1. Field of the Invention
The invention generally relates to measurement systems. In particular, the invention relates to measurement systems for analyzing jitter.
2. Description of the Related Art
Jitter in a digital communication signal is the variation in time of data (or clock) edges from integer multiples of the bit period unit interval (UI) time. In an ideal signal, the edges would occur at exact interval times. In a real signal there is variation in the edge locations due to various phenomena in the signal generation and transmission system. FIG. 1 shows a representation of a digital data signal labeled jittered data 102 relative to a reference clock 104. In the illustrated example, the jittered data 102 is capable of changing states approximately at times corresponding to the rising edges of the reference clock 104. This data signal has variation in the edge locations. The variation is plotted relative to the ideal location, at the bottom of FIG. 1. This variation is known as the jitter 106, or time interval error (TIE), of the signal. It will be understood that whether there is an actual transition in the jittered data 102 corresponding to an edge of the reference clock 104 will depend on the data itself. For example, the data can remain at a “one” or a “zero” state for multiple clock periods.
Many current industry specifications divide jitter into two main categories: unbounded random jitter (RJ), and bounded deterministic jitter (DJ). Random jitter (RJ) is modeled as having a zero-mean Gaussian distribution and is quantified by the standard deviation. Deterministic jitter (DJ) is parameterized as a peak-to-peak value. The total jitter (TJ) is also parameterized as a peak-to-peak value, which is a combination of deterministic jitter (DJ) and random jitter (RJ). Given that the total jitter (TJ) is unbounded on account of the random jitter (RJ) contribution, it is specified as the peak-to-peak time interval between which all but a fraction of the jitter population falls. A fraction commonly specified is 10−12, but it will be understood by one of ordinary skill in the art that the specified fraction can vary in a very broad range and can include larger fractions and smaller fractions. For example, some emerging applications specify fractions that are orders of magnitude smaller than 10−12. A relatively direct method of measuring the total jitter (TJ) under this stipulation is to measure the jitter for 1014 bits in order to obtain reliable statistical information on the total jitter (TJ) range that occurs with a 1-10−12 probability. However, this would be relatively time consuming, taking over 27 hours if 1014 consecutive bits at 1 Gbit/s were to be observed. A more feasible method is to observe the jitter for a shorter period, and estimate the 10−12 peak-to-peak jitter by fitting its distribution to a statistical model.
A simplified jitter model is illustrated in FIG. 2 with periodic jitter (PJ) represented by a dual-Dirac, random jitter (RJ) represented by a Gaussian in an upper trace 202. The resulting convolution of both is shown in a lower trace 204. It should be noted that the dual-Dirac has been scaled for visibility in the plot of FIG. 2. The model typically used to represent the distribution of the jitter components is a zero mean Gaussian for random jitter (RJ), and a dual-Dirac function for deterministic jitter (DJ) (the dual-Dirac function being an approximation to the distribution of a sinusoid). In this case, the total jitter is simply two Gaussian distributions with means offset equal to the offsets in the Dirac functions (see FIG. 2). For this distribution, the approximate calculation of all but 10−12 of the population is given as the sum of the peak-to-peak of the deterministic jitter and 14 times the standard deviation, or RMS value, of the random jitter (see Equation 1 below).TJpp(10−12)=RJpp(10−12)+DJpp≈14RJrms+DJpp  Equation 1
Some instruments and specifications define TJpp explicitly according to Equation 1. Others generate a histogram distribution for total jitter (TJ) based on the convolution of the calculated random jitter (RJ) and deterministic jitter (DJ) distributions. The TJpp is then extrapolated for the specified population by fitting the total jitter (TJ) distribution to a bathtub curve model. In each case however, there is a common underlying problem:                1. The jitter content of a signal will typically be demodulated from the signal itself.        2. The random jitter (RJ) and deterministic jitter (DJ) components will typically be decomposed from the measured jitter and quantified.        3. The TJpp will typically then be calculated based on the combination of random jitter (RJ) and deterministic jitter (DJ) for the specified population.        
