The present invention relates to jitter analysis for digital signals.
Characterization of the transient behavior of high-speed digital circuits, i.e. the transition from a logical zero to a logical one and vice versa, has become increasingly important for designing as well as manufacturing such digital circuits. Timing instabilities such as jitter can cause single transmission errors, or temporary or even permanent outage of an entire communication system, and have to be avoided. The standard overall figure of merit for a communications system is the Bit Error Rate (BER), however a high value of BER does not necessarily indicate timing problems, as there are many other potential sources of error in a system (for example level/threshold mismatch).
One of the key specifications of high-speed circuits with respect to timing is Jitter. ITU-T G.701 defines jitter as short-term non-cumulative variations of the significant instants of a digital signal from their ideal positions in time. The significant instant can be any convenient, easily identifiable point on the signal such as the rising or falling edge of a pulse or the sampling instant. By plotting the relative displacement in the instants between an ideal pulse train and a real pulse train that has some timing jitter, the so-called jitter function is obtained. In addition to the jitter time function, the jitter spectrum can be displayed in the frequency domain. Jitter can also be displayed using so-called Jitter-Histograms showing the likelihood for a transition.
Jitter histograms can be measured using an oscilloscope, a time interval analyzer, or a BER Tester. The applicant Agilent Technologies provides various BER test equipment such as the Agilent® 81250 ParBERT®. The histogram values are obtained from a BER vs. Sample Delay measurement (generally referred to as the so-called bathtub curve) by taking the absolute value of the derivative.
Various ways for jitter analysis are disclosed in the European Patent applications Nos. 02007690.7 or 02006259.2.
It is an object of the invention to provide an improved jitter analysis. The object is solved by the independent claims. Preferred embodiments are shown by the dependent claims.
According to the present invention, a jitter analysis is provided for a digital signal to be measured having transitions between logical levels. At each of a plurality of successive timing points, a detection for a transition occurring in the signal at that timing point is provided. The result of the detection is compared with an expected signal, and an error value is derived therefrom for each timing point. Each error value represents a matching information between a detected transition (or non-transition) and an expected transition (or non-transition) for the respective timing point.
An error signal is then provided representing the derived error values relative to its respective timing points, or in other words, the error signal represents the plurality of the derived error values, each error value being associated with its respective timing point. The error signal thus shows the variation of the error values, with the variation might be provided over the time (absolute or relative time scale) or any other scale derived from the timing points. Thus, the error signal can be e.g. the derived error values over the plurality of successive timing points. Instead of the plurality of successive timing points, other bases of the error values in the error signal can be derived from the plurality of successive timing points, such as an absolute or relative time scale. Accordingly a pseudo time scale can be provided with the plurality of successive timing points as successive events independent of the actual time difference between successive events. This is in particular useful in case the error values are sampled periodically.
A spectral jitter analysis is then provided for the error signal in order to detect spectral components in the error signal which might represent relevant spectral information of jitter contained in the digital signal. It will be appreciated that substantially any known method for spectral analysis can be applied for the spectral jitter analysis of the error signal, such as auto-correlation, cross-correlation, Fourier-Analysis, etc. Preferred examples for spectral analysis are disclosed e.g. in A. Papoulis: Probability, Random Variables and Stochastic Processes, McGraw Hill 1965, or in J. S. Bendat: A. G. Piersol, Random Data, John Whiley&Sons, 1986. It goes without saying that the specific context of different measurements might render one or more of the known spectral analysis method more or less applicable.
The invention thus allows analyzing the digital signal for spectral components resulting from jitter influences. Such spectral components might then be applied for taking further actions e.g. to avoid or reduce jitter at specific frequencies or for quality checks. Preferred examples are evaluating quantitative presence of known spectral jitter components in the digital signal or a pass/fail test if one or more such known spectral jitter components exceed one or more given thresholds.
