Keysight Technologies IBIS-AMI Based Link Analysis of Realistic 56G PAM4 Channels

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1 Keysight Technologies IBIS-AMI Based Link Analysis of Realistic 56G PAM4 Channels White Paper This white paper was first published at DesignCon in January, Reprinted with permission from DesignCon. This information is subject to change without notice. Keysight Technologies, 2016 Published in USA, January 27, EN

2 DesignCon 2016 IBIS-AMI Based Link Analysis of Realistic 56G PAM4 Channels Bob Miller, Avago Technologies Minh Quach, Avago Technologies Bob Elsheimer, Avago Technologies Cathy Liu, Avago Technologies Fangyi Rao, Keysight Technologies

3 Abstract In this paper we report results of IBIS-AMI based link analyses of realistic 56G PAM4 channels. Systems under investigation are represented by channel S-parameters and SerDes AMI models that capture actual chip designs, including impedance, equalizations and embedded tuning. 4-level timedomain input waveforms are processed by Tx and Rx models, which return output waveforms along with sampling times and slicer thresholds. Eye diagram and SER are calculated individually for each eye to measure link performance. Results of upper, center and lower eyes at various data rates are presented. Crosstalk and jitter impacts are investigated. Authors Biography Bob Miller is a 36-year veteran of the Fort Collins, CO ASIC design lab, originally of Hewlett- Packard then Agilent and now Avago Technologies, where he has contributed to the architecture, modelling, design methodology and low-level circuit design of CPU subsystems, IEEE floating point processors, graphics co-processors, networking and other ASICS. While serving as a designer in Avago's SerDes design team he began the company's customer-facing AMI modeling effort for its SerDes designs. He currently is the technical lead in the company's AMI modeling team. Bob received his BSEE in 1977 and his MSEE in 1979 from Virginia Tech. Minh Quach is a Signal Integrity Engineer at Avago Technologies. Minh is presently working on high speed system analysis and simulations. Minh received a BS degree from Oregon State University. Bob Elsheimer has worked for the past 7 years in the areas of SerDes equalization circuit modeling, analysis of channels with regards to equalization, and development of Avago internal tools for analysis of NRZ and PAM4 signals and eyes. Bob has previous experience in the design and manufacturing IC's for fiber-optic transievers, optical and capacitive navigation, and optocouplers. Bob received a BS (1986) and MS (1987) in electrical engineering from the University of Michigan in Ann Arbor, and a BA (1986) from Wheaton College in Wheaton, Illinois. Cathy Ye Liu, the technical director, currently heads up Avago Technologies SerDes architecture and modeling group. Previously she worked as R&D director and distinguished engineer in LSI Corporation which was acquired by Avago Technologies in Since 2002, she has been working on high speed SerDes solutions. Previously she has developed read channel and mobile digital TV receiver solutions. She received her B.S. degree in Electronic Engineering from Tsinghua University, China, in 1995 and received her M.S. and Ph.D. degrees in Electrical Engineering from University of Hawaii in 1997 and 1999, respectively. Her technical interests are signal processing, FEC, and modeling in high-speed SerDes. Fangyi Rao is a master R&D engineer at Keysight Technologies. He received his Ph.D. degree in theoretical physics from Northwestern University in He joined Agilent/Keysight EEsof in 2006 and works on Analog/RF and SI simulation technologies in ADS. From 2003 to 2006 he was with Cadence Design Systems, where he developed SpectreRF Harmonic Balance technology and perturbation analysis for nonlinear circuits. Prior to 2003 he worked in the areas of EM simulation, nonlinear device modeling, and medical imaging.

