# Tim’s Blackboard #4: Your Channel, PRBS and the Eye

Blog Post created by Tim Wang Lee on Jul 12, 2017

Welcome to Tim’s Blackboard! This is the place to find discussions on interesting topics related to signal integrity and power integrity.

This week on Tim’s Blackboard is “Your Channel, PRBS and the Eye.”

# Introduction

Previously on Tim’s Blackboard, we showed the convolution process and the helpful single pulse response. This week, we will extend the previously learned single pulse response (SPR) to explore Pseudo-Random Bit Sequence (PRBS) and the eye diagram, see Fig. 1.

Fig. 1: Left: A Pseudo-Random Bit Sequence. Right: An Eye Diagram.

# What the Single Pulse Is Not Telling Us

Although the single pulse response gives us information on how a single pulse reacts to the channel under test, it does not tell us how previous pulses affect the shape of the current pulse.

In an ideal world, where the channel does not distort the signal with its frequency-dependent loss, the shape of each pulse is not dependent on other pulses. However, since we live in the real world, we often observe Inter-Symbol Interference (ISI) caused by rise time degradation, a consequence of frequency-dependent loss.

Shown in Fig. 2 is the ADS simulation result of two different patterns followed by a single pulse pattern: 01000. After going through a channel with considerable frequency-dependent loss, the single pulse waveform comes after a string of one’s is not the same as the single pulse waveform comes after a string of zero’s. Because the previous symbols-string of one's-is interfering with the single pulse pattern, the voltage that is representing zero increased from 0 V to almost 0.3 V. If we are not careful, this increase would cause false triggering in the receiver.

Fig. 2: Shown in ADS, the shape of the single pulse depends on the pattern before the pulse.

To add, although the single pulse response is helpful, it is rare for one to transmit or receive only a single pulse in practical high speed digital applications. Normally, the data pattern consists of different combinations of one’s and zero’s that we do not know a priori.

To mimic different data patterns and to characterize the level of ISI introduced by the channel, the Pseudo-Random Bit Sequence was born.

# PRBS Pattern and the Channel

Shown in Fig. 3 is an example of PRBS. As the name suggests, the Pseudo-Random Bit Sequence is a sequence of one’s and zero’s that are independent of each other. The randomness provided by PRBS gives us some ideas on how the channel affects transmitted digital data.

Fig. 3: Example of a PRBS pattern at the transmitter side before going through the channel.

Much like the single pulse response, the response of the channel to PRBS is the convolution of the PRBS pattern and the impulse response of the channel.

From the single pulse response, we learned that after going through the channel, the sharp zero-to-one transition of a single pulse becomes a slower rising curve at the beginning. Also, the single pulse gains a longer tail (all thanks to frequency-dependent loss, which we will discuss in the future). In the same way, we should expect the received PRBS pattern to not have a sharp transition between the zero’s and one’s.

Fig. 4: After going through the channel, the sharp transition edges of the original PRBS pattern become slower rising and falling curves.

Fig. 4 shows the PRBS pattern after going through the channel. As expected, after going through the channel, the sharp transition between zero’s and one’s are reduced by the channel impulse response.

# Eye Diagram: The Comprehensive Version of PRBS

Although PRBS gives us an idea on how the channel affects digital data pattern, the information is scattered throughout a large time scale. It is hard to come up with a figure of merit to describe the quality of the channel by looking at data that goes on and on in time.

To create a better representation of the channel, we can manipulate the received PRBS waveform using our knowledge of the data coming in.

For example, if we are sending data at 10 Gbps, we know the unit interval (UI) of each bit is 0.1 nsec. Using our knowledge of the UI, we can “slice” the long received PRBS waveform and examine the waveform one UI at a time. Now, because we are also interested in the transition from one bit to another, we increase our observation window to 2 UI’s, corresponding to half of an UI before and half an UI after the current bit.

Fig. 5: Three example time slices of a received PRBS waveform. The data rate is 10 Gbps, corresponding to 0.1 nsec UI. To observe the bit transitions, the observation window is extended to 0.2 nsec.

Shown in Fig. 5 are example “slices” of the received PRBS waveform. The eye diagram, which is the comprehensive version of the received PRBS waveform, is constructed by overlaying these observed partial waveforms on top of each other, as demonstrated in Fig. 6.

Fig. 6: Illustration of overlaying the three slices of PRBS waveform shown in Fig. 5 to create an eye diagram.

By combining many of these time slices, an eye diagram is formed. The resulting eye diagram for the example channel is shown in Fig. 7. According to the eye diagram, one would say the example channel is a good one because of the clear eye opening. With a clear eye opening, the receiver is able to distinguish the two different voltage levels at 100 psec.

Fig. 7: The eye diagram result of the channel shows an open eye. The receiver can easily tell the high voltage level from low voltage level if a decision is made at 100 psec.

To further specify the quality of the channel, one can now quote the vertical amplitude measurements of an eye (eye height, eye level, etc.) and/or the horizontal timing measurement of an eye such as jitter or eye width.

# How to Deal with a Closed Eye?

Although the example gives us a pretty clean and open eye, it is unlikely to always find such a pristine channel in practice. You are more likely to find a channel with an eye that looks like the one shown in Fig. 8.

Fig. 8: A channel that has an almost closed eye.

To deal with a closed eye, we will need to first find the root cause for the eye closure. We will do that in the next post!

That's this week's Tim's Blackboard. See you in two weeks!