The war on noise now takes us into the next frontier: the high-speed serial backplane. Actually, this is about both noise and jitter, which is a practical approach, if not rigorously correct. Tektronix's Pavel Zivny likes to limit noise to "all things undesirable in the vertical (voltage, or power for optical signaling) direction," distinguishing it from jitter, "which is all things undesirable in the ‘horizontal,' i.e., time, direction." The problem is that it's difficult to separate the two, since they combine to affect bit error rate (BER) performance.

Most serial-data measurements are made, or at least presented for analysis, as eye patterns *(Fig. 1)*. Engineers started using eye patterns qualitatively when storage-tube analog oscilloscopes became available. They would look at two transitions on a
repeating bit pattern, and the overlaid traces would smear out if the data was jittery.

Early digital storage oscilloscopes (DSOs) with color displays, but relatively shallow memories, added a third qualitative dimension by showing the relative distribution of jitter events through the use of color. Today's really fast DSOs, with memories that can store long data sequences and DSP engines capable of data analysis, have made eye-pattern measurements quantitative.

They also simplify setup and provide for standard pattern masks that
enable patterns to be used for go/no-go testing *(see "Eye Pattern Sample
Size and Clocking,").*

To see why noise in the broader sense matters in serial data transmission, consider several eye diagrams. Figure 2a is an eye diagram of a good signal. The receiver will have an easy time detecting transitions. In Figure 2b, the voltages in the eye are settled, so that's not a problem, but the timing of the edges is very jittery. In Figure 2c, the edge timing is good, but the signal has a bad case of vertical "hum," possibly from a power supply.

Figure 2d depicts a signal with both noise and jitter problems. The receiver comparator will have to compare with low noise to navigate the narrow voltage range between the high and low levels. Also, the timing margin for the circuit latching the information will be diminished because of the way transitions move back and forth.

BIT ERROR RATE

The real goal of
these measurements is to assess the effect
of various jitter and noise components of
BER *(Fig. 3)*. Jitter has many components. For noise, the main breakdown is
between random and deterministic noise.

Random noise is what we commonly call noise or RMS noise when we look at a signal with an oscilloscope or a spectrum analyzer. Deterministic noise is split into periodic noise—noise with a clear spectral distribution that's uncorrelated (unrelated) to the signaling bit rate. For example, crosstalk from the power supply will appear as periodic noise. So will the processor clock, assuming your serial data isn't running on the processor clock.

Data-dependent noise (DDN) captures vertical impairments caused at the bit rate in a way that depends on the bit pattern—for instance, a "lonely-low pattern" (zeros surrounded by many ones on both sides). DDN often is caused by ISI (intersymbol interference), that is, by a physical mechanism that couples energy from one bit into adjacent bits due to inductive or capacitive coupling, losses, or transmission line effects.

EYE-PATTERN MEASUREMENTS

According to LeCroy's Mike Hertz,
since the complete data record is available in an instrument's memory, the
location of individual bits can be determined by comparing each bit interval in
the original waveform with a pre-loaded
mask. When mask testing is turned on,
the entire waveform is scanned bit by
bit and compared to the mask.

Upon detecting a mask hit, the bit number is stored, and a table of bit values is generated. This table gets numbered, starting with the first bit in the waveform. It can be used to index back to the original waveform to display the waveform of the failed bit. Certain eye-pattern measurements are specified as required tests for many standards. The basic eye measurements deal with amplitude and timing.

*Eye amplitude *is the difference
between the simple mean of the distribution around the zero level and the
mean of the distribution around the one
level. Eye-amplitude measurements are
formed by distributing amplitude values
in a region near the center of the eye—
normally 20% of the distance between
the zero crossing times.

*Eye height *is a signal-to-noise measurement. It's very similar to eye amplitude, except the standard deviation of
both the one and zero levels is subtracted from the eye amplitude.

*Eye width *indicates the total jitter in
the signal. The time between the crossing points is computed based on the
mean of the histograms at the two zero
crossings in the signal, and the standard
deviation of each distribution is subtracted from the difference between the
two means.

Optical signals on fiber require an
alternate eye-pattern measurement
called the *extinction ratio*. It's necessary
because laser transmitters aren't fully
shut off during data transmission. Not
surprisingly, extinction ratio is the ratio
of the optical power with the laser in the
on state to that of the laser in the off
state. It's a little trickier to make laser power measurements than voltage
measurements because it involves the
use of optical to electrical converters in
front of the measurement device.

Turning to timing measurement, *eye
crossing *is the point where transitions
from zero to one and from one to zero
reach the same amplitude. It's expressed
as a percentage of eye amplitude. A
measurement instrument looks at horizontal slices across the eye diagram and
picks out the slice with the minimum
histogram width.

If you take vertical slices instead of
horizontal, you can measure *average
power, *the mean value across the entire
data stream. Unlike the eye-amplitude
measurement that separates the ones
and zeros histograms, average power is
the mean of both histograms. If the data
encoding is working as it should, average power should be 50% of the overall
eye amplitude.

EXTRACTING BER

The essential element for BER calculations is *time interval error *(TIE), the difference between
data edges and edges of the recovered
clock. Measuring the TIE histogram lets you determine the likelihood of a jitter
value exceeding a given maximum.

To obtain BER, the data sample's TIEs
are presented as a histogram of TIE value versus the number of occurrences of
that value. The objective is to determine
the probability that a data transition
occurs simultaneously with the sampling
of data. The histogram yields the conditional probability of a data edge occurring at a given time within a bit period, given that the data is sampled at that
time. A bathtub curve shows this relationship graphically *(Fig. 4)*.

There's a catch here. Systems typically
specify bit error rates in the 10^{–12 }range. It takes a lot of edges to measure events
with probabilities down to one in
10^{–12}—too many to acquire and store on
a contemporary instrument. That necessitates extrapolation of the histogram
from a smaller set of measurements.