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38 DESIGN007 MAGAZINE I JULY 2023 Huray modelling describes the dendritic surface of the copper as small pyramids of copper balls. Using a scanning electron micro- scope (SEM), the SI engineer can enter the ball count, area, and number of balls in area to prime the Huray model. If this seems a little tedious and only for academics with time on their hands, there is a welcome answer. Bert Simonovich of Lamsim Enterprises has a paper which describes a preprocessor which takes the matte and drum side's Rz roughness mea- surement and, as if by magic, generates a set of Huray parameters. is saves us a lot of time and effort with analysing SEM images. e second relatively recent method for modelling is the gradient method. Its authors propose that rather than model the detail of the surface, that the interface between the copper and the dielectric be treated as a gradi- ent where the characteristics blend from pure conductor to pure dielectric over the RMS (Rq) roughness of the surface. Papers on the gradient method propose that not only does this model help the effects of roughness on loss but also takes quite good care of the effects of roughness on phase. Are You a Snowball or a Ski Slope? e two modern methods take a different approach to roughness modelling with Huray comparing and modelling the surface topology as small stacks of snowballs (further simpli- fied by Bert Simonovich with his Cannonball Huray method). e gradient method offers a "ski slope" down from the pure conductivity of copper, through a blended zone of decreas- ing conductivity, until the rough surface ends in pure dielectric material. Huray takes data analysed from an SEM to model the rough- ness. e Cannonball method uses commonly available Rz roughness data, and the gradient method uses RMS (Rq) roughness data. Figure 1: Smooth and rough copper. (Source: Circuit Foil)