4 1. Introduction In communication system, pulse-amplitude modulation (PAM) is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. Two-level PAM also known as NRZ or PAM2 has been used in serial link system for decades. Recently, to increase the system bandwidth, multi-level PAM modulation such as four-level PAM4 becomes valued. Figure 1 shows signaling format of NRZ (left) and PAM4 (right) modulation. PAM4 signaling has two bits per symbol which results in reducing the symbol rate by half compared with NRZ. Figure 2 plots a few TEC example channels [1] to be considered as 100G and 400G Ethernet systems [2] [3]. In general 35dB is a reference number of channel loss that SerDes can operate within reasonable power and complexity. From Figure 2 we can see that for NRZ case only the channel shorter than 30 trace length and with better material megtron-6 has insertion loss less than 35dB while PAM4 can support channels up to 42 with megtron-6 or 30 with legacy material nulco4000. Recently through deploying 400G systems based upon optical modules of 8-bit wide interfaces operating at up to 56 Gb/s, PAM4 modulation is now adopted as the signaling format for several CEI-56G interfaces, like CEI-56G-VSR-PAM4 [4], CEI-56G-MR-PAM4 [5], and CEI- 56G-LR-PAM4 [6] and IEEE P802.3bs 400 Gb/s Ethernet CDAUI-8 chip-to-chip interface [3]. However, on the other side, the cost of bandwidth reduction is the SNR degradation by level separation from one big eye to three small eyes. If combining both amplitude and jitter impact due to the inter-level interference, we can see from Figure 1 that each PAM4 eye is much smaller than 1/3 of NRZ eye. Level separation loss must be offset by following areas to achieve low BER performance: Large dynamic and linearity range Powerful equalization capability Good tuning and optimization Reduced jitter and noise impairments Forward Error Correction (FEC) The detailed design technologies of those improvements are beyond the scope of this paper. In this paper we will first focus on PAM4 AMI modeling methodology of signaling, SerDes Tx and Rx model consideration, and system performance analysis. Then we will show the PAM4 simulation results of IBIS-AMI based link analyses of realistic 56G channels and comparison with NRZ mode.

5 Figure 1. Signaling formats of NRZ and PAM4 modulation Figure 2. Example channel models for 100G Ethernet and 400G Ethernet system 2. IBIS-AMI Modeling for PAM4 Signaling PAM4 Reserved parameters IBIS-AMI support for PAM4 signaling and channel analysis was defined in BIRD175 and ratified and included in IBIS 6.1 [7]. It provides for relatively seamless extension of familiar NRZ modeling and analysis techniques to support realistic and accurate PAM4 channel analysis. When the PAM4 Reserved_Parameter Modulation is set to PAM4, the EDA tool 1) uses AMI_Init impulse information to create PAM4 eyes and metrics, 2) subdivides the normal [ ] AMI_GetWave input stimulus into four levels [ ], and 3) establishes sample times and thresholds for BER calculations using the six PAM4 Rx Reserved_Parameters PAM4_[Upper Center Lower]EyeOffset and PAM4_[Upper Center Lower]Threshold. An additional parameter, PAM4_Mapping, enables the use of specific mappings of the PAM4 two-bit symbols to the intended PAM4 voltage level. PAM4 Tx AMI Model considerations Adapting an NRZ Tx AMI model to accept PAM4 stimulus and present PAM4 signaling to the channel is almost trivially simple if the model is essentially linear as many realistic Tx NRZ models are. Assuming the model is composed of a tap-controlled linear FFE, output-shaping linear filtering and a LTI analog model describing the output impedance characteristics, one need only add the Modulation parameter the model's AMI Reserved_Parameters and set it to PAM4. Otherwise, unless there are specific PAM4-influenced impairments within the model, that's the entire recipe for conversion. Of course the actual hardware implementation may be a bit more involved, and the