The timing points for detecting transitions in the digital signal are preferably selected in ranges wherein transitions are likely (e.g. under the influence of jitter). Preferably, timing points are selected substantially in the middle of such range wherein transitions are likely under the influence of jitter. Such transition ranges can be determined e.g. using known techniques such as the aforementioned Jitter Histograms, bit error rate (BER) measurements, or eye diagram measurements, etc.
In a preferred embodiment wherein transitions in the digital signal are related to a reference signal (e.g. a clock signal) having a reference frequency, the distance between successive timing points is preferably derived from the reference frequency (e.g. as the period, or multiples or fraction thereof, of the reference frequency). The timing points are preferably selected at timings when transitions are expected without influence of jitter, preferably in the middle of a transition area as e.g. determined using an aforementioned eye-diagram.
The transition detection is possible in various ways, preferably by detecting the signal value at a level threshold at a given reference timing point (BER test equipment) or by evaluating the sampled signal waveform (Oscilloscope).
The invention can be partly or entirely embodied or supported by one or more suitable software programs, which can be stored on or otherwise provided by any kind of data carrier, and which might be executed in or by any suitable data processing unit. The invention may also be partly or entirely embodied or supported by dedicated electronic hardware not related to software or firmware execution such as an hardwired ASIC. Accordingly, combinations of software and hardware solutions might also be employed.
Other objects and many of the attendant advantages of the present invention will be readily appreciated and become better understood by reference to the following detailed description when considering in connection with the accompanied drawings. Features that are substantially or functionally equal or similar will be referred to with the same reference sign(s).
For validation and characterization of digital circuit designs, it is of advantage not only to quantify the amount of jitter measured but also to analyze it for its spectral content to localize its origin and understand the mechanisms of interference. In order to allow elimination or reduction of deterministic jitter in a design, the generated jitter is analyzed for its deterministic content by decomposing it into its spectral contents. Whereas the energy of random jitter modulation is generally spread into wide frequency band, deterministic jitter usually manifests itself with a concentration of energy into (e.g. a few) discrete modulation frequencies. The ability to determine those frequencies might provide insight into root causes and can therefore significantly speed up the debugging process.
In the following, preferred embodiments are described for providing spectral analysis on jitter measured with a bit error rate tester (BERT) such as the aforementioned Agilent® 81250 ParBERT®. However, it is clear that the invention is not limited to BERTs, but that any other test equipment can be provided for deriving the error signal from comparing detected with expected transitions at defined timing points or sampling and evaluating the entire signal waveform.
At the sampling point 20, strobing is provided by comparing each detected signal value with the value expected in the ‘center’ of the data eye (e.g. in the eye to the right, indicated by a reference timing point 25). Whenever a transition is displaced such that the data eye closes (displacement to the right in the eye diagram 10 of
For the sake of better understanding, a sinusoidal jitter modulation 60 onto a random digital data signal shall be assumed. While the random data signal allows an easier explanation, it is clear that the invention can be applied for any kind of digital signal. Without the jitter modulation 60, all transitions of the digital data signal would occur precisely at the sampling point 20. However, the jitter modulation 60 will periodically displace the transitions of the digital data signal ‘around’ the sampling point 20, thus leading to the transition range 30. Just from looking at the jitter histogram 50, no conclusion can be made on the frequency of the jitter modulation 60.
Whenever the jitter modulation 60 displaces the transitions to the right in
Since we assume random data, the BER will be 0.25, because in 50% of the cases during the positive portion 65 of the jitter modulation sine wave 60 adjacent bits are equal in value and no transition will occur between the sampled and the expected bit. Thus the jitter has no impact on that particular bit. In contrary, when the displacement is opposite (i.e. during the negative portion 67 of the jitter modulation sine wave 60 no error will occur. No error occurs, because the data eye to the right is opened by the displacement (displacement to the left in
A well-know statistical method to extract periodic information buried in a random signal is the calculation of the auto-correlation function (as illustrated in more detail e.g. in the aforementioned references by Papoulis or Bendat). The auto-correlation function of a true random signal vanishes after a small bandwidth related delay, whereas any kind of periodic signal yields an auto-correlation function with the same periodicity that does not vanish even for large delays. Therefore the periodic information can be extracted from the auto-correlation function by evaluating the behavior for large delays.
