Printed Circuit Design & Fab - February 2009 - (Page 19)

directly with √f. When ascertaining the total AC resistance, it is necessary to also account for resistance of return current on the reference plane. Furthermore, the conductor AC loss is directly related to Rac and hence proportional with the square root of frequency. Equation 7 is a skin depth expression with σ being the conductor’s conductivity (inverse of resistivity ρ), μ0 is permeability of free space, μr is conductor’s relative permeability and f is sine-wave frequency. When f is in Hz, σ in Siemens/meter and μ0 in Henries/meter (4πE-7), then Equation 7 produces ό in meter. Equation 8 is a simplified skin depth formula 34 applicable to copper ( σ = 5.6E7 Siemens/m and μr =1), with fmhz being frequency in MHz and δcu in micron. In Equation 9 αdiel represents attenuation associated with dielectric loss 32 in dB/in, fghz is frequency in GHz and Er is substrate dielectric constant. FiGurE 10 presents dielectric loss - αdiel (based on Equation 9) for several materials, generated with the aid of Mathcad. The curve RO4 (Rogers 4350) displays the least and FR-6 the most attenuation in this comparison. NeS (Nelco N4000-13SI), which utilizes S glass, is less lossy than NeE (Nelco N4000-6 Hi Tg FR4), based on E glass. At high frequencies, for typical PCB trace dimensions, the dielectric losses being proportional to frequency can become dominant 32 over conductor DC losses (frequency independent) and AC losses (proportional to √f ). In addition to conductor and dielectric losses, the effects due to roughness of conductor surface can be significant. Conductor roughness is often expressed as tooth structure14 and the amount of surface variations is portrayed as tooth size. Conductor surface roughness can effectively increase the material resistance when the mean surface roughness is a significant percentage of skin depth. For instance, at a frequency of ~ 200 MHz, the skin depth of copper is 4.667 micron, which approximately equals the typical PCB surface roughness ( ~ 4 microns to 7 micron). Frequency harmonics exceeding 200 MHz will then deviate from the ideal loss formulae14. For producing low loss interconnects, it is desirable to have smooth copper foils. Conclusion When selecting PCB materials, some parameters that need to be considered include the conductor and dielectric losses, the electrical characteristics, the mechanical/thermal properties and the price. There are other important contemplations involved when ascertaining optimum materials for PCB stackup, such as impact of glass weave35 in PCB laminates on Gigabit per second signals and also meeting standards (IPC specifications). These will be discussed in Part 4 of this article. pCd&f rEFErEncES 26.Gary Melchior, “LMh0034 PCB Layout Techniques, National Semi” conductor Application Note 1372, July 2006. 27. eric Bogatin, “Board Stackup’s Important Tool, Printed Circuit Design ” & Manufacture, December 2003, pgs. 18-20. 28. Stephen C. Thierauf, “high-Speed Circuit Board Signal Integrity, ” Artech house, Inc., 2004, pgs. 2-9. 29. Clyde F Coombs, Jr., “Printed Circuits handbook, Fifth edition, . ” McGraw hill handbooks, 2007, Chapter 5. 30. helen holder, “Introduction to Surface Mount Technology, April ” 2002. 31. Al Williams, “Build Your Own Printed Circuit Board, McGraw-hill, ” 2004, p. 14, p. 168. 32. Abe Riazi, “engineer’s rule of thumb simplifies PCB signal integrity, ” ee Design, August 19, 2002. 33. “Calculating Track Resistance, Polar Instruments Ltd., Application ” Note AP144. 34. Abe Riazi, “Maxwell’s Influence on Signal Integrity, Printed Circuit ” Design & Fab, December 2007. 35. “PCB Dielectric Material Selection and Fiber Weave effect on highspeed Channel Routing, Altera Corporation, AN-528-1.0, May 2008. ” Editor’s Note: References 1-25 can be found in Parts 1 and 2 of the series. dr. aBE (aBBaS) riaZi is a senior staff scientist hardware development with Broadcom Corporation in Irvine, Califor- nia. He can be reached at ariazi@broadcom.com. FiGurE 9. A set of equations related to transmission line resistance, skin depth and loss. FiGurE 10. Dielectric loss per unit length vs. frequency for several different PCB materials. printEd CirCuit dESign & fAB 19 FEBRUARY 2009

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Printed Circuit Design & Fab - February 2009 Contents Our Line Market Watch Around the World Happenings ROI Tip Jar BGA Bulletin Interconnect Strategies Final Finsh Forum Defects Database Embedded Active Components In Multilayer LCP Packages Simulation: The Need for Speed Advanced Registration Systems The DC Design Squeeze Ad Index Do You Really Want a Better Autorouter? Designing With Conductive Materials, Part 1 Off th eShelf Marketplace On the Forefront

Printed Circuit Design & Fab - February 2009

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