1. Taking Measurement Bandwidth into Consideration for High Speed Serial Data
When measuring high speed serial data signals and devices, whether for compliance, for design, or for troubleshooting purposes, measurement bandwidth is an important concern. The measuring oscilloscope can have a large or small bandwidth relative to the signal’s frequency content. What is the correct bandwidth for particular standard? And how has this relationship changed with recent standards?
Here we’ll review the rationale for prescribing the measurement bandwidth, and how that rationale has evolved with the latest standards.
Basic spectral properties of a high-speed serial data signal (Figure 1) show characteristic lobes of energy at the odd harmonics of the signal. The fundamental (1st harmonic) is at ½ of the fBaud, where fBaud is the frequency that numerical equals to the symbol rate of the signal, e.g., for a signal at 53 GBd the fBaud is 53 GHz; and the Nyquist frequency, fNyquist, is at ½ of 53 GHz.
The signal of the Device Under Test or DUT (blue) is clearly rolling off quickly, and no usable energy beyond the 2nd harmonic is visible. This is a desired characteristic for signaling at 10s of GBd: high speed energy much past fNyquist is not important to the transfer of information: the electrical channel will suppress it anyway; furthermore, it might cause additional undesirable crosstalk. Finally, an attempt at recovery of the highly suppressed energy would be too noisy and would generate a higher error rate than a receiver design that rolls off soon after the necessary minimum, i.e., the Nyquist frequency.
In contrast, a high-speed laboratory signal source (green) might have higher lobes of energy. Yet this too is academic – this source is overdesigned, it will generate too much past the typical DUT transmitter (Tx), and its energy won’t even propagate into the DUT except with extremely high-speed connectors and cables.
Figure 1. Basic Spectral Properties of an Amplitude Modulated Signal; also shown is the response of a Bessel-Thomson 4th order filter (in red) with bandwidth matching the fNyquist i.e., 0.5 * fBaud as used for PAM4 reference filters.
As mentioned, the BERT signal (green trace example in Figure 1) is extreme in its richness of high frequency energy many times past Nyquist frequency. But since that energy is there, do we need to measure it?
Over the time, various standards have wrestled with this question and established rules for recommending the correct bandwidth. By way of an example, we will use IEEE 802.3 wired / fiber-based signaling to discuss this.
The development of a required measurement bandwidth in the high speed electrical IEEE 802.3 standards is shown in Figure 2 and Figure 3; please note the time range (in years) is approximate.
Figure 2. Bandwidth for Measurement of Electrical Standards, over Time (Approximate Time Schedule)
Figure 3. Bandwidth for Measurement of Optical Standards, over Time (Approximate Time Schedule)
The comparison shows clearly that the measurement bandwidth is decreasing over time: why?
The electrical signal (from the Tx to the Receiver or Rx) today is more bandwidth-limited by the media – the lossy channel over which the signal is propagating – than it used to be in the NRZ (PAM2 NRZ) signals. Note that the size of the eye is now, in PAM4 signaling, only about 1/3 of the whole amplitude swing.
It’s also interesting that in optical signaling the measurement bandwidth has been significantly slower – relative to electrical media – for quite a few years. Let us see why.
2. Why Measurement Bandwidth Has Decreased over Time
In older, simpler systems, the signal from the transmitter is not exposed to a large loss in the channel. The receiver can recover the reasonably open eye directly or with just a light equalization. See Figure 4.
Figure 4. Simple Electrical Link; Note the Far-End Eye Is Still Mostly Opened
In contrast, complex systems operating at a higher channel loss over f/fBaud are recovering a very small signal past the Nyquist frequency; significant effort has to be applied, and the eye will typically not open without a large amount of RF gain. However, a large RF gain spells trouble in the form of noise amplification – and noise causes errors in transmission.
Figure 5. Complex Electrical Link; Note the Far-End Eye Is Still Fully Closed (3rd from Right)
As the more complex transmission system (Figure 5) has to perform complex equalization, i.e., equalization with more gain, that system must also filter out most of the noise found at high frequencies, i.e., frequencies above Nyquist. This rapid bandwidth limiting improves noise performance when the transmission channel is highly lossy.
3. Relationship of DUT Receiver Bandwidth to Measurement Bandwidth
The guiding philosophy for measurement bandwidth is that the measurement should observe only a slightly larger spectral window than the DUT receiver.
