Enhanced signal quality analysis on high-speed serial channels

Using a high-speed serial interface to obtain error-free data is a challenge, whether the interface is a Gigabit Ethernet physical layer that connects a client or router, or a low-voltage differential signaling port that sends high-definition video content to the display. However, you can use the bit error rate (BER) test to obtain the bit error rate, determine the quality of the serial channel, and get a visual representation of the stability and redundancy of the physical channel through the eye diagram, thereby increasing Data transmission rate while minimizing bit error rate.

From the user's point of view, the basic criterion for determining the performance of a digital communication system is the bit error rate (BER). In general, users are more interested in the digital information itself than in the loss of information. (Information loss and improvement of data transmission methods are left to engineers to solve this problem.) For users, the simplest and most accurate test of the overall performance of the communication system is the BER test, which provides a single statistical value about the entire A useful measure of system fidelity.

Unfortunately, the BER test has some drawbacks: the equipment used for measurement is often very expensive; the influence of process and temperature on the signal timing may cause reading errors; the test time is directly proportional to the test quality; too little BER reading does not indicate the cause of the problem. In addition, users only care about whether the system works well, and it is the engineer's responsibility to improve the system.

The goal of many designs (non-wireless) is one-trillion BER (BER = 10-12). The amount of mobile information on the Internet is measured in terabits. It is significant to further increase this target number. However, despite the complexity, time, and cost of performing an effective BER test, such tests still cannot account for the loss of information. BER testing is great for users, but engineers urgently need to understand the causes of error problems. For this reason, they often add a simulation supplementary tool—eye diagram—in the digital BER test. However, the analog domain does not have the function of error checking and error correction as in the digital domain.

The use of eye diagrams is very common among digital communication/network engineers, especially since the introduction of digital oscilloscopes. A professionally trained communications engineer, after analyzing several eye diagrams, can often make accurate guesses about the root cause of the problem. After the introduction of the RS-232 communication standard, eye diagrams have been used to measure the performance of digital transmission systems and will continue to provide guidance and recommendations for performance improvement in the future. Forty years later, digital communication protocols still use eye diagrams to determine signal integrity.

The USB specification requires an eye diagram to handle some issues related to rise and fall times and timing jitter tolerance. Digital broadcast television uses 8-vestigous sideband modulation (8VSB) to produce an 8-level eye diagram for estimating performance. Similarly, eye diagrams on Fast Ethernet and Sonet networks can provide visual feedback to digital diagnostic tools to help pinpoint potential performance issues. Many BER test manufacturers now add eye diagram functionality to their devices.

Eye measurement

The significant advantage of the eye diagram over the BER test is that the former can indicate the root cause of the problem and the ways to improve it. Random data streams are sampled at each trigger interval, and the sampled graphs are continuously added together to obtain the eye diagram. Since each sampled data is random, this overlay generates various types of graphics, superimposed on each other, and the last displayed graphic resembles the human eye (Figure 1).

In the early stages of analog oscilloscopes, engineers used various input signals to describe jitter variations. Today's digital oscilloscopes have other functions in addition to this function. For example, Tektronix' CSA8000 can set the sampling duration (persistence), provide a histogram of timing jitter and amplitude changes, and list statistics for each parameter (such as average, median, and standard deviation). In short, it can provide accurate quantitative data needed for statistical purposes in BER estimation. The CSA8000 normalized Gaussian variables to statistical data.

In an ideal channel without timing jitter, the transition points within each time interval occur at the same time. However, in actual situations, due to the presence of jitter, the transition point will shift (Figure 2). Jitter includes random jitter (RJ) and deterministic jitter (DJ). Random jitter is unbounded and can be described by a Gaussian random variable. Deterministic jitter is bounded and there are many reasons. The total jitter (TJ) can be measured from the histogram of Figure 2. TJ is the sum of random jitter and deterministic jitter (TJ = RJ + DJ).


There are several techniques that can be used to separate the random components of jitter. Both random jitter and deterministic jitter should be taken into account when estimating the BER. However, in terms of accuracy, there is no way to qualify for a fully mature BER test. Therefore, eye diagram estimation should not be used as a substitute for the BER test.

