Tool · Datacenter optics

PAM4 Eye & TDECQ Explorer

How many decibels of penalty does a PAM4 transmitter’s bandwidth, noise, jitter and level spacing cost, as the conformance test counts them? The explorer synthesizes a PAM4 waveform with those impairments, passes it through the fourth-order Bessel-Thomson reference receiver and a 5-tap feed-forward equalizer, and computes TDECQ from the equalized histograms, showing the eye, the histograms and the tap weights. Background: TDECQ, PAM4, and eye diagram.

Transmitter

Preset

The waveform is normalized: OMA_outer = 1, baud = 1. At 106.25 GBd these shapes correspond to a 200G-per-lane transmitter.

TX bandwidth (× baud)

Gaussian response, 3 dB point. 0.35 to 1.2 times the symbol rate.

Extinction ratio (dB)

Sets the power floor under the eye. OMA stays fixed at 1.

TX noise (% of OMA, RMS)

White Gaussian, added at the receiver input. RIN, amplifier noise, and scope noise all enter this way.

Random jitter (UI, RMS)

Gaussian timing error on every symbol transition.

Level skew (0 to 1)

Pushes the middle levels upward, the way a compressed modulator transfer function does. RLM falls as this rises.

Readouts

The 3.4 dB tag is a representative ceiling: IEEE clauses in the 200G-per-lane generation set TDECQ limits near this value, with the exact number depending on the PMD. Consult the clause for compliance.

Learn with it

Four short experiments. Each sets the controls, asks for a prediction, then shows the result.

The eye · after the reference receiver

Two unit intervals of the waveform after the Bessel-Thomson reference filter, all 2048 symbols overlaid. Dashed horizontals are the measured level means; the amber verticals mark the two histogram phases, 0.047 UI either side of the chosen sampling instant (at 64 samples per UI, the nearest sample to the standard's 0.05 UI).

Equalized histograms · where TDECQ is decided

Amplitude histograms of the equalizer output at the two phases. TDECQ asks: how much Gaussian noise can be poured onto these histograms before the symbol error ratio crosses 4.8 × 10⁻⁴? Dashed lines are the decision thresholds.

Reference equalizer · the five taps

Checked against

These rows run in your browser on every load. The filter and constants are checked in closed form; the TDECQ values are checked against an independent reference implementation of the same procedure, run offline, to a tolerance of 0.01 dB.

Check	Expected	Computed	Tolerance

The table checks the reference receiver filter and the SER target in closed form, and the TDECQ, C_eq and RLM values against an independent reference implementation of the same procedure, run offline. A ± tolerance is the largest absolute difference that still passes, in the units of the Expected column; a percentage is relative to the expected value; “condition” means the Expected entry is itself the test, and “exact” means the outcome must match.

running validation…

The model

TDECQ compares the noise an eye can tolerate with the noise an ideal eye of the same outer OMA could tolerate. The ideal eye, with thresholds midway between four evenly spaced levels, reaches the symbol error ratio target of $4.8 \times 10^{- 4}$ at a Gaussian noise of

σ_{i d e a l} = \frac{O M A}{6 Q_{t}}, Q_{t} = 3.414

For the measured eye the tool fits five T-spaced equalizer taps $c_{i}$ by least squares against the transmitted levels, samples the equalized signal at two instants 3/64 UI either side of the chosen phase, places the decision thresholds midway between the transmitted levels, and bisects for the largest added noise $σ_{G}$ at which the symbol error ratio, averaged over both instants, stays at the target. The added noise passes through the equalizer, so it is scaled by the noise gain $C_{e q}$ :

C_{e q} = \sqrt{\sum_{i} c_{i}^{2}}

T D E C Q = 10 \log_{10} \frac{σ_{i d e a l}}{σ_{G}}

The OMA is measured from the means of symbols whose neighbors carry the same level, and the sampling phase is the one that minimizes TDECQ over a coarse then a fine search. The transmitter is modeled as a Gaussian low-pass filter of adjustable bandwidth, the reference receiver has its 3 dB point at half the symbol rate, and noise is added after both filters. The 5-tap equalizer is the 100G-per-lane reference; P802.3dj specifies 15 feed-forward taps and one decision feedback tap for 200G per lane, and since a longer equalizer can only lower TDECQ, the values here are an upper bound for that receiver. The synthetic waveform is 2048 symbols long, so the result is a model of the procedure rather than a substitute for an oscilloscope measurement.

Worked example

Select the bandwidth-limited preset: transmitter bandwidth 0.45 × baud, 6 dB extinction ratio, no noise, jitter or skew. The measured OMA is 1.000, so $σ_{i d e a l}$ = 1.000 / (6 × 3.414) = 0.0488. The fitted taps are 0.019, −0.161, 1.305, −0.184 and 0.025, giving $C_{e q}$ = 1.328, or 2.46 dB. The bisection settles at $σ_{G}$ = 0.0348, and 10 log₁₀(0.0488 / 0.0348) = 1.47 dB, the TDECQ the readout shows at a sampling phase of −0.016 UI. The clean preset (bandwidth 0.80 × baud) gives 0.67 dB. For reference, the 400GBASE-DR4 transmitter limit in IEEE 802.3 clause 124 is 3.4 dB. The oscilloscope procedure is described in Measuring TDECQ on a PAM4 transmitter.

Related: the datacenter link budget explorer shows the loss, dispersion and power ledgers of a whole link, against which a transmitter penalty of this size is weighed.

References: IEEE Std 802.3-2022, IEEE Standard for Ethernet, clauses 121.8.5 (TDECQ) and 124 (400GBASE-DR4). IEEE P802.3dj, draft amendment for 200 Gb/s per lane operation.