Clearly, as XAUI backplane designs move to the 5-Gbit range and beyond and begin playing a more active role in communication architectures, jitter will become a bigger concern when running time domain analyses. And during the design of these backplanes, deterministic jitter and receive-end equalization will be vital factors to consider.
In Part 1 of this article, we looked at reasons why engineers needed to evaluate the performance of emerging 5- to 6.25-Gbit/s backplanes in the time and frequency domains. Now, in Part 2, we'll focus in on the impact that deterministic jitter and receive-end equalization have on active backplane architectures. Part 3 will then offer a set of test platforms engineers can use to evaluate backplane performance. But before getting there, let's kick off this discussion with a look at deterministic jitter.
Deterministic jitter (DJ) has a non-Gaussian probability density function (PDF) and is characterized by its bounded peak-to-peak amplitude (Figure 6).
Figure 6: Histogram depicting deterministic jitter (DJ).
There are several types of DJ, including periodic jitter (PJ), duty cycle distortion (DCD) and intersymbol interference (ISI). DCD and ISI are types of data dependent jitter (DDJ). (Other types of DDJ are still being investigated.) PJ, also referred to as sinusoidal jitter, has a signature that repeats at a fixed frequency. For example, PJ could be the result of unwanted modulation, such as electromagnetic interference (EMI). PJ is quantified as a peak-to-peak number, specified with a frequency and magnitude.
DCD is the result of any difference in the mean time allocated for the logic states in an alternating bit sequence (e.g., 0, 1, 0, 1). Different rise and fall times and threshold variations of a device could cause DCD.
DCD and ISI are functions of the data history that occur when the transition density changes. For example, fibre channel systems and devices are commonly tested with a compliant jitter tolerance pattern (CJTPAT) that stresses DCD and ISI by alternating long strings of 0s or 1s with short strings of 0s or 1s within the pattern. It is the DCD and ISI caused by the time difference that is required for the signal to arrive at the receiver threshold when starting from different places within the bit sequence (symbol). ISI occurs when the transmission medium propagates the frequency components of data (symbols) at different rates. One example of DCD and ISI is when jitter changes as a function of edge density.
Quantifying jitter components from measured data is the foundation of true signal integrity analysis. It involves statistics, digital signal processing (DSP), algorithms, and basic assumptions about the data histograms.
In the time domain, jitter data is typically collected from one particular edge to another edge. For example, a period measurement is taken between a rising edge and the next rising edge. The histogram of period measurements contains a mixture of DJ and RJ processes.
Traditionally, the TJ histograms included DJ and RJ components, and were quantified by a peak-to-peak value and a 1σ. However, given the Gaussian nature of the random component, it is incorrect to quantify a jitter histogram with a peak-to-peak number without specifying the number of samples. Therefore, for a given jitter histogram containing RJ, the peak-to-peak value will increase with more samples.
Furthermore, in the presence of DJ, the 1&sigma of the total distribution does not depict the Gaussian component RJ. The TJ histogram represents the TJ PDF. However, if the DJ and RJ processes are independent, then the total PDF is the convolution of the RJ PDF and DJ PDF. If DJ was absent from the jitter histogram, then the distribution would be Gaussian.
Adding DJ to the histogram effectively broadens the distribution while maintaining Gaussian tails. Adding DJ to the distribution effectively separates the mean of the right and left Gaussian distribution. The difference between the two means, μL and μR, is the DJ (Figure 7). The tail portions of the histogram represent the RJ component of the TJ histogram. Other methods can also be used to determine RJ and DJ. One of these uses a bathtub curve from a BERTand assumes a double delta model for DJ. A curve fitting routine is used to determine the values for RJ and DJ.
Figure 7: Bimodal distribution containing RJ and DJ.
Sources of DJ
Understanding the underlying cause of jitter is crucial to signal integrity analysis. Determining the source of jitter allows the designer to characterize and eliminate the potential problem.
In this article, we'll examine the most frequent causes of DJ and RJ. These include: electromagnetic interference (EMI), crosstalk, and reflections.
EMI is the result of unwanted radiated or conducted emissions from a local device or system. Switching-type power supplies are common sources of EMI. These devices can radiate strong, high frequency electric and magnetic fields, and they can conduct a large amount of electrical noise into a system if they lack adequate shielding and output filtering. EMI can couple or induce noise currents in a signal conductor and corrupt the signal by altering its bias. Because the interfering signal is deterministic, the resulting jitter is also deterministic. EMI may also corrupt a ground reference plane or a supply voltage plane by introducing transient noise currents. Noise currents can sporadically alter the effective input thresholds of signal receivers. Given that logic signals require a finite time to change states, a sporadic change in receiver threshold results in signal jitter.
Crosstalk occurs when the magnetic or electric fields of a signal on a conductor are inadvertently coupled to an adjacent signal-carrying conductor. The coupled signal components algebraically add to the desired signal, and can slightly alter its bias depending on the amount of coupling and the frequency content of the interfering signal. The altered bias translates into jitter as the signal transitions the receiver's threshold.
