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62 The PCB Design Magazine • June 2016 and differential—plus he discusses clock jitter in detail. 3. Advanced High-Speed Signal Propagation Now I am ready for the final seminar. I am so glad I did the first two seminars, rather than jumping straight into the advanced level. I am now fully prepared, with all the background knowledge, to move forward with the more complex issues of signal integrity. This seminar is for experienced digital designers, who need to drive their designs to the upper limits of speed and distance. Howard stated, "…without signal integrity tools, you do not know how close you are to that limit. It is our responsibility, as de- signers, to push the system as close as possible to the edge without ever failing." As seasoned designers, we are used to look- ing at circuit parameters in the time domain, like a waveform on an oscilloscope. However, as clock frequencies and edge rates continue to accelerate, one needs to focus instead on scat- tering parameter (S-parameter) models in the frequency domain in order to effectively evalu- ate signal propagation in a lossy medium. A two port S-Parameter model of a transmission line is derived in both matrix and equation form. However, cascading networks cannot be evalu- ated from input to output but rather need to have combined S-parameters for multiple port analysis. The power spectral density of a digital sig- nal is typically below the knee frequency and if the parasitic impedances are not significant, then digital signals tend to pass undistorted. This is illustrated in Figure 4. Howard prefers to conservatively over-estimate the bandwidth, so that all effects, above the knee frequency, can be safety ignored. Next is a detailed look at the transmission line model. Howard uses the transverse electro- MASTERING "BLACK MAGIC" WITH HOWARD JOHNSON'S SEMINARS Figure 4: Power spectral density of a digital signal.