Agilent Measurement Journal - Issue 5 - 2008 - (Page 40)

Another method used to solve Equations 15 and 16 is the Poisson regression.7 While this method provides better results than the Gaussian approximation, the most accurate results come from empirically evaluating Equations 15 and 16. In order to ﬁnd the required conﬁdence levels, the values of k and n are varied systematically and for a given g, Equations 15 and 16 are computed. Figure 6 is generated by picking those values of k and n for which CLu or CLl is one of the three values, 90, 95 or 99 percent. From this graph it is clear that the measured BER approaches the target BER, g, asymptotically from either direction. If we examine the red curve corresponding to the 95 percent level, in Figure 6, we notice that at n = 3 x 108, the observed value of k is zero, giving the measured BER of 0. But from the graph we can interpret this to mean that the actual probability of error Pe is less than the target value of 10-8 with a conﬁdence level of 95 percent. The same result can be obtained with the help of Equation 18. Unfortunately, since the BERT has a ﬁnite delay resolution, it is virtually impossible to locate the sampling delay that corresponds exactly to these points. Even if there were sufﬁcient timing resolution, an inﬁnite number of bits would still need to be observed to prove that the Pe is exactly 10-12. Bracketing approach Because we are unable to locate a single point on the slope where the Pe is exactly 10-12, we instead target an interval that brackets it. The point where Pe is equal to 10-12 lies within this interval with a high conﬁdence level. Figure 7 depicts this process for the right slope. We search for an interval [x–, x+] that brackets the xL point, where x+ and x– are separated by no more than the desired delay-step resolution of the TJ measurement, ∆x. We don’t need to know the exact Pe values at x+ and x–. It is sufﬁcient to assert that Pe(x–) is greater than 10-12 and Pe(x+) is less than 10-12 at a desired conﬁdence level. If we choose 95 percent, we have determined that xL is within the interval [x–, x+] with a conﬁdence level better than 90 percent. For lack of better knowledge, we assume that xL is in the middle of the bracketing interval. Now the distance between x– and x+ is ∆x, and hence xL is only accurate to ±0.5 ∆x. Replicating the same procedure for the right half of the bathtub curve yields xR with the same accuracy. TJpp can then be calculated as before with an accuracy of ±∆x. 1.0E-006 1.0E-007 1.0E-008 Bit error rate, Pe 1.0E-009 1.0E-010 1.0E-011 1.0E-012 1.0E-013 1.0E-014 1.0E-015 -13p -12p XL -10p Time, ps -8p -7p Finding total jitter Using the BERTSCAN technique to ﬁnd 10-12 Pe points, and therefore TJ, would be very time consuming. To increase the speed of measurement, without any approximations, we can use the concepts developed in the previous section. Since we are purely interested in the TJ result, it is sufﬁcient to ﬁnd the sample delay offsets on the left and right slope of the bathtub curve where the Pe is exactly 10-12. We call these points xL and xR. The peak-to-peak total jitter, TJpp, is then simply the bit interval minus the difference between xL and xR. X+ X– DX Figure 7. Deﬁnitions for the bracketing approach, on the right slope lower BER region 40 Agilent Measurement Journal

Table of Contents Feed for the Digital Edition of Agilent Measurement Journal - Issue 5 - 2008

Agilent Measurement Journal Issue 5 Finding a New Path when Assumptions Break Down Contents Testing MIPI D-PHY Protocols Oscilloscope Firmware Update DNA Replication Joining the LTE/SAE Trial Initiative Testing Proteins Praise for DC Power Analyzer Scripting Features for AMDS Testing Hybrid PCBA Systems Improving the Gene Expression System Workflow Turning a “Good Enough” Test Strategy into One That’s Reliable, Repeatable and Traceable Understanding the Effects of Limited-Bandwidth Channels on Digital Data Signals Introducing the 3GPP LTE Downlink Validating the 26 Validating the Physical and Protocol Layers in DDR Memory Interfaces Understanding Total Jitter Measurements of Low Probabilities Using Behavioral-Model Simulation to Accurately Predict First-Order PLL Performance Creating Synchronous High-Frequency Sampling across Multiple Digitizers Overcoming the Challenges of Testing FlexRay Networks Understanding Operating Life and Repeatability of Electromechanical Switches and their Effect on Total Cost of Ownership Implementing Micro and Nano LC/MS Techniques for High Sensitivity Lipidomics Analysis

Agilent Measurement Journal - Issue 5 - 2008

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