Embedded Systems Design Europe - June/July 2008 - (Page 28)

debugging cause costly product recalls if not ﬁxed. They can be the most challenging kinds of problems to solve and a fast MSO waveform update rate is key to their identiﬁcation and solution. This article discusses update rate and how to measure it and then uses this to compute the statistical probably of ﬁnding an infrequent or random event during debug. A typical measurement example is included. What is update rate? Update rate is deﬁned as the number of waveforms per second the scope can acquire, process, and display. Scope vendors will specify their fastest update rate in waveforms (acquisitions) per second. Digital scopes repetitively ﬁll their memory buffers with signal detail. After every acquisition the oscilloscope must process the previous acquisition’s data before acquiring new information. The time it takes for a scope to process an acquisition before re-arming its trigger for the next acquisition is called the dead time. During dead time, the scope is blind to any changes in target signal activity. Measuring a scope’s update rate is not that difﬁcult. Most scopes provide a trigger output signal – typically used to synchronize other instruments to the scope’s triggering. You can measure a scope’s waveform update rate by measuring the average frequency of this output trigger signal using an external counter. However, to be accurate the potential trigger rate of the signal used as a trigger source for the scope must exceed the scope’s anticipated update rate otherwise the scope’s update rate will be limited by the slower trigger rate. Once the scope’s update rate for a speciﬁc setup condition is known, the dead-time can be calculated by the following relationship: DT = W – 1/U % DT = 100 x (1- UW) Where DT = dead-time U = waveform update rate 28 Fig 1: Oscilloscope dead-time versus display acquisition time. W = display window = timebase setting x 10 (divisions) In addition, it is now also possible to compute and compare the statistical probabilities of capturing random and infrequent events. CAPTURING INFREQUENT AND RANDOM EVENTS Capturing infrequent events on a scope with a given update rate adheres to the laws of probability. To understand how, consider the rolling of a die. The probability of getting a 6 in one roll of a die is 1/6. Given multiple rolls, the probability of getting a 6 on any one of the rolls increases with each new roll. The probability of obtaining a 6 on any one of N rolls is deﬁned by the following equation. PN = 100 x (1 – [(S-1)/S]N) Where S= number of sides on the die N = number of rolls After 1 roll the probability is just 1/6 or 17%, while after 10 rolls the probability increases to 84%. For oscilloscope capture probabilities, “S” is the ratio of the average occurrence time of an anomalous event relative to the oscilloscope’s display window time. So for example, if a glitch occurs once every 10 ms (100 times per second) and the oscilloscope’s timebase is set at 20 ns/div, then the on-screen acquisition time is 200 nanoseconds and S = 10 ms/200 ns, or 50,000. In this example we effectively have a 50,000-sided die that has a waveform anomaly on just one side. The odds of Where Pt = Probability of capturing anomaly in “t” seconds t = Observation time U = Scope’s measured waveform update rate R = Anomalous event occurrence rate W = Display acquisition window = Timebase setting x 10 Using the above probability equation it is now possible to measure, compute and compare dead-time percentage and the probability of capturing an infrequently occurring metastable state (glitch). There are many factors that determine a scope’s actual waveform update rate and dead time. In this example the measurement commenced by initializing the MSO with a default capturing a glitch once after just one acquisition are just 1 part in 50,000. To improve the scope’s probability of capturing the infrequently occurring glitch requires that the scope try to acquire the signal multiple times – and as fast as possible. This is where the scope’s waveform update rate factors into the equation. “N” which is now the number of oscilloscope acquisitions, is equal to the scope’s waveform update rate multiplied by a reasonable observation time. The observation time is the time that you might be willing to view a waveform on the scope’s display to determine if it is normal or not before moving your probe to another test point. So the anomalous event capture probability equation reduces to: Pt = 100 x (1 – [1-RW](U x t)) JUNE – JULY 2008 | embedded systems design europe | www.embedded.com/europe http://www.embedded.com/europe

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Embedded Systems Design Europe - June 2008 Contents Work in Progress to Define Compact PCI Plus Power.org Demonstrates New Tools Project Supports Multi-core System Programming Altium Links Electronic to Mechanical Design PLDs Look to Cut Power Budget and Costs Project to Provide Coverage Analysis Tool Microsoft Details Windows Embedded Update Cover Feature: Leveraging Virtual Hardware Platforms for Software Allocating Memory in MATLAB-to-C Code MDD & IDEs: Making the Twain Meet in Embedded System Designs Debugging Mixed Signal Designs for Infrequent & Random Events Why Open Source is the Natural Choice for High-security Systems Bringing the Benefits of Low Power CPUs to Modular Design New Products Advertising Contacts

Embedded Systems Design Europe - June/July 2008

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