In Part 1, Ransom Stephens showed the need for a reflection specification that accounts for equalization, but he never said what ERL actually is; this time he does.

In Part 1, we saw that, at transmission rates over about 30 Gbaud and especially for notoriously noise-limited PAM4 (4-level pulse amplitude modulation) signals, S-parameter mask requirements (**Figure 1**) can’t assure serdes-channel-serdes interoperability. There are too many cases where a channel that fails the template performs just fine in a system with equalization. In particular, decision feedback equalization (DFE) can equalize the effects of reflections that occur within the number of unit intervals (UIs) over which the DFE extends; that is, if the DFE has *N _{b}* taps, then it can equalize reflections over

*N*UIs.

_{b}**Figure 1 (a) Sdd22 or RL(f), and (b) Sdd21 or IL(f) masks for a typical PAM4 28 Gbaud application.**Graphic courtesy of Ransom’s Notes.

The ultimate performance question must be defined with respect to the error ratio which, for PAM4 systems, is symbol error ratio (SER). Effective return loss (ERL) was introduced by Rich Mellitz, a Distinguished Engineer at Samtec, to combine return loss and equalization into a figure of merit that is traceable to SER.

Like channel operating margin (COM), ERL is derived from the pulse response of a channel under specific assumptions about the quality of the transmitted signal. With ERL, we now consider the pulse response’s *reflection*.

Think of a pulse as a long string of NRZ 0s (or PAM4 S0s) followed by a 1 (or a PAM4 S3) followed by another long string of zeros (or PAM4 S0s). The pulse response is the waveform that results from the transmission of a pulse through a channel. The reflected pulse response consists of the combination of all reflections due to a transmitted pulse. It can be calculated from TDR (time domain reflectometry) by using an incident pulse (PTDR) rather than the usual voltage step. The result is PTDR(t), the reflected waveform. PTDR(t) can also be calculated from the channel’s S-parameters.

R_{EFF}(t), the “effective reflection waveform,” is calculated from PTDR(t) by applying time gating multiplied by weighting functions (**Figure 2**). The time gating function is simple: zero prior to signal transmission and one thereafter. Two weighting functions are applied; one eliminates reflections within the *N _{b}* unit interval range of the DFE, and the other accounts for how insertion loss dampens reflections. Both of the weighting functions are only applied over

*N*unit intervals.

_{b}**Figure 2. Top, PTDR(t); middle, R**Courtesy of Samtec.

_{EFF}(t), bottom time gating and weighting function.R_{EFF}(t) is sampled *M* times per UI over *N* UIs resulting in R_{EFF}(*n*, *m*) with a total of *NM* samples.

To calculate the impact of reflections on the SER, R_{EFF}(*n*, *m*) is convolved with a pseudo-random binary sequence quaternary (PRBSQ)—the PAM4 version of the PRBS waveform. The result gives the probability density functions (PDFs) for vertical eye closure caused by reflections. The worst case of the *M* samples in each UI is used in the ERL calculation.

Similar to how COM is calculated, ERL is given by the *ratio of the signal amplitude to the amount of eye closure caused by reflections, defined with respect to a prescribed SER*. The prescribed SER is called the detector error ratio (DER_{0}). Typically DER_{0} = 1E-6 (**Figure 3**).

**Figure 3. Depiction of signal amplitude and eye closure defined with respect to an SER.**Courtesy of Rohde and Schwarz.

The advantage of a requirement like ERL >3 dB rather than S-parameter mask requirements is that ERL incorporates the effects of equalization and S-parameter masks do not. (Hopefully) ERL provides a figure of merit for channels, including transmitter and receiver packages and every potential impedance mismatch in the signal path, that more closely reflects (not punny!) the channel performance of equalized systems.

It’s important to notice that since ERL is a signal-to-noise-like parameter: larger values of ERL correspond to *smaller* amounts of reflection!

*—Ransom Stephens is a technologist, science writer, novelist, and Raiders fan.*

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