PAM4: Symbol levels and voltage
compression measurements
Ransom Stephens - April 26, 2016
IEEE and OIF-CEI each offer different techniques for measuring PAM4 symbol levels. While they
both measure the voltage levels of electrical PAM4 signals and are strongly correlated, they're not
the same.
We should expect that as technologies mature, some techniques will fall out of favor and others will
move in. In this case, one of the techniques strikes me as nostalgic. There's nothing wrong with
using an obvious technique, but I prefer measurements that can be related to system performance,
which for PAM4 is either the SER (symbol error ratio) or BER (bit error ratio).
The first technique, from IEEE’s 100 GbE 802.3bj (as well rumors from people who have seen the
latest draft of the emerging 400 GbE specs) uses the transmitter linearity test pattern (Figure 1).
Figure 1. Transmitter linearity test pattern, which could be used for testing 400 GbE.
(Graphic, Copyright Ransom's Notes, used with permission).
The test pattern consists of clearly defined symbols: 16 consecutive level A (or level 0) symbols
followed by 16 consecutive level B (or 1), and so on as shown in the graphic. The levels are
measured after the signals have settled, whether or not de-emphasis is employed, 7 UI (unit
intervals) after the transition. The levels {VA, VB, VC, VD} are given by the average value of the
voltages over the center 2 UI of each 16 UI symbols.
The effective symbol separations are given by:
Where the average voltage is given by the average of the four symbol voltage measurements, ¼(VA +
VB + VC + VD). The ideal symbol separations are ES1 = ES2 = 1/3.
One of the PAM4's complications is the possibility of amplitude compression: the variation in the
voltage (or power) swing between adjacent symbols. One way to measure voltage compression is to
define the minimum signal level, SMIN, as half of the swing between the closest adjacent symbols:
SMIN = ½ min (VB – VA, VC – VB, VD – VC).
so that the level separation mismatch ratio is:
A linear transmitter should have RLM = 1.0; the 100 GbE PAM4 spec 100GBASE-KP4 requires RLM
≥0.92.
Another way to measure the symbol levels is to extract them from a PAM4 eye diagram (which was
once likened to the iris of a mutated goat). First, define a ¼ UI vertical mask through the center of
the middle eye. Then project histograms of the three symbols. The symbol levels {V0, V1, V2, V3} are
given by the mean of the corresponding histograms (Figure 2).
Figure 2. You can measure PAM4 symbol levels with a horizontal eye mask. Courtesy of
Tektronix.
{V0, V1, V2, V3} should be pretty close to {VA, VB, VC, VD}, but because the histograms, especially the
top and bottom, are likely to be asymmetric it's unreasonable to expect the two sets of symbol levels
to be the same.
By defining the symbol separations as AVlow = V1 – V0, VMID = V2 - V1, and VMID = V3 – V2, we can also
define the eye linearity as the ratio of the largest to the smallest adjacent symbol voltage swings,
While the first technique, the one that uses the transmitter linearity test pattern, is appealing in its
simplicity, I prefer the second. By measuring symbol levels and compression with a real eye diagram
it's much easier to relate the measurement to SER (symbol-error ratio) or BER (bit-error ratio).
There are bones to pick with the second technique. We could measure the symbol levels at the level
of maximum SER and there's no great argument for requiring each eye to have the same center. The
standards have separate timing linearity requirements for aligning them. We’ll see what comes out.
They're running a bit late; PAM4 is difficult so we don't blame them.
In principle, I think that the best measurements
1. Can be interpreted in terms of the SER or BER,
2. Can be measured on common lab equipment, like oscilloscopes, and
3. Are simple enough that they are repeatable even when using the invariably unique techniques
employed by different test and measurement companies.
There's a third technique that's in common use, but it doesn't appear in any standards and I think
it's silly because it can't hope to be traced to SER or BER. One of these days, if I get moody, I’ll
disparage it in this space.
Also see
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PAM4: A new measurement science
The next generation's modulation: PAM-4, NRZ, or ENRZ?
OFC 2016: OIF shows off 56G PAM4, NRZ
DesignCon Panel Highlights 25G, PAM4