rms噪声和pp噪声.pdf

Application Note:HFAN-4.0.2 Rev.2;04/08 Converting between RMS and Peak-to-Peak Jitter at a Specified BER Maxim Integrated Products Application Note HFAN-4.0.2(Rev.2,04/08)Maxim Integrated Products Page 2 of 5 Table of Contents 1 Introduction.3 1.1 Voltage Noise vs.Time Noise.3 1.2 RMS to Peak-to-Peak Jitter Conversion.3 2 How Peak-to-Peak Jitter Relates to RMS Jitter.3 2.1 Peak-to-Peak Jitter and Oscilloscope Measurements.4 3 More about Gaussian Statistics.4 List of Figures Figure 1.PDF of a Gaussian distribution with a variance of 1.5 Application Note HFAN-4.0.2(Rev.2,04/08)Maxim Integrated Products Page 3 of 5 Converting between RMS and Peak-to-Peak Jitter at a Specified BER 1 Introduction There are several ways to quantitatively state the amount of random jitter within a system.The following discussion addresses the differences between two conventions.The first method is to give a standard deviation of the jitter distribution(or equivalently the RMS value),and the second method is to select a bit error rate(BER)threshold and define the random jitter as a peak-to-peak value.1.1 Voltage Noise vs.Time Noise Jitter is essentially variation in the zero crossing times of the data eye.There are two ways that noise can cause bit errors in a system.One way occurs when the noise causes the data waveform to dip below the decision threshold voltage at the sampling instance(voltage noise).Also noise can cause errors by inducing jitter(timing noise).Jitter causes errors in a system by moving the data eye across the vertical sampling instance.1.2 RMS to Peak-to-Peak Jitter Conversion To convert between RMS and peak-to-peak random jitter,the BER must be specified.The following equations can be used to convert between the two:RMSPPJitterJitter*=and PPRMSJitterJitter=Where is determined by BER2*2erfc21=?.Table 1.Scaling Factors()for Different BER Tolerances BER 10-3 6.180 10-4 7.438 10-5 8.530 10-6 9.507 10-7 10.399 10-8 11.224 10-9 11.996 10-10 12.723 10-11 13.412 10-12 14.069 10-13 14.698 10-14 15.301 10-15 15.883 10-16 16.444 2 How Peak-to-Peak Jitter Relates to RMS Jitter A Gaussian distribution describes random jitter.Qualitative analysis shows that the tails of a Gaussian distribution extend indefinitely on either side of the mean.Therefore,it is impossible to specify a peak-to-peak jitter range that bounds the jitter 100%of the time.Instead we want to identify a Application Note HFAN-4.0.2(Rev.2,04/08)Maxim Integrated Products Page 4 of 5 range that contains the jitter,for example,99.99999%of the time.This means that 0.00001%of the time the jitter will be outside of our peak-to-peak range.Calculating peak-to-peak jitter is important for jitter budget analysis.It is assumed that any samples that fall outside the peak-to-peak range will cause errors.Therefore,if a BER target of 10-12 is selected,it is necessary to select a range that will contain the jitter all but 0.0000000001%of the time.2.1 Peak-to-Peak Jitter and Oscilloscope Measurements When using an oscilloscope in histogram mode to measure random jitter,usually the measured peak-to-peak jitter is of little practical value.Most oscilloscopes generate the peak-to-peak value by simply finding the time difference between the two furthest points captured in the histogram.Because this measurement is dependant upon a number of factors,including the number of samples acquired,it is not a statistically valid figure of merit for specifying peak-to-peak jitter.3 More about Gaussian Statistics The assumption made in quantifying random jitter is that it is approximated by a Gaussian distribution.Generally this is true when the dominant source of noise in the system is thermal noise.In practice this seems to be valid.On the other hand,deterministic or pattern-dependent jitter is decidedly not Gaussian in nature.Statistics textbooks tell us a Gaussian distribution can be completely defined by two parameters:mean and standard deviation.The mean of the distribution determines the horizontal location and is dependent upon the frame of reference selected.In this discussion,the ideal edge of the data eye is set to be t=0.Figure 1 is a graph of Gaussian probability density function(PDF).The PDF is a representation of the probability of an event happening at a certain time.In this example,it shows how the zero crossing of the data will move relative to the ideal position(set at 0 on the x-axis).A fundamental property of the PDF is that the area it contains(or its integral)is equal to 1.Figure 1 also shows how the Gaussian distribution can be limited to include a percentage(+=+12.72*sigma Bounds 99.9999999%6.18*sigma Bounds 99.9%