Eye Diagram

The eye diagram is a powerful oscilloscope-based measurement technique used to visually assess the quality of a baseband digital signal after it passes through a communication channel. By superimposing many successive symbol intervals on a single display, the eye diagram reveals the combined effect of ISI, noise, timing jitter, and bandwidth limitations in a single intuitive picture.

How the Eye Diagram Is Generated

To construct an eye diagram, the received waveform after filtering is fed into an oscilloscope that is triggered at the symbol rate 1/T. The oscilloscope repeatedly overlays segments of the waveform, each exactly one or two symbol periods long, on the same display. After many traces are overlaid, the resulting pattern forms an eye-shaped opening in the centre of the display.

The shape of the eye opening directly reflects the signal quality. A wide open eye indicates that ISI and noise are small, providing a large margin for the decision threshold. A partially closed or fully closed eye indicates severe ISI or noise that will result in high bit error rates. Engineers use the eye diagram as a first-line diagnostic tool because it integrates all impairments into one visual display.

Parameters Extracted from Eye Diagram

The vertical opening of the eye at the optimal sampling instant is called the eye height or eye amplitude. This directly represents the noise margin: the maximum noise amplitude that can be tolerated before a decision error occurs. If the eye height is H and the total signal swing is S, the normalised noise margin is H/S.

The horizontal opening of the eye is called the eye width. It represents the time interval within which sampling can occur without ISI-induced errors. A wide eye width means the system is tolerant of clock timing errors and jitter. The narrowing of the eye width is a direct measurement of jitter, which is the variation in zero-crossing times of the signal transitions.

The eye crossing percentage or crossing level is the vertical position of signal transitions. Ideally it is at 50 percent of the signal swing. Any deviation indicates a waveform asymmetry. The slope of the eye transitions reflects the rise and fall time of the filtered pulses, which depends on the channel and filter bandwidth.

Mathematical Relationship to ISI and BER

The eye opening is directly related to the worst-case ISI contribution. If the pulse response at the receiver has values p(0) = 1 at the sampling instant and nonzero values at other sampling points, the ISI penalty reduces the effective eye opening. The worst-case eye closure in a binary system is 2 * (sum of |p(kT)| for k not equal to 0). A fully closed eye means this sum equals or exceeds p(0), making error-free detection impossible.

For an AWGN channel with raised cosine pulse shaping (no ISI), the BER for binary signaling is Q(sqrt(2*Eb/N0)). With ISI, the effective SNR at the sampler is reduced by the eye closure, so BER degrades even at the same transmit power. This is why ISI is described as creating an error floor independent of SNR.

Given:
Received signal swing (peak to peak) = 2.0 V
Eye opening (vertical, at optimal sampling instant) = 1.4 V
Jitter width (horizontal eye narrowing) = 0.15 T

Why this formula applies:
Noise margin percentage = (eye height / signal swing) * 100
Timing margin percentage = (eye width / T) * 100

Formula:
Noise margin % = (Eye_height / Signal_swing) * 100
Timing margin % = (1 - Jitter/T) * 100

Substitution:
Noise margin % = (1.4 / 2.0) * 100
Timing margin % = (1 - 0.15) * 100

Calculation:
Noise margin % = 70%
Timing margin % = 85%

Final Answer:
Noise margin = 70% of signal swing, meaning significant ISI/noise headroom remains.
Timing margin = 85%, indicating the system can tolerate up to 0.425 T/2 of clock error.

Exam Tip: A fully closed eye diagram implies BER = 0.5 regardless of SNR increase. GATE questions may ask what parameter of the eye diagram directly measures noise margin (eye height) versus jitter tolerance (eye width). Do not confuse the two.

Quick Revision

• Eye diagram is formed by overlaying multiple symbol-period segments of the received waveform on an oscilloscope triggered at symbol rate.
• Eye height (vertical opening) = noise margin. Larger eye height means the signal can tolerate more noise before decision errors.
• Eye width (horizontal opening) = timing margin. Wider eye width means the system tolerates more clock jitter.
• ISI causes eye closure in both vertical and horizontal dimensions simultaneously.
• A completely closed eye means error-free reception is impossible regardless of how much power is added.
• GATE trap: eye opening is measured at the optimal sampling instant, not at any arbitrary time point.
• Crossing level deviation from 50% indicates pulse asymmetry; slope of transitions indicates bandwidth or rise-time limitations.