## Slippery Slopes

Noise in a serial link causes jitter. The relationship between additive noise in your circuit and the incremental amount of jitter that that noise causes depends on the slope of your data waveform.

For example, suppose you have a 1V p-p signal with a 10 to 90% rise-and-fall
time of 200 psec. At each transition, this signal has a maximum slope (dV/dt) of
(1V)/(200 psec)=5×10^{9}V/sec.

Suppose further that additive noise with a worst-case peak-to-peak amplitude, *ΔV*_{p-p}, is afflicting your signal. In this case, the
peak-to-peak jitter, *Δt*_{p-p}, induced in the zero crossings of
the incoming data waveform equals *ΔV*_{p-p} divided by the slope
(dV/dt) of the data waveform.

In this example, let the noise have a peak-to-peak amplitude equal to 0.1 V.
That amount of noise can cause peak-to-peak shifts in the zero crossings of your
data waveform as big as (0.1V)/(5×10^{9}V/sec)=20 psec, or ±10 psec in
either direction.

The foregoing analysis assumes your receiver can pass a 200-psec edge undistorted. That scenario may not be possible in a practical system, especially if you have intentionally limited the bandwidth of your receiver to reduce other forms of interference. A complete analysis of jitter examines not only the waveform at the input pins of the transceiver, but also the waveform at the actual input to the slicer within the transceiver.

Glossing over the bandwidth issue for a moment, the basic jitter relationship suggests that in the presence of additive noise, a faster slope produces less jitter, and a slower slope produces more jitter—a good general conclusion for many systems.

Next comes the real subject of this column: What happens when you delay
one-half of a differential pair (*differential skew*)?

In Figure 1, waveforms A and B on the left represent signals at the (+) and (–) terminals of a differential receiver. In a differential system, the additive-noise jitter relationship still applies, but you must pick either the differential or the odd-mode signal-description convention and stick with it for expressing both the waveform slope and the additive noise. Don't mix and match conventions. This discussion uses the odd-mode convention, defined as (A–B)/2.

A useful visual trick for finding the odd-mode signal is to form the *average* of the signals A and –B. At the top right of the figure
(no skew), signals A and –B fall practically on top of each other, so the slope
of the average (the odd-mode slope) is the same as the slope for either A or B
taken separately.

At the bottom right (with skew), you can see that adding differential skew by sliding waveform –B to the right substantially reduces the slope of the odd-mode signal. Reducing the slope increases your susceptibility to jitter, which is one reason that differential systems often specify tight limits of differential skew.

A differential skew equal to 10% of the rise or fall time increases the
signal-transition time by 10% That increase reduces the received slope by 10%,
which then *increases* your susceptibility to additive-noise jitter by
10%.