![On-off keying eye diagram](https://upload.wikimedia.org/wikipedia/commons/d/d4/On-off_keying_eye_diagram.svg)
In
telecommunication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...
, an eye pattern, also known as an eye diagram, is an
oscilloscope
An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
display in which a
digital signal
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at ...
from a receiver is repetitively sampled and applied to the vertical input, while the data rate is used to trigger the horizontal sweep. It is so called because, for several types of coding, the pattern looks like a series of eyes between a pair of rails. It is a tool for the evaluation of the combined effects of channel noise, dispersion and
intersymbol interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
on the performance of a baseband pulse-transmission system. The technique was first used with the
WWII
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
SIGSALY
SIGSALY (also known as the X System, Project X, Ciphony I, and the Green Hornet) was a secure speech system used in World War II for the highest-level Allied communications. It pioneered a number of digital communications concepts, including the ...
secure speech transmission system.
From a mathematical perspective, an eye pattern is a visualization of the
probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
(PDF) of the signal,
modulo the
unit interval
In mathematics, the unit interval is the closed interval , that is, the set of all real numbers that are greater than or equal to 0 and less than or equal to 1. It is often denoted ' (capital letter ). In addition to its role in real analysis, ...
(UI). In other words, it shows the probability of the signal being at each possible voltage across the duration of the UI. Typically a
color ramp is applied to the PDF in order to make small brightness differences easier to visualize.
Several
system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...
performance measurements can be derived by analyzing the display. If the signals are too long, too short, poorly synchronized with the system clock, too high, too low, too
noisy, or too slow to change, or have too much undershoot or
overshoot, this can be observed from the eye diagram. An open eye pattern corresponds to minimal signal
distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
. Distortion of the signal
waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
due to
intersymbol interference
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have a similar effect as noise, thus making ...
and
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
appears as closure of the eye pattern.
Calculation
Source data
The first step of computing an eye pattern is normally to obtain the waveform being analyzed in a quantized form. This may be done by measuring an actual electrical system with an oscilloscope of sufficient bandwidth, or by creating synthetic data with a
circuit simulator in order to evaluate the signal integrity of a proposed design. A combination of the two approaches may be used as well: simulating the effects of an arbitrary circuit or
transmission line
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
on a measured signal, perhaps to determine whether a signal will still be intelligible after passing through a long cable.
Interpolation may also be applied at this time in order to increase the number of samples per UI and produce a smooth, gap-free plot which is more visually appealing and easier to understand.
Slicing
Next, the position of each sample within the UI must be determined. There are several methods for doing this depending on the characteristics of the signal and the capabilities of the oscilloscope and software in use. This step is critically important for accurate visualization of
jitter
In electronics and telecommunications, jitter is the deviation from true periodicity of a presumably periodic signal, often in relation to a reference clock signal. In clock recovery applications it is called timing jitter. Jitter is a significa ...
in the eye.
Triggering
A very simple method of slicing is to set the oscilloscope display to be slightly more than one UI wide, trigger on both rising and falling edges in the signal, and enable display persistence so that all measured waveforms "stack" into a single plot. This has the advantage of being possible on almost any oscilloscope (even fully analog ones) and can provide decent visualization of noise and overall signal shape, but completely destroys the jitter content of the signal since the instrument's trigger re-synchronizes the plot to each UI. The only jitter visible with this method is that of the oscilloscope itself, as well as extremely high frequency jitter (frequencies with period less than the UI).
Fixed rate
A simple way to have the eye pattern display jitter in the signal is to estimate the
symbol rate of the signal (perhaps by counting the average number of zero crossings in a known window of time) and acquiring many UIs in a single oscilloscope capture. The first zero crossing in the capture is located and declared to be the start of the first UI, and the remainder of the waveform is divided into chunks one UI long.
This approach can work adequately for stable signals in which the symbol rate remains exactly the same over time, however inaccuracies in the system mean that some drift is inevitable so it is rarely used in practice. In some protocols, such as
SATA
SATA (Serial AT Attachment) is a computer bus interface that connects host bus adapters to mass storage devices such as hard disk drives, optical drives, and solid-state drives. Serial ATA succeeded the earlier Parallel ATA (PATA) standard to ...
, the symbol rate is intentionally varied by use of
spread spectrum clocking
In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency doma ...
, so assuming a fixed rate will lead to the eye grossly exaggerating the actual jitter present on the signal. (While spread spectrum modulation on a clock is technically jitter in the strict sense, receivers for these systems are designed to track the modulation. The only jitter of interest to a signal integrity engineer is jitter much faster than the modulation rate, which the receiver cannot track effectively.)
