Unified approach to interconnect conductor surface roughness modelling

Commonalities of five conductor roughness models are analysed and unified form of roughness correction coefficient (RCC) is suggested in the paper. It is shown that Hammerstad, Huray, Groiss, Hemispherical and Bushminskiy roughness correction coefficients can be written in the following unified form K=1+(RF-1)*F(SR), where RF is roughness factor that has meaning of maximal possible increase of losses with frequency due to the conductor roughness. F is a frequency-dependent function describing transition from zero at lower frequencies to one at higher frequencies (roughness transition function). It is shown that the unified RCC can be used in multi-level additive form for surfaces with two or more dominant discontinuity sizes or in multi-level multiplicative form for surfaces with fractal type discontinuities. Measurements on a test board are used to identify and compare all five RCCs.