The Eyes Have It


Reducing PCI Express 3.0 “fuzz” with multi-tap filters

Modern PHYs include transmitters which implement multi-tap FIR filters (e.g. three taps for PCIe3) and receivers which typically implement both linear equalizers and DFEs. The purpose of all of this equalization capability is to compensate for the frequency dependent attenuation of the channel.

 An example of a channel is shown in the figure above.  A transmitted data signal passing through this channel will experience a different amount of attenuation depending on its frequency content. To understand how signals contain different frequency content we can consider four examples of forty bit data patterns shown in the figure below.

 The data pattern at the top left contains alternating 1010 data, which is the data pattern which has the highest frequency content possible (Note: this is known as Nyquist data). For the case of PCIe3, the frequency content of this signal is 4GHz. (Note: As the signal is shown as a square wave it is actually composed of many frequency components, however this serves as a first order approximation.)  The data pattern at the top right has an alternating 11110000…. pattern, which has a lower frequency content compared with the Nyquist data. The data pattern at the lower left has 20 ‘0’s followed by 20 ‘1’s, which represents the signal with the lowest frequency content we can get with a 40 bit pattern. The data pattern at the lower right is a combination of the lowest frequency data pattern with a lone bit placed in the middle of the low-frequency part of the signal. This combination of low frequency and high frequency content is a challenging pattern, as will be seen. The signals at the output of the channel with a 1V TX launch amplitude are shown below.


Looking at the frequency response of the channel one would expect a large amount of attenuation at high frequency, and indeed looking at the top left eye for the Nyquist data pattern the resulting eye opening at the output of the channel is relatively small. For the eyes at the top right and bottom left it can be seen that lower frequency content results in the large signal amplitude at the top and bottom of the eye, and the eye openings are larger than they were for the Nyquist pattern. At the bottom right we see that the resulting eye opening for lone bit pattern is very small (the small oval at the centre of the eye diagram), much smaller than the eye opening for even the Nyquist pattern.  The effect where different data patterns result in different resulting signal amplitudes (hence different eye diagrams) is known as Inter-Symbol Interference (ISI).

For each of the eye diagrams above well defined trajectories can be seen. The reason for this is that in these data patterns there are only a small number of data patterns, and each data pattern will result in a particular trajectory. However in a random data pattern an almost infinite number of data patterns are present, hence an almost infinite number of trajectories, and these act to essentially fill in the spaces in the eye diagrams shown above. The resulting eye diagram for a random data pattern is shown below.


 An ideal equalizer would perfectly compensate for the frequency dependent attenuation in the channel. If the transfer function of the equalizer was the exact inverse of the channel then the resulting bandwidth of the channel + equalizer would be flat, and thus there would be no ISI. Unfortunately it is not possible to make an ideal equalizer, and hence one is not able to perfectly equalize the channel.

Putting the signal from the above diagram through a simple linear equalizer significantly improve the eye opening, as shown below.

The ISI that remains after equalization is known as residual ISI. The thickness of the fuzz is an indication of how well the equalizer is able to equalize the channel. As the equalization improves, the amount of residual ISI decreases, and when looking at the resulting eye diagram what will be seen is a reduction in the thickness of the fuzz.

For PHYs which operate at high data rates (e.g. PCIe3, 10GBASEKR, CEI11 and above) adaptive equalizers are needed in order to be able to compensate for a wide variety of channels. Adaptive equalizers have many different settings, and in order to select the right one there needs to be some measure of how well a particular equalization setting works. Measuring the thickness of the fuzz is one such figure of merit which can be used to quantify the performance of the equalizer.

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