Use eye diagrams to estimate BER

The experience of the lab tells us that opening an eye diagram means that the data loss rate is low and works normally. Therefore, the ideal eye diagram is where the transition points within each trigger interval occur at the same time. Functionally, we can describe this requirement with an ideal impulse function (Figure 3). Actual random jitter can cause immediate changes in the transition point, which can sometimes be described by a random variable. The most commonly used random jitter model is a Gaussian model. We model this change as a Gaussian random variable because the true system model is Gaussian; the mathematical principles of Gaussian random variables are easy to understand, and many digital sampling oscilloscopes (such as the CSA8000) normalize the data to Gaussian. Statistical data.

Due to jitter, the transition point can be expressed as a probability distribution and described using a Gaussian probability density function (Figure 3). Another option is to model the sampling points as Gaussian random variables and find the probability of error conditions. The answer to these two methods is the same.

The probability density function (PDF) of a2 in Figure 3 is:

Here, a2 is the average transition point, z is a random variable, and s is the standard deviation or RMS value. To find the probability that our random variable is error-free, we integrate Equation 1 over the interval shown. In this way, the error probability is the area under the curve (Figure 4). This area represents the transition between a2 (actually sampled at a1 or a3), or at a1 and a3 (actually sampled at a2).

For the random variable a2, the area under the curve is:

and

The sum of the above two equations is multiplied by 2 to get the total error probability. 2 This factor reflects the conditional probabilities associated with a1 and a3. We assume that it is symmetrical about the conditional probability of a2.

To solve the error probability of a2, the integration interval in Equation 4 is from sampling point a1 to infinity, and from sampling point a0 to negative infinity. Due to symmetry, this equation can be simplified to Equation 5. Graphically, it represents the shaded area below the curve in area chart 4.

Perhaps you have forgotten the formula 5 solution method, but fortunately you do not need to know. The CSA8000 histogram provides statistics normalized to Gaussian random variables. Gaussian statistics are easy to use because only two parameters are required: mean and standard deviation. It is usually possible to normalize the mean to zero and reduce it to one parameter.

The standard deviation represents random jitter. Ideally, random jitter should be separated from deterministic jitter. To do this, a known sampling pattern must be fed into the system and random jitter is removed by averaging the known sample data. We assume that the noise and random jitter appear as Gaussian random variables with zero mean, so that the average sampling removes the random jitter and only the deterministic jitter remains. Thus, the standard deviation can be modified to include deterministic jitter and BER estimation can be continued with the new standard deviation.

Once the standard deviation is found, the standard deviation from the average to the next sampling interval, z, can be calculated. Thus, the probability is a function of the distance from the average value, which can be obtained from statistical data (Figure 6). The error probability given by 6-sigma(6s) is close to one-billionth and 7-sigma is one trillionth of an trillion, showing an exponential decline.


If there is no sigma table, Equation 5 can be used to solve Equation 5 in the appropriate interval. By permutation, Equation 5 can be normalized to a zero-mean Gaussian distribution. If

Then dz = sdu, Equation 5 is simplified to Equation 6:

For random variables above 3-sigma, the above formula (fortunately) can be approximated as:

As long as a single variable (x) is given, Equation 7 can be used to estimate the bit error rate. The value of X is the average distance from the transition point to the center divided by the standard deviation (Figure 7).


Examples

Figure 8 shows an eye diagram based on the CSA8000 oscilloscope and a histogram taken at a transition point. The histogram gives statistical parameters such as mean and standard deviation, see figure right. The average is normalized to zero and the distance from the average to the next sample point is measured by the cursor to 710 ps. The standard deviation is 69.83 ps. Therefore, the value of X is 10.2, and this value is brought into Equation 7, and the estimated error rate can be obtained.

If you solve the BER in Figure 8, you get an infinitesimal probability of error. We must remember that an open eye like Figure 8 shows that the signal quality on the channel is good. Different data rates can have the same BER, as long as the defect originates from the receiver's clock data recovery (CDR) circuit. (The above analysis does not take the jitter tolerance of the CDR circuit into consideration.) In addition, the factors causing the bit error rate include amplitude noise, bandwidth limitation, and signal distortion (overshoot and undershoot). Engineers must understand the limitations of the BER estimation and clearly explain how to interpret it.


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