Printed Circuit Design & Fab - June 2008 - (Page 19)

ferent types of CPW transmission lines including grounded CPW13 that has an additional ground below the substrate and ungrounded CPW (for which the side grounds coplanar to the signal trace provide the only return path). CPW can have a lower loss tangent than microstrip (signals coupled mostly through air) and higher skin effect losses (fields concentrated on the edges of trace and grounds). CPW is generally defined by center strip width w, gap width g, substrate height h, and substrate dielectric material. Metal thickness t can be also important, especially when t ≥ 0.1w or t ≥ 0.1g. The characteristic impedance Z0 of CPW can be controlled14 by varying the trace width, the spacing-to-ground, and the dielectric thickness or material. Coplanar transmission line structures offer similar advantages to a microstrip in that signal is carried on an exposed surface trace where a surface mount component can be attached. However, unlike a microstrip, the CPW (at least in an ungrounded form) can have low parasitic losses between surface mounted components and an underlying ground plane. It is also possible to narrow the traces13 to match component pad widths while maintaining constant impedance. CPW can also provide good inherent crosstalk immunity for two layer boards, because it is less sensitive to the presence or absence of a backside of board ground plane. The primary disadvantage of CPW is that it is more difficult to design compared to microstrip or stripline. If the CPW’s aspect ratio (the ratio of gap to trace width) becomes too high or too low, parasitic modes can replace the desired CPW mode resulting in poor performance. Grounded coplanar geometry is depicted in FiGurE 7. A Mathcad script for computing the impedance of this type of coplanar structure is illustrated by FiGurE 8. In FiGurES 7 and 8, a denotes trace width and b denotes the sum of trace width and separation, which is the same notation used in Wadell13. However, in many other publications the trace width is represented by w, and spacing to adjacent ground traces is given by s (or gap width g). In FiGurE 8, the expressions for Ratio1 and Ratio2 are called ratios of complete elliptic13 integrals of the first kind. In signal integrity there arise certain quantities containing complex (real and imaginary) terms. For instance, permittivity of dielectric materials15 includes a real part (dielectric constant) and an imaginary part (loss). Another example of this is found in the impedance through a bypass capacitor16 that has a real part, the equivalent series resistance ESR, and an imaginary term, capacitive/inductive reactance. Determining these quantities can necessitate the use of complex algebra or calculus. Mathcad accepts complex numbers17 of the form Re + (Im)i, where (Re) and (Im) represent ordinary numbers. Imaginary numbers may be followed by either i or j; however, Mathcad normally displays them followed by i where i equals the square root of negative 1. When typing complex numbers into a Mathcad formula, it is important to note that i or j alone cannot be used to represent the imaginary unit. Instead, it is necessary to type 1i or 1j, otherwise i or j will be interpreted as a variable. When the cursor is outside an equation having 1i or 1j, Mathcad will hide the superfluous 1. In Part 3 of this article, Mathcad applications to single-ended and differential signal propagation will be discussed. pcd&f acknowlEdGEMEntS I am thankful to Mr. Mohammad Tabatabai of Broadcom Corporation. dr. aBE (aBBaS) riaZi is a senior staff electronic design scientist with Broadcom Corporation in Irvine, CA and can be reached at ariazi@broadcom.com. rEFErEncES 11. “even and odd mode impedances” Microwave encyclopedia, 2006. 12. “even mode impedance – an introduction” Polar Instruments Ltd., Appli, cation Note AP157 . 13. Brian C. Wadell, “Transmission Line Design Handbook” 1991, Artech , House, PP 73-89, PP 464-467 . . . 14 . Rick Hartley, “RF / Microwave PC Board Design and Layout” L Avion-3 ics systems. 15. A. Kumar and s. sharma, “Measurement of Dielectric Constant and Loss Factor of the Dielectric Material at Microwave Frequencies’, Progress in electromagnetic Research, PIeR 69, 47-54, 2007. 16. Douglas G. Brooks, esR and Bypass Capacitor self Resonant Behav” ior How to select Bypass Caps” UltraCAD Design Inc., 2000. , 17. Alan Felzer, “Introduction to Mathcad” August 2003. , ! FiGurE 7. Coplanar structure with ground plane. JUNE 2008 FiGurE 8. A Mathcad script for coplanar structure. ! printEd circuit dESign & fAB 19

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Printed Circuit Design & Fab - June 2008 Contents Our Line Market Watch Around the World Happenings ROI Tip Jar Interconnect Strategies Final Finish Forum DFA/DFT Signal Integrity From the Field DFA Fab Basics Drill Off the Shelf Marketplace Ad Index BGA Bulletin

Printed Circuit Design & Fab - June 2008

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