6 actual PAM4-enabled design will almost certainly have altered performance characteristics which require the model's linear components to be appropriately adjusted. But nothing in the Tx model's overall structure need change merely to enable it to function as a PAM4 model. PAM4 Rx AMI Model considerations While the Tx adaptation can be a trivial matter, the Rx presents a few more challenges. First, just as in the Tx, the Rx's analog front-end components, if present, can generally be used unmodified (except as the desired equalization space is modified by PAM4 equalization considerations). However, in addition to the Modulation switch, the Rx model must implement and understand the Threshold and EyeOffset parameters. Understanding these parameters implies replacement of the typical NRZ model's decision node slicer with a trio of upper center lower slicers, each slicer's threshold linked to its respective PAM4_[Upper Center Lower]Threshold parameter and timing offset relative to the recovered clock linked to PAM4_[Upper Center Lower]EyeOffset. The three logic values produced by these three slicers represent a thermometer-encoded PAM4 symbol which can either be used directly or encoded into a four-level data stream for use in recovered-data-controlled components such as DFE equalization or DC recovery modules. These downstream modules may themselves require adaptation for PAM4 or may be almost trivially utilized, depending on their original coding architecture and level of abstraction from actual gatelevel components. An additional complexity to the Rx model adaptation is clock recovery. While specific details of the adaptation of an NRZ model's CDR are hugely dependent on the details of the hardware the model's CDR is emulating, in general the CDR must utilize PAM4 recovered edge and data symbols and gate its phase detection appropriately. One simple scheme, detecting phase of only symmetrical inter-symbol transitions, should require only minor enhancements to the NRZ model's existing CDR if, as in the other recovered-data-driven components, the level of abstraction is already fairly significant. Finally, embedded tuning algorithms, if present, must be expanded to accommodate PAM4 signaling. In particular, the thresholds (and offsets if used) must be correctly set to resolve PAM4 data. The typical correlation engine driving DFE tuning must also be expanded to understand and correctly correlate PAM4 data. Adapting the tuning algorithms is probably the most time-intensive part of NRZ-to-PAM4 model conversion. PAM4 AMI_Init (statistical flow) EDA considerations When running a PAM4 statistical analysis, the EDA tool does not need to do anything differently in the channel analysis simulation flow than it does in classic NRZ analysis. This is because the multilevel signaling is abstracted away in the impulse-driven simulation. The amplitude of the impulse is defined to represent to the model the lowest-to-highest-level signaling amplitude, and if the model executable performs any conversion to true time-domain PAM4 signaling internally in AMI_Init, it does so based on this definition. After the received (decision-node) impulse is returned to the EDA platform for post-simulation analysis and processing, the EDA tool also understands this convention and performs the equivalent of convolving this impulse with infinitely-long string of random PAM4 {-0.5, , 0.166, 0.5} data symbols instead of NRZ [-0.5, 0.5} symbols to generate the statistical PDF to analyze and post-process.

7 It is important for the end user to understand that the statistical flow assumes strict LTI behavior of the Tx and Rx in this mathematical post-processing. And non-linearity is a major impairment to PAM4 channel performance, producing such effects as time-skewing and compression of the outer eyes relative to the inner eyes. None of this behavior will be apparent in the statistical eyes produced by linear manipulation of the AMI_Init impulse into statistical PDFs. PAM4 AMI_GetWave (bit-by-bit flow) EDA considerations When running a PAM4 bit-by-bit (time-domain) analysis, the EDA tool must present the correct PAM4 signaling to the Tx model, using the encoding scheme specified by PAM4_Mapping and preserve the Tx's resultant signaling through the channel convolution into the Rx model. The resultant Rx model waveform must be understood and post-processed into eye diagrams, BER calculations, bathtubs, etc. based on this and the PAM4_Offset and PAM4_Threshold parameters as returned and possibly modified by the models if they provide initial or adaptive tuning support. Unlike the statistical (AMI_Init) simulation, in the GetWave simulation the EDA platform can construct the eye PDF and bathtub curves from a time-domain response which can capture all nonlinear effects, including voltage compression and time-skewing of upper/lower eyes relative to the center eye. Under these conditions, the correct slicer trio s sample time alignment can be communicated by the combination of the model s returned clock_times and PAM4_Upper Center LowerEyeOffset parameters to provide accurate CDR and sample time alignment. Adaptive tracking of sample times and thresholds is also possible if the model implements adaptive tuning of these parameters in GetWave. 3. SER Measurement on PAM4 Eyes Output of the Rx model, including waveform v(t), upper slicer threshold V U (t), center slicer threshold V C (t), lower slicer threshold V L (t), clock times t clk (n), upper slicer sample time offset t U (n), center slicer sample time offset t C (n), and lower slicer sample time offset t L (n), are used to calculate symbol error rates (SER). To analyze PAM4 link performance at different signal levels, SER is measured at each of the three slicers by constructing three individual eye diagrams for upper, center and lower eyes. The upper eye is generated with waveform segments of expected level 2 and level 3 symbols, denoted as v 2 (t) and v 3 (t), respectively. The center eye is generated with v 1 (t) and v 2 (t), and the lower eye v 0 (t) and v 1 (t), where v 0 (t) and v 1 (t) are waveform segments of expected level 0 and level 1 symbols, respectively. To construct the three PAM4 eyes, their centers need to be determined. Recall that in the NRZ case the horizontal eye center is placed at the slicer sampling times t clk (n)+ui/2 in order to capture the Rx CDR jitter. The vertical eye center is placed at the slicer threshold, which is always 0V for the NRZ differential signal. This approach can be adopted in PAM4 by centering the upper eye at the upper slicer sampling times t clk (n)+ t U (n)+ui/2 and the upper threshold V U (t), the center eye at the center slicer sampling times t clk (n)+ t C (n)+ui/2 and the center threshold V C (t), and the lower eye at the lower slicer sampling times t clk (n)+ t L (n)+ui/2 and the lower threshold V L (t). In particular, to center the upper eye vertically with a time-varying upper slicer threshold, V U (t) is subtracted from v 2 (t) and v 3 (t). The resulting waveform segments, v 2 (t)-v U (t) and v 3 (t)-v U (t), are sampled within the UI starting at t clk (n)+ t U (n) to construct the upper eye, capturing the upper slicer sampling jitter. Similarly, the center eye is constructed by sampling v 1 (t)-v C (t) and v 2 (t)-v C (t) within the UI starting at t clk (n)+ t C (n), and the lower eye by sampling v 0 (t)-v L (t) and v 1 (t)-v L (t) within the UI starting at t clk (n)+ t L (n). This procedure is described in Table 1.