Reference clock
With some protocols, such as
HDMI
High-Definition Multimedia Interface (HDMI) is a proprietary audio/video interface for transmitting uncompressed video data and compressed or uncompressed digital audio data from an HDMI-compliant source device, such as a display controller, ...
, a reference clock is supplied along with the signal, either at the symbol rate or at a lower (but synchronized) frequency from which a symbol clock can be reconstructed. Since the actual receiver in the system uses the reference clock to sample the data, using this clock to determine UI boundaries allows the eye pattern to faithfully display the signal as the receiver sees it: only jitter between the signal and the reference clock is displayed.
Clock recovery
Most high speed serial signals, such as
PCIe
PCI Express (Peripheral Component Interconnect Express), officially abbreviated as PCIe or PCI-e, is a high-speed serial computer expansion bus standard, designed to replace the older PCI, PCI-X and AGP bus standards. It is the common ...
,
DisplayPort
DisplayPort (DP) is a digital display interface developed by a consortium of PC and chip manufacturers and standardized by the Video Electronics Standards Association (VESA). It is primarily used to connect a video source to a display device su ...
, and most variants of
Ethernet
Ethernet () is a family of wired computer networking technologies commonly used in local area networks (LAN), metropolitan area networks (MAN) and wide area networks (WAN). It was commercially introduced in 1980 and first standardized in 198 ...
, use a
line code
In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained c ...
which is intended to allow easy
clock recovery
In serial communication of digital data, clock recovery is the process of extracting timing information from a serial data stream itself, allowing the timing of the data in the stream to be accurately determined without separate clock information. ...
by means of a
PLL. Since this is how the actual receiver works, the most accurate way to slice data for the eye pattern is to implement a PLL with the same characteristics in software. Correct PLL configuration allows for the eye to conceal the effects of spread spectrum clocking and other long-term variation in the symbol rate which do not contribute to errors at the receiver, while still displaying higher frequency jitter.
Integration
The samples are then accumulated into a two-dimensional
histogram
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to " bin" (or "bucket") the range of values—that is, divide the ent ...
, with the X axis representing time within the UI and the Y axis representing voltage. This is then
normalized by dividing the value in each histogram bin by the value in the largest bin.
Tone mapping
Tone mapping is a technique used in image processing and computer graphics to map one set of colors to another to approximate the appearance of high-dynamic-range images in a medium that has a more limited dynamic range. Print-outs, CRT or L ...
, logarithmic scaling, or other mathematical transformations may be applied in order to emphasize different portions of the distribution, and a color gradient is applied to the final eye for display.
Large amounts of data may be needed to provide an accurate representation of the signal; tens to hundreds of millions of UIs are frequently used for a single eye pattern. In the example below, the eye using twelve thousand UIs only shows the basic shape of the eye, while the eye using eight million UIs shows far more nuance on the rising and falling edges.
Eye_pattern_2.png, Eye pattern of twelve thousand UIs of a 1.25 Gbit/s signal
Eye_pattern_example.png, Eye pattern of eight million UIs of a 1.25 Gbit/s signal
Modulation
Each form of baseband modulation produces an eye pattern with a unique appearance.
NRZ
The eye pattern of a
NRZ signal should consist of two clearly distinct levels with smooth transitions between them.
MLT-3
The eye pattern of a
MLT-3
MLT-3 encoding (Multi-Level Transmit) is a line code (a signaling method used in a telecommunication system for transmission purposes) that uses three voltage levels. An MLT-3 interface emits less electromagnetic interference and requires less band ...
signal should consist of three clearly distinct levels (nominally -1, 0, +1 from bottom to top). The 0 level should be located at zero volts and the overall shape should be symmetric about the horizontal axis. The +1 and -1 states should have equal amplitude. There should be smooth transitions from the 0 state to the +1 and -1 states, however there should be no direct transitions from the -1 to +1 state.
PAM
The eye pattern of a
PAM signal should consist of N clearly distinct levels (depending on the PAM order, for example PAM-4 should have four levels). The overall shape should be symmetric about the horizontal axis and the spacing of all levels should be uniform.
PSK
Channel effects
Many properties of a
channel
Channel, channels, channeling, etc., may refer to:
Geography
* Channel (geography), in physical geography, a landform consisting of the outline (banks) of the path of a narrow body of water.
Australia
* Channel Country, region of outback Austral ...
can be seen in the eye pattern.
Emphasis
Emphasis applied to a signal produces an additional level for each value of the signal which is higher (for pre-emphasis) or lower (for de-emphasis) than the nominal value.
