Enhance Signal-Quality Analysis On High-Speed Serial Channels

If a sigma table isn’t available, you can solve Equation 5 within the proper limits by an approximation. You can normalize Equation 5 to zero-mean Gaussian by making a substitution:

Let .

Then dz = sdu, and Equation 5 simplifies to Equation 6:

                              (6)

For random variables beyond 3-sigma, the equation (fortunately) can be approximated:

                                    (7)

Equation 7 can then be used to estimate the bit-error rate given a single variable (x). The value of x is the mean distance from the transition point to center, divided by the standard deviation (Fig. 7).

Example
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 the mean and standard deviation, shown on the right. The mean is normalized to zero, and the distance from the mean to the next sampling point, obtained through the use of cursors, is measured to be 710 ps. The standard deviation shown is 69.83 ps. The value of x is 10.2, and if you plug that value into Equation 7, it yields an estimate of the bit-error rate.

If you solve for the BER in Figure 8, you get an error probability that’s infinitesimally small. We have to remember that an open eye like that of Figure 8 indicates good signal quality across the channel. Different data rates can have the same BER, if the limitation is in the clock-data recovery (CDR) circuitry of the receiver. (The above analysis doesn’t take into account the jitter tolerance of the CDR circuitry.) Otherwise, bit errors are also caused by factors that include amplitude noise, bandwidth limitations, and signal distortions like overshoot and undershoot. As an engineer, you must understand the limitations of an estimate and know how to interpret it.

Zeeshawn Shameem, customer applications engineer, received a BSEE from the University of California at Los Angeles. He can be contacted at zeeshawn_shameem@maximhq.com.

References:
1. Strassberg, Dan, “Eyeing Jitter,” EDN, pp. 42-52, May 2003.

2. “Universal Serial Bus Specification Revision 2.0,” pp. 131-165, April 2000.

3. Lauterbach, Michael, “Getting More out of Eye Diagrams,” IEEE Spectrum, pp. 61-63, March 1997.

4. Application Note 1181, “Measuring Random Jitter on a Digital Sampling Oscilloscope,”http://www.maxim-ic.com/appnotes.cfm/appnote_number/1181, September 2002.