# The biggest change in PAM4: How do the eyes line up?

-October 17, 2017

Many things change in the transition from good old baseband, logic-emulating non-return-to-zero  (NRZ) signaling to 4-level pulse-amplitude modulation (PAM4): We get three eye diagrams instead of one, a signal-to-noise ratio that drops like a lead zeppelin, 12 distinct transitions instead of two, and six rise and fall times instead of one of each. Although we've been dealing with eyes, signal-to-noise ratio (SNR), and rise/fall times for ages, the biggest change is that now we have to worry about the relative positions and shapes of those three eyes.

Eye linearity comes in two flavors: compression and skew. Eye Compression is shown in Figure 1 (left); the eyes align in time-delay but vary in eye height. Eye Skew is shown in Figure 1 (right); the centers the eyes vary in their time-delay.

Figure 1. PAM4 eye compression (left) and skew (right). Graphics courtesy of Ransom's Notes.

We face two essential questions: (1) measuring skew and compression and (2) living with them. Technology standards committees limit the maximum allowed compression and skew. In the process, they provide measurement techniques. But the standards are still converging so we need to keep at least one "eye" on them.

The level separation mismatch ratio (RLM) combines the spacing of the four levels into a ratio that spans from 0 to 1. As shown in Figure 2, RLM of 1.0 means that the levels are perfectly spaced. RLM of 0.5 means they’re pretty well compressed. Typically, standards require RLM greater than 0.9 or so.

Figure 2. PAM4 eye diagrams with RLM = 1.0 (left) and RLM = 0.5 (right). Graphics courtesy of Ransom’s Notes.

I’m not a fan of RLM because it can't be traced to a SER (symbol error ratio). Notice I used "symbol" instead of "bit," SER instead of BER, because each PAM4 symbol encodes two bits (if the signal is properly Gray coded, SER and BER are usually very close). Generally, it’s a better practice to specify performance criteria that can be traced to the occurrence of errors since… "if there are no errors we have experienced glorious victory and are free to move on."

Another way to measure compression is to compare the vertical openings of the three eyes. The "Vertical eye opening" can mean the rail-to-rail amplitude swings of each eye or even better, their vertical eye opening defined in terms of SER, i.e., EHn (eye height at SER=1E-n).

The amplitude swings are, for an electrical signal,
AVUPP = V3 – V2,
AVMID = V2 – V1, and
AVlow = V1 – V0.

Eye height is the vertical eye opening defined at a SER, so EH5 means the vertical opening of the eye defined at SER = 1E-5. To compare EH5LOW, EH5MID, EH5UPP, we have to choose a time-delay at which to measure them. This is a key step because it includes the effect of eye skew.

The current standards define the time-delay position of the three-pupil PAM4 eye diagram at the center of the middle eye, we’ll call it tCENTER. The center of the middle eye is halfway along a horizontal line across its SER= 1E-5 contour measured at either the voltage where the SER is lowest or halfway between crossing points—notice that these two voltages are not necessarily the same.

The PAM4 compression is then the ratio of min to max eye amplitudes: min(AVLOW, AVMID, AVUPP)/max(AVLOW, AVMID, AVUPP); the ratio of the minimum to maximum eye heights: min(EH5LOW, EH5MID, EH5UPP)/max(EH5LOW, EH5MID, EH5UPP); or the smallest of the ratios of eye amplitude to eye height: min(AVLOW/EH5LOW, AVMID/EH5MID, AVUPP/EH5UPP).

The impact of inter-eye skew on the SER (and hence the BER) depends on the receiver technology.

If the receiver uses an ADC or three voltage slicers set at a common time-delay to distinguish the four symbols, then a special type of mask test can be used to check signal compatibility with receiver technology.

The mask is quite different from what we’re accustomed to in NRZ eye analysis; it’s a vertical stripe centered on the midpoint of the middle eye. The width of the strip is given by ESMW (eye symmetry mask width) which is specified by standards, typically about 0.2 UI. To pass, the SER=1E-5 horizontal eye openings of all three eyes defined at t=tCENTER and at the vertical sampling points must extend beyond the mask.

Figure 3. Eye symmetry mask test (left) passing, (right) failing. Graphics courtesy of Ransom’s Notes.

If the receiver uses timing-independent slicers for each eye, then the explicit inter-eye skew determines the best timing offsets of the three slicers. The explicit inter-eye skew is given by the time-delay separation of the centers of the three eyes. The eye centers are the three independent points in time-delay and voltage (tLOW, VLOW), (tMID, VMID), (tUPP, VUPP) where the SER for each eye is a minimum. The skew in ps, is then max(|ti – tj|) for i and j = LOW, MID, UPP.

The PAM4 standards, 400G Ethernet, OIF CEI-56G, 64GFC, 256 GFC, and Infiniband HDR have evolved a lot in the last two years and still have a way to go. A good practice that will make the transition from what you do now to what you have to do once the specifications are released is to measure PAM4 compression and skew in ways that can be tracked to the SER.

Ransom Stephens is a technologist, science writer, novelist, and Oakland Raiders fan.

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