Printed Circuit Design & Fab - December 2007 - (Page 23)

W T H FIGURE 4. A microstrip geometry used for eddy current analyses. FIGURE 5. Conductor current distribution computed applying Maxwell SV. DC magnetic fields and eddy-current solvers applicable for analyses and the design of numerous electronic components. Let’s apply the eddy-current solver of Maxwell SV to compute the field distribution inside a microstrip trace at a frequency of 400 MHz. The geometry as depicted by FIGURE 4 includes a trace having the following: width W = 5 mils, thickness T = 2 mils, height H = 4 mils. The substrate and conductor materials are FR-4 and copper, respectively. The simulation outcome is presented by FIGURE 5. Current density is described by a color map (with red being the highest and blue being lowest). The results indicate that current intensity is largest close to the conductor surface, due to skin effect. For skin effect analyses using Maxwell SV, one pitfall to avoid is not to assign a “perfect conductor” as the material property for the trace and the ground plane. A perfectly conducting structure (i.e., infinite conductivity) allows only surface currents with skin depth approaching zero. Subsequently, to produce accurate eddy current results, the trace and ground plane need to be assigned finite conductivity (i.e., for copper conductivity σ = 5.6E7 Siemens/m). Skin depth (δ) is defined as the depth below the surface of the conductor at which the current density decays to 1/e (approximately 0.37) of the current density at the surface. It can be calculated2 via: δ = 1 / sqrt (σπfµoµr) EQUATION 1 Where, δ is in meter, σ is conductor’s conductivity (in Siemens/m), f is frequency (in Hz), µo is free space permeability (1.257E-6 H/m) and µr is conductor’s relative permeability. For copper (with σ = 5.6E7 Siemens/m, µr = 1), a simpler equation can be obtained: δ = 66/sqrt(f) EQUATION 2 tion 2 yields skin depth δ = 3.3 micron (or 0.129 mil). The skin effect has important/practical applications in several engineering branches such as design of radio frequency and microwave circuits. The current distribution in most PCB interconnects will be skin-depth limited2, and resistance will be frequencydependent for frequency components exceeding 10 MHz. Skin effect can be measured7 by applying Time Domain Transmission (TDT) techniques. The skin effect losses may be compensated8 by plating the outer conductor surfaces with gold (for microwave/RF PCBs) to enhance conductivity, or by increasing the width of traces (applicable for logic PCBs) to enlarge the surface area. PCD&F DR. ABE (ABBAS) RIAZI is a senior staff electronic design scientist with ServerWorks (a Broadcom Company) in Santa Clara, CA; ariazi@serverworks.com. CHICAGO. SPRING. YOU. MAY 2008. ACKNOWLEDGEMENT I would like to thank the members of Broadcom SI Council, especially Sam Karikalan (chairman) and Amit Agrawal (co-chairman). Join us for PCB East 2008 May 11-16 in Tinley Park, IL. www.pcbeast.com REFERENCES 1. Andrew Zimmerman Jones, “Electromagnetic Spectrum of Light, About.com: Physics. ” 2. Eric Bogatin, Signal Integrity – Simplified, Prentice Hall, 2004, pp. 23-26, pp. 109-192, pp. 340-342. 3. Peter Signell, “Gauss’s Law For Spherical Symmetry, Physnet, MISN-0-132, Michigan ” State University. 4. “Introduction to Common Printed Circuit Transmission Lines, Dallas Semiconductor/ ” Maxim Application Note 2093, June 2003. 5. Howard Johnson and Martin Graham, HighSpeed Signal Propagation: Advanced Black Magic, Prentice Hall, 2003, pp. 513-514. 6. Timothy Hochberg and Henri Merkelo, “Propagation Characteristics of Coaxial Cable with a Helically Wound Ground Shield, 1996 IEEE, pp. 888-892. ” 7. Roy G. Leventhal and Lynne Green, Semiconductor Modeling For Simulating Signal, Power, and Electromagnetic Integrity, Springer, 2006, pp. 34 and 126. 8. Lee W. Ritchey, Right the First Time: A Practical Handbook on High-Speed PCB and System Design, Vol. 1, Speeding Edge, 2003, p. 19. where δ is in microns and f in MHz. At f = 400 MHz, for copper EquaDECEMBER 2007 PRINTED CIRCUIT DESIGN & FAB 23 http://www.pcbeast.com/brochure/ http://www.pcbeast.com/brochure/

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Printed Circuit Design & Fab - December 2007

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