8 One set of bathtub curves and SER contours is calculated for each of the above mentioned PAM4 eyes. Note that the center of each resulting timing bathtub represents the sampling times of the corresponding slicer. Eye Traces Horizontal eye center Upper v 2 (t)-v U (t) and v 3 (t)-v U (t) t clk (n)+ t U (n)+ui/2 Center v 1 (t)-v C (t) and v 2 (t)-v C (t) t clk (n)+ t C (n)+ui/2 Lower v 0 (t)-v L (t) and v 1 (t)-v L (t) t clk (n)+ t L (n)+ui/2 Table 1. Procedure of PAM4 eye construction for SER calculations.

9 4. Simulation Results of Realistic PAM4 Channels In this section, PAM4 considerations for horizontal and vertical bathtubs will be discussed based on bit-by-bit simulation results of 10 6 PRBS31 bits. The effect of system impairments such as linearity, jitter, and crosstalk on the horizontal and vertical bathtubs and eye margin will also be investigated. A comparison of PAM4 versus NRZ (PAM2) with regards to eyes and bathtubs will be presented. Below is a typical AMI simulation schematic. Figure 3: AMI simulation schematic 56Gbps (28Gbaud) PAM4 Analysis Three channels are used in the investigation. The insertion loss (IL) and the return loss (RL) of channel 1 are plotted in Figs. 4 and 5, respectively. At 14GHz the IL is about 24dB. IL and RL of the other two channels are similar to those of channel 1. The crosstalk transfer functions of three channels are plotted in Fig. 6. As indicated in Fig. 6, the crosstalk effect increases from channel 1 to channel 3. Figure 4: PAM4 victim channel 1 insertion loss

10 Figure 5: PAM4 victim channel 1 return loss Figure 6: PAM4 aggressor channel 1-3 transfer functions Results for a baseline simulation in channel 1 at 56Gbps with PAM4 modulation is shown below in Figs. 7, 8 and 9. The baseline simulation has no Tx jitter, no crosstalk, and has optimized Rx equalization settings which includes minimizing any non-linearity in the Rx equalization path. The three eyes appear to have good symmetry and have similar margin versus BER. Note that compared to NRZ, the PAM4 vertical margin without system impairments has been reduced by 3X and the horizontal margin similarly by 2X. A system with Rx bandwidth at Nyquist, and having no ISI, jitter, crosstalk, and having perfect linearity can have a horizontal margin no greater than 0.5UI, as illustrated in Fig 1 due to inter-level interference.