Reflections in a data signal channel create DJ due to the signal interfering with itself. Signal reflections occur when impedance mismatches are present in the channel. With copper technology, optimum signal power transfer occurs when the transmitter and receiver have the same characteristic impedance as the medium. If an impedance mismatch is present at the receiver, a portion of the energy is reflected back through the medium to the transmitter. Reflections typically come from uncontrolled stubbing and incorrect terminations. Reflected energy, or energy not available to the receiver, reduces the signal-to-noise ratio (SNR) at the receiver and increases jitter. If the transmitter is also mismatched, the transmitter absorbs a portion of the reflected signal energy while the remainder is reflected toward the receiver (again). Eventually, the delayed signal energy arrives at the receiver, out of phase with the original signal. The portion that is absorbed is algebraically summed with first-time arriving signal energy, resulting in DJ (specifically, ISI) from the receiver's perspective.
Receive End Adaptive Equalization
To account for jitter and other problems on the line, designers can implement a receive-end adaptive equalization technique. In one technique, the equalization algorithm works by applying the inverse transfer function of the frequency-dependent attenuation losses over copper medium. This is expressed as:
where ks is the skin loss, and kd is the dielectric loss. Key to using this function is to note that it is exponentially linear with length. A simple exponential approximation can then be used to obtain an equation that is linear with length:
Hence a single response shape is used, but the gain is varied to match the length and attenuation combination of the copper trace. Generally, the relationship between skin and dielectric losses is fairly consistent for traces with different physical characteristics. Although there may be minor differences in the attenuation shape, in general it is close enough that it works for a wide variety of media, trace thickness, and trace width. Good performance can be achieved for any length up to a maximum attenuation. This attenuation is usually specified at half the baud rate since the majority of the energy lies below this frequency.
Unfortunately, in the backplane, the channel rarely follows the attenuation characteristics exactly. Capacitances and inductances due to channel discontinuities and multiple reflections between discontinuities add distortions to the channel. Moreover, these distortions will change in a random fashion from channel to channel. It is therefore impossible to tune the channel response for a particular channel since it can vary significantly even for two adjacent channels of the same length.
However, a method exists that can predict the degradation in the signal based upon the signal characteristics. The figure of merit is the channel ripple, which is defined as the maximum variation from the ideal attenuated channel at half the data rate. Of course, some interpretation must be made since it is rare that a minimum will occur precisely at half the baud rate. Figure 8 shows a comparison of simulation and measured results.
Figure 8: Impact of various source jitter components on equalized link performance.
Dealing with Crosstalk
In the receive channel, Crosstalk generally occurs in the connector, although poor daughtercard or backplane design can cause crosstalk between traces. Both near-end crosstalk (NEXT) and far-end crosstalk (FEXT) contribute to the signal, although generally FEXT is considered to have less of an impact since it suffers the same channel attenuation as the desired signal. However it must still be taken into account.
Figures 9 and 10 show a near-end crosstalk response in both time and frequency domain.
Figure 9: Crosstalk in S-domain.
Figure 10: Step response of crosstalk in the time domain.
Based only on the step response of the crosstalk, one would expect that the peak-to-peak contribution of the crosstalk would be on the order of 20 mV, which is the peak-to-peak value shown in Figure 10. However, the durations of the peaks are longer than a symbol period at 5 Gbit/s, and hence the maximum crosstalk effect will be higher. This is illustrated in Figure 11, which shows multiple overlapping symbols. The peak-to-peak ripple is around 120 mV, or six times higher than the step response.
Figure 11: Impact of multiple symbols on crosstalk noise levels at 5 Gbit/s.
It is clear from a comparison of Figure 9 and Figure 10 that it is not enough to simply measure a step response for the crosstalk and assume that the peak-to-peak levels apply. Additionally, since all channels are linear, multiple crosstalk sources add linearly. Similarly, the crosstalk in an adjacent channel is proportional to the peak-to-peak transitions in that channel (with some additional effect from the transition times).
The worst-case effect of crosstalk on jitter can be simply calculated. Since the system is linear, the crosstalk noise appears as an envelope around the received signal without crosstalk (Figure 12).
Figure 12: Jitter contribution due to crosstalk.
The additional jitter contributed by crosstalk is dependent on the vertical contribution due to the crosstalk, and the slope of the signal at the threshold (in mV/ps). Note that when considering the impact of crosstalk on a signal going through a receive end equalizer; the crosstalk after the equalizer must be used.
On To Part 3
That wraps up our look at deterministic jitter and receive-end adaptive equalization. In Part 3, which will appear online next week, we'll provide some test platforms that designers can use to evaluate backplane performance. Note: To view Part 1 of this article, click here.
Editor's Note: A previous version of this article was presented at DesignCon 2003. It has been republished with permission of the IEC (www.iec.org).
About the Authors
Ken Lazaris-Brunner is a product definition specialist with Gennum Corporation. He holds a B.Sc. (Honors, Physics) degree from Queen's University (Kingston, Canada) and a M.Eng from McMaster University (Hamilton, Ontario). Ken can be reached at email@example.com.
John D'Ambrosia is the manager of semiconductor relations for Tyco Electronics. He received a B.S. in Electrical Engineering Technology from the Pennsylvania State University and a Master's Degree in Engineering Management from the National Technology University. John can be reached at firstname.lastname@example.org
John Patrin is currently the director of product marketing at Wavecrest. He received a BS in physics from St. John's University in Collegeville, MN and a Ph.D. in Materials Science from the University of Minnesota in Minneapolis. John can be reached at email@example.com.
Craig Emmerich is currently product marketing engineer at Wavecrest. He received a BS in Electrical Engineering from the University of Minnesota in Minneapolis. Craig can be reached at firstname.lastname@example.org.