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24 The PCB Design Magazine • February 2015 ity (4πx10 -7 H/m) and is the copper conductiv- ity, typically (5.6x10 7 S/m). The skin depth (um) can be approximated by: Looking at this equation, it is apparent that skin depth decreases with increased frequency. Figure 1 shows the skin depth compared to frequency. At low frequency (1MHz), the skin depth is 66um but this decreases to 0.66um at 10GHz. So, at 10GHz, only the very outer sur- faces of the trace carry the current. Also, the red horizontal lines represent the trace copper weight and thickness. This shows that at about 10MHz, a signal traveling in a ½ oz. (17.78um) copper trace would not use the entire trace cross-section, but rather the skin effect would be dominant. In a previous column, Beyond Design: Sur- face Finishes for High-Speed PCBs, I pointed out that the nickel content of ENIG surface finish has a ferromagnetic property that can adversely affect electromagnetic fields in the high fre- quency domain. One could argue that since the nickel is plated on top of the microstrip surface, that it would have little effect on properties of the trace. And that due to the skin effect, the current will travel the path of least inductance, which is on the lower surface of the copper closest to the reference plane. However, it has been found that at approximately 2.7GHz, the resonant behavior of the nickel component in ENIG, increases insertion loss. It is for this rea- son that solder mask over bare copper (SMOBC) processing should be considered for all high- speed designs. Most substrates are copper clad with either Rolled Annealed (RA) copper, electrodeposited copper (ED) or reverse-treated foil (RTF). RA copper is both smooth and consistent in thick- beyond design EFFECTS OF SURFACE ROUgHnESS On HIgH-SPEED PCBS continues Figure 1: skin depth (um) vs. frequency (Mhz).