FIG. 3 is a tree diagram that illustrates selected components of jitter. Jitter at each level of the hierarchy in the tree diagram is not necessarily independent, for example, duty cycle distortion (DCD) jitter 316 may be due to inter-symbol interference (ISI) jitter 314. Deterministic jitter (DJ) 306 is commonly subdivided further into the following components: periodic jitter (PJ) 308, data-dependent jitter (DDJ) 310, and bounded uncorrelated jitter (BUJ) 312, with data-dependent jitter (DDJ) 310 further subclassified as linear inter-symbol interference (ISI) jitter 314 and duty cycle distortion (DCD) jitter 316.
Periodic jitter (PJ) 308 includes tones that are uncorrelated with the data. Data-dependent jitter (DDJ) 310 is correlated to the data pattern where: inter-symbol interference (ISI) jitter 314 is due to band-limiting in the system, and duty cycle distortion (DCD) jitter 316 is related to a mismatch between the falling and rising edges of the signal due to the signal transmitter. Bounded uncorrelated jitter (BUJ) 312 is the grouping of other effects that are bounded but are not correlated to the data pattern, and do not exhibit a periodic behavior. One possible source of bounded uncorrelated jitter (BUJ) 312 is cross-talk from asynchronous aggressors. Although most current specifications only state limitations on random jitter (RJ) 304, deterministic jitter (DJ) 306, and total jitter (TJ) 302, the subcomponents of deterministic jitter (DJ) 306 are often of interest for device analysis.
Conventional Jitter Analysis
There are several standard methods in the industry to deal with the problem of jitter decomposition. They are based on either a method of undersampling the data, typically with the use of a time interval analyzer, or oversampling the data with a single-shot sampling oscilloscope. After the jitter data has been recovered from the captured data, it is typically separated using one of two methods. The first method involves the construction of a histogram of the jitter in the time domain. This histogram is divided into its random and deterministic parts through an analysis of its shape. The second method involves the transformation of the jitter into the frequency domain using a Fourier Transform (FT), such as a Fast Fourier Transform (FFT). Once in the frequency domain, it is stated that the deterministic components may be identified as tones in jitter spectrum, while the random components make up the noise floor of the spectrum. The spectrum is then separated into two parts and the random jitter (RJ) 304 is calculated from the noise floor, and the deterministic jitter (DJ) 306 is calculated from the tones.
While these existing methods may be applied successfully to make jitter approximations in specific cases, there are many situations in which these methods fail.
General Undersampling Methods
FIG. 4 illustrates a sampled waveform and its corresponding time interval error (TIE). Some industry standard methods are based on the use of undersampled data. See, for example: U.S. Pat. Nos. 6,185,509; 6,356,850; and 6,449,570. These methods can use either an undersampling time interval analyzer or an undersampling oscilloscope. The methods were typically developed in this way due to hardware limitations that would not allow for every contiguous edge to be measured. One problem with such methods is that sporadic events that are not correlated with the data and do not occur regularly can be completely overlooked. FIG. 4 shows the jitter data for a signal where this is the case. When measured using an undersampling time interval analysis method, this signal yields a total jitter value of less than 0.25 UI (well within specifications), even though this signal causes a failure in the receiver. Using an oversampling method reveals that the total jitter is actually greater than 0.5 UI.
Time Interval Analyzer Span Measurements to Acquire Jitter Data and to Determine Data Dependent Jitter Component
The method of time interval analyzer span measurements is implemented to calculate the data-dependent jitter (DDJ) component of jitter in a signal. See for example: U.S. Pat. Nos. 6,185,509; 6,356,850; and 6,449,570. Collections of time interval measurements are gathered for every edge in a repeating data sequence. These collections are processed to generate a histogram distribution of jitter for each edge independently. The mean offset of each histogram represents the data-dependent jitter (DDJ) associated with the edge in question. The difference between the maximum and minimum mean offsets is the peak-to-peak data-dependent jitter (DDJ). This method is dependent on a priori knowledge of the repeating data pattern and will fail if the pattern is not repeating or if the pattern is unknown.
Time-Domain Histogram Tail-Fitting Method
The tail-fitting method is based on the generation of a histogram of the jitter data. See, for example, U.S. Pat. No. 6,298,315. It has been suggested by conventional techniques that fitting Gaussian curves to the tail portions of the distribution can identify the random jitter (RJ) content. The RMS value of the random jitter (RJ) is then calculated as average value of the standard deviation of the two Gaussian curves, and the peak-to-peak deterministic jitter (DJ) is calculated as the separation between the means of the two Gaussian curves.