In simpler systems as were used in the past, this was often implied by the 5th harmonic, rule. In today’s more complex systems, where (as shown above) the channel exhibits a large loss (as a fraction of f/fBaud), the DUT Rx has to severely limit high frequency noise by rolling off more sharply. This will be somewhat approximated in the measurement system by lowering the measurement bandwidth, e.g., to 3rd harmonic range.
3.1. The Role of 4th Order Bessel-Thomson System
Another consideration is that since the newest – e.g., PAM4 – systems operate with highly noise limited data recovery, it is imperative that the measurement device’s roll-off doesn’t present artifacts into the time-domain view of the signal. The low-pass filter built into an oscilloscope therefore has to be without ringing or large overshoot in time domain. For this reason, a 4th order Bessel-Thomson filter is mandated by the standards. This is a filter design optimized for smooth phase response and smooth voltage transition. Besides specifying the filter, the standard also mandates that this filter has to be followed past the -3 dB point, i.e., if a 40 GHz Bessel-Thomson 4th order filter is specified, it does not mean that a 40 GHz DUT oscilloscope is usable; in fact, even a 50 GHz oscilloscope will not be complaint to the standard because the beneficial Bessel-Thomson roll-off would be truncated too soon.
See Figure 1, red trace, for a Bessel-Thomson 4th order filter matching the signals signaling rate (-3dB at fNyquist, as in typical PAM4 standard. Observe how little energy remains after the effect of both the signal roll-off combined with the red-line Bessel-Thomson 4 filter.
What does this mean for today’s standards?
4. Fastest Standards in 2021 / 2022
Electrical standards. The expectation is that IEEE 802.3ck is finishing one of the fastest practical electrical standard, with data throughput of 100 Gb/s per lane, with variants such as the 400GBASE-CR4 or 400GBASE-KR4 or 400GAUI-4, in 2021, and with final ratification likely in mid-2022. The signaling symbol rate of these standards is 53.125 GBd, hence the Nyquist frequency of the signal is 25.5625 GHz.
It is expected that the standard will mandate an oscilloscope measurement bandwidth of 40 GHz bandwidth (i.e., -3 dB) Bessel-Thomson filter of 4th order with the end of controlled roll-off at around 55 GHz. Such acquisition will be fast enough to capture the majority of the signal and its potential fidelity problems while not compromising the SNR of the measured signal with excess bandwidth beyond what is implemented in the DUT receivers.
The OIF-CEI standard uses the same concepts but uses a slightly different filter. We’ll discuss that in a future post.
Optical standards. The measurement of optical signal using PAM4 signaling, aka Optical Direct Detect PAM4 NRZ, has been established for several years now as part of the IEEE 802.3bs effort behind the 400GBASE-DR4 standard. In optical signaling, the considerations for receiver bandwidth are different from those of electrical signaling present in, for example, IEEE 802.3ck. At 53 GBd the optical signal in a single mode fiber experiences relatively little bandwidth roll-off (relative to electrical channels), and for this reason the equalization process is simpler, and there is less impact from reflections on short links, so the optical receiver will not be severely affected by such reflections. Due to these link properties the measurement bandwidth mandated by the optical standards is at only 0.5*fBaud, i.e., at the Nyquist frequency, as measured on the electrical side of the receiver.
This turns out to be a Bessel-Thomson filter with bandwidth electrical of 26.5625 GHz for 53 GBd signals; in typical single mode systems, the end of controlled roll-off is just past 60 GHz.
Why is there – in optical standards – a difference in bandwidth electrical and bandwidth optical? The optical-to-electrical conversion in an optical receiver squares the power relationship between the optical and the electrical side; therefore, the optical bandwidth is different – higher – than the electrical bandwidth. (The bandwidth is at a fraction of full power; the square-law of a typical O/E changes that ratio.) The optical bandwidth is not used to specify the relationship between the Bessel-Thomson filter and the Nyquist frequency.
In some case the optical link is stressed for capacity “at any cost” in electronics (e.g., very expensive links, such as submarine links between continents). The whole design – including the signal roll-off – is then dominated by concerns for spectral efficiency and much sharper roll-off of transmitter energy and of the measurement tools applies.
Conclusion
The bandwidth for measurements in high speed serial data systems is lower (as a fraction of symbol rate) for higher speed standards than it used to be in less equalized standards of the past. This development simply confirms the design tradeoffs that the link designers have to make today. The measurements are performed with bandwidth of around at the 0.5 * fBaud, rolling off in a time-domain friendly way of the 4th order Bessel-Thomson filter in most standards. A slightly faster roll-off is likely in the future.