An alternative way to obtain the same spectral information is by directly calculating the Fourier transform of the error signal. The obtained (complex) values of the Fourier transform may then be multiplied with its conjugate complex values. The result is the same spectral power density of the error signal as obtained by calculating the Fourier transform of the auto-correlation function.
Pure sinusoidal jitter rarely occurs in reality. Typically real systems show intrinsic random jitter caused by thermal and scattering noise. Since it is the result of many different uncorrelated contributors the intrinsic random jitter generally shows up with a Gaussian distribution. An example where sinusoidal jitter artificially injected and intrinsic random noise is mixed is shown in
As long as the peak-to-peak amplitude of the sinusoidal jitter 460 (dotted line) does not substantially exceed the rms value of the random jitter 400, the distribution of the composite jitter in the Jitter Histogram 450 still shows up with a bell like distribution that makes separation of sinusoidal and random jitter difficult.
When random and sinusoidal jitter are mixed and the sinusoidal jitter 460 does not exceed the random jitter 400 by far, the error signal 470 generated by sampling in the sampling point 20 (here: crossover point of the transitions) again shows up with a periodic modulation of the error density. The difference to the pure sinusoidal jitter (as depicted in
Since a broadband noise signal represents a continuous flat power density spectrum, the energy is equally distributed over a wide range of frequencies and thus is typically small in magnitude in a narrow section of the spectrum. In contrary when a periodic signal is contained in a broadband noise signal the power density of the periodic signal is strongly concentrated in few discrete lines and can clearly be distinguished from the broadband noise power density.
Therefore, when the Fourier transform is deployed to the auto-correlation of the error signal caused by both random and sinusoidal jitter, the resulting power density spectrum shows the spectral information of the sinusoid in terms of a strong peak. The result of the respective simulation is shown in
The fact that the power density of the random portion gets distributed over many frequencies while the spectral power of the sinusoidal portion stays concentrated in a single line significantly enhances the detection of spurious periodic jitter deeply buried in random jitter. Thus even small sources of deterministic jitter can be identified.
The influence of the position of the sampling point 20 is explained schematically in more detail in
The aforedescribed ways to analyze composite jitter containing deterministic (periodic) and random jitter and to decompose it into its spectral components, has been shown particularly useful for design validation and debugging when the jitter frequencies of the deterministic portions are unknown.
In case, however, when it is already known or expected that a problem caused by deterministic jitter of a well-known frequency may exist, a pass/fail test might be provided useful e.g. for production testing. A typical case might be e.g. when process variations or other manufacturing defects result in jitter crosstalk from a known source. Such pass/fail test might be applied in a production test-flow to test for the occurrence of such faults for the deterministic jitter.
In one embodiment to determine the existence of a jitter with known frequency for pass/fail testing or to quantify jitter of a known frequency contained in a mix of random and deterministic jitter, a cross-correlation function (or covariance) is determined between the error signal and a sine wave of the expected frequency. Alternatively, another deterministic signal representing the potentially occurring jitter frequency can be used instead of a pure sine wave for calculating the cross-correlation. In case the deterministic signal is contained with the given frequency in the error signal and thus in the composite jitter of the data signal, the cross-correlation function will show up with a strong signal of the expected frequency. A Fourier transform of the cross-correlation signal may then show a strong peak at that frequency. When it is not contained in the composite jitter the cross-correlation function will show only a negligible signal induced by the noise and thus the Fourier transform will only show a minimal excitation.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/EP02/04841 | 5/3/2002 | WO | 6/17/2005 |