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34 The PCB Design Magazine • May 2015 while the anode terminal is submerged in the solution. A DC voltage supplies the anode and cathode with the correct polarity. As the drum slowly rotates, copper is depos- ited onto it. A finished sheet of ED copper foil has two sides. The matte side faces the copper sulfate bath, while the drum side faces the ro- tating drum. Consequently, the drum side is al- ways smoother than the matte side. The matte side is usually attached to the prepreg sheets, prior to final pressing and cur- ing, to form the core laminate. Prepreg is the term commonly used for a weave of glass fi- ber yarns pre-impregnated with resin which is only partially cured. To enhance adhesion, the matte side has additional treatment applied to roughen the surface. For high frequency boards, sometimes the drum side of the foil is laminat- ed to the core. In this case it is referred to as reversed treated (RT) foil. Even after treatment, it is still smoother than standard treated foils. Various foil manufacturers offer ED copper foils with varying degrees of roughness. Each supplier tends to market their product with their own brand name. Presently, there seems to be three distinct classes of copper foil: • Standard • Very-low profile (VLP) • Ultra-low profile (ULP) or profile free (PF) Some other common names referring to ULP class are HVLP or eVLP. In lieu of scanning electron microscopy (SEM) analysis, profilometers are often used to quantify the roughness tooth profile of electro- deposited copper. Tooth profiles are typically reported in terms of 10-point mean roughness (R z ) for both sides, but sometimes the drum side reports average roughness (R a ) in manufactur- ers' data sheets. Some manufacturers also report RMS roughness (R q ). Modeling Roughness Several modeling methods were developed over the years to determine a roughness correc- tion factor (K sr ). When multiplicatively applied to the smooth conductor attenuation (α smooth ), the attenuation due to roughness (α rough ) can be determined by: equation 1 The most popular method, for years, has been the Hammerstad and Jensen (H&J) model, based on work done in 1949 by S. P. Morgan. The H&J model assumes a triangular corru- gated surface, representing the tooth structure of rough copper. It was thought that when the skin depth is small, compared to the tooth height, current begins to flow along the cor- rugated surface; thereby increasing its loss due to the longer path length. However, the theory breaks down from a physics perspective because there is no evidence of additional time delay CANNONBALL STACk FOR CONDuCTOR ROuGHNESS MODELING continues Figure 1: Comparisons of measured insertion loss of a 40-inch trace vs simulation. eye diagrams show that with -3dB delta in insertion loss at 12.5 Ghz there is half the eye opening at 25GB/s. Modeled and simulated with Keysight eesof eDa aDs software. article

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