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PCBD-May2015

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46 The PCB Design Magazine • May 2015 International , vol., no., pp.407,409, 28-30 May 1980 doi: 10.1109/MWSYM.1980.1124303. [3] S. Hall, H. Heck, "Advanced Signal Integ- rity for High-Speed Digital Design," John Wiley & Sons. [4] Huray, P. G. (2009) "The Foundations of Signal Integrity," John Wiley & Sons. [5] Y. Shlepnev, "PCB and package design up to 50 GHz: Identifying dielectric and conductor roughness models," The PCB Design Magazine, February 2014, p. 12-28. [6] Y. Shlepnev, "Sink or swim at 28 Gbps," The PCB Design Magazine, October 2014, p. 12–23. [7] E. Bogatin, D. DeGroot , P. G. Huray, Y. Shlepnev , "Which one is better? Compar- ing Options to Describe Frequency Dependent Losses," DesignCon2013 Proceedings, Santa Clara, CA, 2013. [8] Wikipedia, "Close-packing of equal spheres." [9] Simberian Inc., Las Vegas, Nevada. CANNONBALL STACk FOR CONDuCTOR ROuGHNESS MODELING continues article Figure 12: Cannonball model (left) vs hammerstad-Jensen model (right). Figure 13: Close-packing of equal sphere model variations. hexagonal close-packing of equal spheres, hCPes (left) as described in DesignCon 2015 paper [1] ; square close-packing of equal spheres, sCPes (center); and triangular close-packing of equal spheres, TCPes (right).

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