The eye pattern for a signal with emphasis may be mistaken for that of a PAM signal at first glance, however closer inspection reveals some key differences. Most notably, an emphasized signal has a limited set of legal transitions:
* Strong state to corresponding weak state (1-1 or 0-0 bit pattern)
* Strong state to opposite strong state (second transition of a 1-0-1 or 0-1-0 bit pattern)
* Weak state to opposite strong state (second transition of a 1-1-0 or 0-0-1 bit pattern)
An emphasized signal will never transition from a weak state to the corresponding strong state, a weak state to another weak state, or remain in the same strong state for more than one UI. A PAM signal also normally has equally spaced levels while emphasized levels are normally closer to the nominal signal level.
High-Frequency Loss
Loss of printed circuit board traces and cables increases with frequency due to
dielectric loss
Dielectric loss quantifies a dielectric material's inherent dissipation of electromagnetic energy (e.g. heat). It can be parameterized in terms of either the loss angle ''δ'' or the corresponding loss tangent tan ''δ''. Both refer to the ...
, which causes the channel to behave as a
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...
. The effect of this is an increase in signal rise/fall time. If the data rate is high enough or the channel is lossy enough, the signal may not even reach its full value during a fast 0-1-0 or 1-0-1 transition, and only stabilize after a run of several identical bits. This results in vertical closure of the eye.
The image below shows a 1.25 Gbit/s NRZ signal after passing through a lossy channel - an RG-188 coaxial cable approximately 12 feet (3.65 meters) in length. This channel has loss increasing in a fairly linear fashion from 0.1 dB at DC to 9 dB at 6 GHz.
The top and bottom "rails" of the eye show the final voltage the signal reaches after several consecutive bits with the same value. Since the channel has minimal loss at DC, the maximum signal amplitude is largely unaffected. Looking at the rising edge of the signal (a 0-1 pattern) we can see that the signal starts to level off around -300
ps, but continues to rise slowly over the duration of the UI. At around +300 ps, the signal either begins falling again (a 0-1-0 pattern) or continues rising slowly (an 0-1-1 pattern).
![Eye pattern LPF](https://upload.wikimedia.org/wikipedia/commons/5/51/Eye_pattern_LPF.png)
As high frequency losses increase the overall shape of the eye gradually degrades into a sinusoid (once higher frequency harmonics of the data has been eliminated, all that remains is the fundamental) and decreases in amplitude.
Impedance Mismatches
Stubs, impedance mismatches, and other defects in a transmission line can cause
reflections visible as defects in the edges of the signal. Reflections with a delay greater than one UI often render the eye completely unreadable due to
inter-symbol interference (ISI), however those with a shorter delay can be easily seen in the shape of the eye.
In the image below, a roughly one inch (25.4 mm) open circuited stub is present in the line, causing an initial low-impedance effect (reduced amplitude) followed by a positive reflection from the end of the stub with a delay of about 320 ps or 0.4 UIs. This can be clearly seen as a "step" in the rising edge in which the signal rises to a fraction of the full value, levels off for the round trip delay of the stub, then rises to its full value when the reflection arrives.
![Eye pattern mismatch](https://upload.wikimedia.org/wikipedia/commons/c/cf/Eye_pattern_mismatch.png)
In the image below, an additional three inches of cable is added to the end of the same stub. The same "step" is present but is now four times as long, producing reflections at about 1280 ps or 1.6 UI. This produces extreme ISI (since the reflection of each UI arrives during the subsequent UI) which completely closes the eye.
Measurements
There are many measurements that can be obtained from an eye diagram:
Amplitude measurements
*Eye amplitude
*Eye crossing amplitude
*Eye crossing percentage
*Eye height
*Eye level
*Eye signal-to-noise ratio
*Quality factor
*Vertical eye opening
Time measurements
*Deterministic jitter
*Eye crossing time
*Eye delay
*Eye fall time
*Eye rise time
*Eye width
*Horizontal eye opening
*Peak-to-peak jitter
*Random jitter
*RMS jitter
*CRC jitter
*Total jitter
Interpreting measurements
See also
*
Constellation diagram
A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying. It displays the signal as a two-dimensional ''xy''-plane scatter diagram in the ...
*
Signal integrity
Signal integrity or SI is a set of measures of the quality of an electrical signal. In digital electronics, a stream of binary values is represented by a voltage (or current) waveform. However, digital signals are fundamentally analog in nature, ...
*
Raised-cosine filter The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simp ...
*
Extinction ratio
Notes
References
*
*
External links
* {{cite web
, url = https://www.youtube.com/watch?v=my7CI84le5g
, title = An Eye is Born
, first = Hermann
, last = Ruckerbauer
, website =
YouTube
YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...
Gives an example video of construction of an eye pattern
Understanding Data Eye Diagram Methodology for Analyzing High Speed Digital Signals
Data transmission