In reference to the dual-Dirac and Gaussian model described earlier in connection with FIG. 2, this suggested solution is a relatively accurate approximation. The convolution of the dual-Dirac with the Gaussian has a negligible effect on the shape of the tails. It should be noted that the shape of the tail corresponds to the sum of the Gaussian with its shifted duplicate. Due to the rapidly decaying nature of the Gaussian curve, if there is significant separation between the two Gaussian distributions, then the value of the tail portion of one will be insignificant at the tail location of the other as illustrated in FIG. 2. However, if the dual-Dirac distribution model is replaced with one representing an actual tone, or multiple tones for deterministic jitter (DJ), the suggested solution is relatively inaccurate. In generating the total jitter (TJ) distribution, by convolving the Gaussian and the new deterministic jitter (DJ) distribution, the shape of the resulting tail region will be significantly altered from the original Gaussian. The parameters estimated from this data set will be biased due to model mismatch.
Frequency-Domain Spectral Separation Method
The spectral separation method is based on oversampled data acquired using a single-shot sampling oscilloscope. See, for example, U.S. Patent Application Publication US2003/0004664. The threshold crossings for each consecutive edge are interpolated between the sample points, and the jitter data is derived. The jitter data is transformed into the frequency domain using a Fourier Transform (FT). It is claimed that the deterministic jitter (DJ) components can be distinguished from the random jitter (RJ) as peaks in the spectrum. Although this may be accurate for a simple case where the deterministic jitter (DJ) is composed of a single periodic jitter (PJ) tone, or a very small amount of data-dependent jitter (DDJ), this method will fail in the presence of multiple periodic jitter (PJ) tones, periodic jitter (PJ) tones of relatively large amplitudes, or a significant amount of data-dependent jitter (DDJ). Due to the windowing effects of the Fourier Transform (FT), a certain amount of power from any tones in the spectrum will be distributed into side lobes of the tone. When the major lobe, or peak, of the tone is removed from the spectrum, the side lobes will remain and inappropriately contribute to the random component of the jitter. In cases where the side lobes are relatively few and relatively small, then this will not matter. However, in cases where there are relatively many sidelobes, or they are relatively large, then the random component can be dramatically inflated. Examples of this are described.
In a first example, in cases where there is a relatively large tone in the spectrum whose frequency does not fall precisely on a bin center, the side lobes may become significant. This occurs in jitter tolerance testing when signals with relatively large amounts of periodic jitter (PJ) are artificially created to stress device receivers.
In a second example, in cases where there are relatively many tones in the spectrum, the sum of all the resultant side lobes becomes significant. This occurs commonly with data-dependent jitter (DDJ), when the high frequency content of the signal is approaching the bandwidth of the transmission channel. Jitter tones due to data-dependent jitter (DDJ) occur throughout the spectrum at multiples related to the bit pattern length. A relatively large amount of data-dependent jitter (DDJ) can be intentionally introduced in jitter tolerance measurements to stress device receivers. Relatively large amounts of data-dependent jitter (DDJ) are also common in system intrinsic jitter measurements where signals are measured after long transmission channels such as back-planes and multiple connectors.
FIG. 5 illustrates an example of time interval error (TIE) associated with data-dependent jitter (DDJ). The frequency domain spectral separation method is dependent on a repeating data pattern so that data-dependent jitter (DDJ) shows up as tones in the jitter spectrum. In the case of random data, data-dependent jitter (DDJ) does not show as tones in the spectrum. Rather, it is broadband and cannot be distinguished from the noise floor. Therefore, this method fails in the presence of random data. FIG. 5 depicts a simulated random data signal containing only data-dependent jitter (DDJ) (no random jitter (RJ) or periodic jitter (PJ)), the TIE signal, and the power spectrum of the TIE signal.
Further Jitter Component Analysis
FIG. 6 illustrates an example of further components of jitter that can advantageously be distinguished using the techniques disclosed herein. It will be shown that by doing this a more accurate calculation of the total jitter (TJ) 302 can be performed, and a better analysis can advantageously be performed on the jitter content to aid in the identification of sources of jitter in the signal. FIG. 6 illustrates selected additional jitter categories that can be recognized using the techniques disclosed herein versus the limited categories previously described in connection with FIG. 3.