11 Figure 7: 56Gbps (28Gbaud) baseline PAM4 simulated eye density (PDF) Figure 8: 56Gbps (28Gbaud) baseline simulated horizontal bathtubs Figure 9: 56Gbps (28Gbaud) baseline simulated vertical bathtubs

12 Effect of SerDes Rx Circuit Linearity The linear range of an amplifier is the signal range within which gain vs. signal level is constant, and linear methods are valid for analysis of signals (pulse response, step response, transformations). When signals exceed the linear range for an amplifier, signal compression occurs. In NRZ signal compression caused distortion of the upper and lower portions of the eye. Signal compression in NRZ occurs with large signal swings and therefore large eyes. Thus, the penalty for compression compared to the eye opening in NRZ was small. In PAM4, signal compression causes inner transitions (level1 to level2 for example) to behave differently than outer transitions (level0 to level3 or level0 to level1 for example). Linear methods are no longer valid, and the outer eyes are compromised in terms of eye opening and achievable BER. Figs 10 and 11 show the eye diagram and vertical bathtubs, respectively, with significant gain nonlinearity being introduced. Compared to Figs 7 and 9, the outer eyes are compressed, and their BER floors increase to 1e-6 from 1e-14. Meanwhile, the nonlinear impact on the center eye is minor. Signal compression in the SerDes Rx is usually a function of the Tx and Rx equalization settings. Tx equalization settings affecting launch amplitude can be used to keep the Rx signal path linear. Similarly Rx equalization settings affecting Rx block to block amplitudes can be used to maintain linearity. The SerDes tuning algorithm needs to take the effects of non-linear behavior into account. Figure 10: 56Gbps (28Gbaud) PAM4 eye density with nonlinear gain compression

13 Figure 11: 56Gbps (28Gbaud) PAM4 vertical bathtub with nonlinear gain compression

14 Effect of Jitter and Crosstalk on PAM4 Eyes and Bathtubs Figure 12 shows the effect of jitter and crosstalk on the PAM4 vertical bathtubs. The red curve in Fig. 12 is the simulation results with no jitter and no crosstalk. The blue curve adds Tx jitter. The red and blue bathtubs are offset at high BER (Q=4-6), but the slope at lower BER (Q>6) is similar between the cases. Addition of crosstalk (pink line) causes the slope of the overall bathtubs to decrease, especially at low BER (Q>6). Figure 12: 56Gbps (28Gbaud) PAM4 jitter and crosstalk effects on vertical bathtub Simulation results at 56Gbps (28Gbaud) PAM4 are shown below in Figs for the cases of Tx jitter and increasing crosstalk. As Tx jitter is added to the simulation, the minimum achievable BER is increased from 1e-14 to 3e-11 (vertical bathtub for the top eye). As crosstalk=1mv rms, 2mV rms, and 4.3mV rms, the minimum achievable BER continues to increase as shown in Table 2. Figure 13: Channel 1 results for 56Gbps (28Gbaud) PAM4 with Tx jitter

15 Figure 14: Channel 1 results for 56Gbps (28Gbaud) PAM4 with Tx jitter and crosstalk=1mv rms Figure 15: Channel 2 results for 56Gbps (28Gbaud) PAM4 with Tx jitter and crosstalk=2mv rms Figure 16: Channel 3 results for 56Gbps (28Gbaud) PAM4 with Tx jitter and crosstalk=4.3mv rms A summary of the vertical eye margin at BER=1e-6 (Veye@1e-6) and the minimum achievable BER across all three PAM4 eyes is shown in Table 3 for 56Gbps (28Gbaud). Without crosstalk, The Tx jitter reduces the vertical margin by about 40mV in each channel, but all eyes remain open at BER=1e-6. With both Tx jitter and crosstalk, only the channel with the least crosstalk has open eyes at BER=1e-6, while eyes in the other two channels are close. The crosstalk amounts per

