Printed Circuit Design & Fab - October 2008 - (Page 23)

Figure 6. Behavioral model. SIGNAL intEGrity Convolution integral { PRBS, 6.25 Gbps, 211 – 1 bits } + Overlay each bit, synchronous with the clock = FiGurE 6. behavioral model. FiGurE 4. An example of the measured four-port S-Parameters for a backplane channel up to 20 GHz, showing just the magnitudes of the 16 S-Parameters. there is another set of 16 phase plots not shown here. Figure 4. An Example of the measured 4-port S-Parameters for a backplane channel up to 20 GHz, showing just the magnitudes of the 16 S-Parameters. There is another set of 16 phase plots not shown here. Weak coupling Weak coupling Tight coupling Tight coupling FiGurE 5. Frequency domain and of one line Figure 5. Frequency domain and time domain views of the same S-Parameters which is microstrip timepart of aneighbor while in the secondIn oneitcase, the line is tightly coupled to its domain differential pair.of the same views case, is loosely coupled. S-Parameters of one line which is part of a microstrip differential pair. In one case, the line is tightly coupled to its neighbor while in the second case, it is loosely coupled. Port 1, it can do a number of things. It can scatter, reflect back through Port 1 or it can be scattered out one of the other Ports (2, 3 or 4). The ratio of the sine wave coming out to the sine wave going in, at each frequency, is the S-Parameters. With four ports, there are 16 possible combinations (FiGurE 4) of sine wave going ins and coming outs. This makes it essential to use the port index numbers to keep track of each S-Parameter. By convention, the index labels are in reverse order of the going in and coming out order. S21 refers to the sine wave going in at Port 1 and coming out at Port 2. This would be the transmitted signal in one line of the differential pair, also called the insertion loss. All 16 combinations of S-Parameters can be tracked in a simple 4 x 4 matrix. Each S-Parameter will have a magnitude and phase at each frequency measured. Because this is an enormous amount of information, it is important to use the formalism to describe the S-Parameters in order to manage the information contained in the S-Parameters. Each S-Parameter matrix element, between its OCTOBER 2008 magnitude and phase, explains a piece of the behavior of the interconnect. Even though these S-Parameters might have been measured or simulated as the single ended behavior of the channel, with a little manipulation of the terms, they can be converted into the differential S-Parameters, that describe the behavior of differential and common signals on the interconnect. If we have the behavior in the frequency domain, we can use a little algebra to convert this into the time domain which would look similar to the traditional TDR and TDT response of the interconnect seen in FiGurE 5. Even though the performance of the connector might be measured as the single ended response in the frequency domain, it can be converted into the differential response in the time domain. The information is embedded in the original S-Parameters. It is just with a little algebra that it can be re-displayed. One format that it can be converted into is the impulse response. If we know the impulse response of an interconnect, sometimes called the Green’s Function, we can use this as a behavioral model to predict how any arbitrary, time domain signal might interact with the interconnect. This behavioral model (FiGurE 6) is a surrogate for the actual connector. In a four-port device, measured from 10 MHz to 20 GHz, if the magnitude and phase, the singleended and differential, the frequency domain and the step and impulse time domain responses are included, there are over 100,000 individual data elements. The S-Parameter formalism, borrowed from the RF world, has become a simple, compact way of manipulating and interpreting this wealth of information. Everything you ever wanted to know about the electrical performance of an interconnect is contained in these S-Parameters. By mastering S-Parameters, you can master high-speed electrical performance. pCd&f YOU’RE dr. Eric boGatin, signal integrity evangelist can be reached at eric@betheSignal.com. For additional information on this and other signal integrity topics go to www.betheSignal.com. printEd CirCuit dESign & fAB 23 http://www.photoplot.com http://www.beTheSignal.com

Table of Contents Feed for the Digital Edition of Printed Circuit Design & Fab - October 2008

Printed Circuit Design & Fab - October 2008 Contents Our Line Market Watch Around the World Happenings Test and Inspection ROI Tip Jar Interconnect Strategies Final Finish Forum The New Wave in High-Speed Modeling The PCB Design Library Mixed Signal Design Considerations Modeling Conductor Surface Roughness Copper Erosion: The Influence of Metallurgy on Copper Dissolution The Wave of the Future Ad Index Building a Profitable Niche Marketplace Off the Shelf BGA Bulletin

Printed Circuit Design & Fab - October 2008

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