Data-Dependent Random Jitter (DDRJ) 602
Random jitter (RJ) 304 may be further categorized as data-dependent random jitter (DDRJ) 602. In certain cases, the random jitter (RJ) 304 standard deviation is dependent on the data surrounding any given transition. This phenomenon has been observed in data where the slew rate of each edge is also data dependent. It is most evident in situations where signals are intentionally degraded for jitter tolerance testing, and random jitter (RJ) 304 is imposed on the signal through the addition of amplitude noise. The transformation of amplitude noise into random jitter (RJ) 304 is a linear function of the slew rate.
Conventional jitter decomposition methods disadvantageously assume an equal distribution for random jitter (RJ) 304 across all edges in the signal, and calculate random jitter (RJ) 304, and subsequently total jitter (TJ) 302, based on this assumption. This can result in an underestimation of the critical peak-to-peak random jitter (RJ) contribution. Advantageously, disclosed techniques include a method to account for these effects in the RJpp and TJpp computations.
Device State Dependent Jitter (DSDJ) 604
Data generation and transmission systems are subject to performance variations depending on the pattern content of the data, and other factors within the system that relate to the data. For example, the transmission of data with a high transition density, e.g., 01010101, can consume relatively more power than data with a low transition density, e.g., 00001111. Power fluctuations and other phenomena can dramatically affect the jitter content of the signal, contributing to device state dependent jitter (DSDJ) 604. Analyzing device state dependent jitter (DSDJ) 604 can be useful in identifying problems in a system. Existing jitter decomposition methods lump device state dependent jitter (DSDJ) 604 and inter-symbol interference (ISI) jitter 314 together, whereas disclosed techniques advantageously permit them to be distinguished from one another.
Current state of the art jitter analysis and decomposition is represented by the following public domain publications, the disclosures of which are incorporated herein by reference in their entirety:
U.S. Pat. No. 6,298,315: Method and Apparatus for Analyzing Measurements
U.S. Pat. No. 6,298,315 to Li, et al describes a method of analyzing data to separate it into random and deterministic components. The method generates a time-domain histogram of the data and identifies the tail segments of that histogram. A Gaussian curve is fitted to each of the tails. The Gaussian curves are associated with the random component and the remainder of the distribution is associated with deterministic component.
U.S. Pat. No. 6,356,850: Method and Apparatus for Jitter Analysis
U.S. Pat. No. 6,356,850 to Wilstrup, et al., describes a method and apparatus for separating the components of a jitter signal. It identifies a reference edge in a repeating data signal and makes multiple time span measurements between that reference edge and the other edges in the data signal. The variation in these time span measurements is a representation of the jitter in the signal. It generates variation estimates of the time spans, calculates the autocorrelation function of the jitter signal, and transforms the autocorrelation function into the frequency domain using a Fourier Transform (FT). The random and deterministic components are separated in the frequency domain using a Constant False Alarm Rate (CFAR) filter, where the peaks of the frequency spectrum are associated with the deterministic components. This technique is limited to the analysis of periodic waveforms, such as repetitive digital bit sequences.
U.S. Pat. No. 6,185,509 and U.S. Pat. No. 6,449,570: Analysis of Noise in Repetitive Waveforms
U.S. Pat. No. 6,185,509 to Wilstrup, et al., and U.S. Pat. No. 6,449,570 also to Wilstrup, et al., describe a method for measuring time intervals in a repeating pattern, and characterizing the variation in those time intervals. It is directly applied to measuring the jitter in a repeating pattern.
US2003/0004664: Apparatus and Method for Spectrum Analysis-Based Serial Data Jitter Measurement
U.S. Patent Application Publication No. US2003/0004664 by Ward, et al., describes an apparatus and method of jitter separation for repeating patterns. It is based on spectral analysis of the jitter signal to separate deterministic jitter and random jitter. The jitter signal is transformed into the frequency domain using a Fourier Transform (FT). The CFAR filter using a single sliding window is employed to separate the deterministic jitter (DJ) components from the random jitter (RJ) component. The data-dependent components (DDJ), periodic jitter components (PJ), and duty cycle distortion (DCD) components are separated by analyzing the spectrum of the components identified as deterministic jitter (DJ).