects of Non-Gaussian Surface Roughness on Conductor Loss in High-Frequency Transmission Lines

A simulation method is proposed to study the impacts of surface roughness with additional features, skewness and kurtosis on the conductor loss in high-frequency transmission lines, in which the non-Gaussian surface is generated using digital filtering techniques and Johnson transformation system. The results indicate that the conductor loss increases with the frequency substantially and Sq predominantly affects the conductor loss of the stripline models 15.4 μm in thickness. Taking the signal frequency of 40 GHz as examples, the conductor loss is increased by 14.9%, as the Sq value is increased from 0.4 μm to 2.0 μm. The effects of skewness and peak-valley agglomeration are minor, with the conductor loss increasing only by 4.46% as the surface skewness is changed from -1.5 to 1.5, and by 3.89 % when peak-valley clustering occurs. The impact of kurtosis is slight, with the conductor loss increasing only by 2.06 % as the surface kurtosis is increased from 1.04 to 5. However, if the thickness of copper foils is considerably reduced down to several microns, the variation range and impact of Sq will become limited, and the influences of skewness and kurtosis will be strengthened remarkably. As examples, for a set of stripline models 3 μm in thickness at a frequency of 40 GHz, the insertion loss is increased by 5.10%, as Sq is increased from 0.10 μm to 0.40 μm, while it is increased prominently by 7.70%, as the skewness varies from -1.5 to 1.5, and by 3.13%, as the kurtosis is increased from 1.04 to 5. The results highlight that the influences of other surface features, skewness and kurtosis, on the conductor loss should be considered for the design of high-frequency, high-speed transmission ultra-thin copper foils.