16 Vertical Eye Opening (mv pkpk) Horizontal Eye Opening (UI pkpk) channel number are: Channel 1 crosstalk=1mv rms, Channel 2 crosstalk=2mv rms, Channel 3 crosstalk=4.3mv rms. The associated crosstalk transfer curves are shown in Fig. 6. Channel No jitter or Crosstalk Jitter Only Jitter + Crosstalk Veye@1e-6 mv pkpk Min BER Veye@1e-6 mv pkpk Min BER Veye@1e-6 mv pkpk Min BER e e e e e-8 0 2e e e-9 0 1e-4 Table 3: 56Gbps (28Gbaud) PAM4 vertical eye margin and minimum BER across all PAM4 eyes NRZ Limitations and Effect of Jitter and Crosstalk on Eyes and Bathtubs To compare the maximum operating data rate between PAM4 and NRZ, NRZ mode is also simulated. The channel 1 vertical and horizontal eye opening data at BER=1e-12 in Fig. 17 below shows the limitations of NRZ modulations in terms of signaling rate (34Gbits/second in this case). At 36Gbps the eye is closed as the vertical and horizontal margins at BER=1e-12 are less than 0mv and 0UI, respectively. Veye@e-12 Heye@e Veye@e Heye@e-12 Data Rate (Bits/Second) Data Rate (Bits/Second) Figure 17: NRZ vertical and horizontal margins versus data rate To study the jitter and noise sensitivity of NRZ mode as well, the same symbol rate of 28Gbps is applied to NRZ mode. The 28Gbps NRZ horizontal and vertical bathtub results in Figs show the decrease in eye margin with increasing jitter and crosstalk. The red curves are simulation results with no Tx jitter and no crosstalk. The blue curves are results with Tx jitter and no crosstalk. The pink curves are results with both Tx jitter and crosstalk. Note that similarly to PAM4 the addition of Tx jitter shifts the bathtubs starting at high BER (1e-4) but preserves the slope at low BER (<1e-12). Addition of crosstalk reduces the slope at low BER (<1e-12).

17 Figure 18: 28Gbps NRZ bathtub results with Tx jitter and crosstalk=1mv rms Figure 19: 28Gbps NRZ bathtub results with Tx jitter and crosstalk=2mv rms Figure 20: 28Gbps NRZ bathtub results with Tx jitter and crosstalk=4.3mv rms

18 Table 4 shows a summary of the NRZ results for horizontal and vertical margin at BER=1e-12 and 28Gbps versus jitter and crosstalk. Horizontal Eye Margin from the Bathtub Channel Heye@1e-12 No jitter and No Crosstalk (UI) Heye@1e-12 Jitter Only (UI) Heye@1e-12 Jitter + Crosstalk (UI) Vertical Eye Margin from the Bathtub Channel Veye@1e-12 No jitter and No Crosstalk (mv pkpk) Veye@1e-12 Jitter Only (mv pkpk) Veye@1e-12 Jitter + Crosstalk (mv pkpk) Table 4: 28Gbps NRZ eye margin results at BER=1e-12 vs jitter and crosstalk Table 5 compares Veye degradation caused by jitter and crosstalk in the 56Gbps PAM4 at BER=1e- 6 and in the 28Gbps NRZ at BER=1e-12. Channel Veye Degradation with Tx Jitter (mv pkpk) from No Jitter or Crosstalk Veye Degradation with Crosstalk (mv pkpk) from Tx Jitter Only NRZ@1e-12 PAM4@1e-6 NRZ@1e-12 PAM4@1e ~ >46 Table 5: Vertical Eye degradation with jitter and crosstalk

19 5. Conclusion In this paper, link performance of realistic 56G PAM4 channels is investigated with AMI simulations. The AMI models capture PAM4 SerDes behaviors such as analog front end, equalization, CDR and nonlinearity. The channels are represented by S-parameters. The results show that at 56Gbps (28Gbaud) the system is able to compensate long reach channel loss and open the eyes at BER=1e-6. SerDes nonlinearity is found to compress the outer eyes and have minor impact on the center eye. Tx jitter and crosstalk are shown to degrade the eye opens. As a comparison, NRZ signaling is also simulated, and the results indicate that it can only support data rate up to 34Gbps in the same channels.

20 References [1] TEC channels submitted to IEEE P802.3bj task force, [2] IEEE P802.3bj /D3.2, Draft Standard for Ethernet Amendment 2: Physical Layer Specifications and Management Parameters for 100 Gb/s Operation Over Backplanes and Copper Cables [3] IEEE P802.3bs 400 Gb/s Ethernet Task Force, [4] CEI-56G-VSR-PAM-4 baseline text proposal, oif [5] CEI-56G-MR-PAM-4 baseline text proposal, oif [6] CEI-56G-LR-PAM-4 baseline text proposal, oif [7] IBIS Spec 6.0

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