PAM-4 is a signaling technology utilized for high-speed SerDes links over electrical backplanes needing to deliver a data rate of greater than 56 Gbps per lane. Its ability to increase the data rate without having to enhance the hardware channel has significant hardware cost advantages. New transmitter and receiver technologies are already showing viability for PAM-4 end-to-end links. As a result, the technology is now under serious consideration for use in the next-generation OIF and IEEE signaling standards. To fully exploit the advantages of PAM-4 signaling, a new measurement and simulation eco-system must be established and validated.

Understanding the Ecosystem

The PAM-4 ecosystem includes the connecting channel between the transmitter (Tx) and Receiver (Rx). SERDES channel components must be validated for use with this new multi-level signaling. The IEEE and OIF standards provide frequency dependent loss and crosstalk suggestions for Input-Output (IO) connectors and cabling, but no direct correlation to actual eye opening statistics. This can be accomplished with either end-to-end link measurements or channel simulations.

For end-to-end link measurements, PAM-4 signal generation is performed by combining discrete components or using a state-of-art arbitrary waveform generator (AWG). The measurement setup includes a commercially available PAM-4 arbitrary waveform generator, a physical high-speed link assembly and a digital oscilloscope to capture the data. The digital sampling oscilloscope receiver provides a hardware clock and data recovery (CDR), as well as a variety of software equalization techniques (CTLE, DFE, FFE) for opening the eye when making measurements with lossy channels. Measurements by the oscilloscope also include post-processing techniques for basic waveform analysis. Simulation of PAM-4 signals are performed using the IBIS-AMI methodology, with an IBIS-AMI signal generator, an S-parameter channel model and remote access software for receiver data recovery.

This generic PAM-4 end-to-end link is then used to validate the correlation between simulation and measurement. Basic measurements like eye-height, eye-width and bit-error-rate (BER) provide a good starting point for correlation with simulation, although advanced signal-to-noise ratio (SNR) analysis often provides a faster quality check.

The Physical Link

For the purposes of this discussion, a QSFP28 IO connector and cable is used to demonstrate a process for correlating simulations and measurements that validates a component for use within a PAM-4 SERDES channel. The QSFP28 board connector is a quad small form-factor pluggable connector with a bandwidth of 28 Gbps per channel. The physical link under consideration uses a directly attached copper cable. This cable is purely passive, as it does not do any data processing, amplification or equalization of the signals. It just transfers data. The usage of such a cable depends heavily on the full link. The industry standards describe this end-to-end link and give the losses that are permitted within the cable assembly, board connector and module compliance boards (MCBs). Thicker conductor sizes result in lower high-frequency losses and thus, longer cable lengths.

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Figure 1. A QSFP28 end-to-end link employing module compliance boards that is in agreement with industry standards

The end-to-end link or device under test (DUT) used to validate the correlation between simulations and measurements for PAM-4 multi-level signaling is shown in Figure 1. A waveform generator transmits an equalized waveform through the link and an oscilloscope captures the data at the other end, possibly employing additional equalization techniques to achieve open eye diagrams. The employed four-channel twin-pair cable assembly is three meters long and has a 30 AWG conductor size.

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Figure 2. Pin assignment of the measurement setup

On the MCBs, all high-speed 28-Gbps connections are accessible through 2.92-mm connectors. Figure 2 shows the QSFP+ pin numbering for the two Tx to Rx differential pairs used for measurement. This choice allows for far end crosstalk analysis. Figure 3 shows the measured insertion loss curve of just the MCB using a simple through connection that is twice the QSFP28 signal routing trace length. The data shows resonant free behavior that goes beyond 1.5 times the 14-GHz Nyquist clock rate (21 GHz) and validates the PCB material properties and 2.92 mm connectors for this application.

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Figure 3. Insertion loss curve of the through line on the MCB (twice the trace length to the connector)

Measuring DUT Performance

To check the high-speed performance parameters of passive cable assemblies, various types of equipment can be used, such as a Vector Network Analyzer (VNA), Time Domain Reflectometry/Transmissivity (TDR/TDT) or Bit Error Rate Tester (BERT). Each type of equipment, and its underlying measurement technique, has its own advantages and disadvantages.

For this application, the cable assembly is very long compared to the employed data-rate of 28 Gbps. Consequently, high losses will likely be recorded when measuring the DUT. These losses can only be captured by a device with sufficient dynamic range, such as a VNA. A 67-GHz bandwidth VNA was selected to collect the scattering parameters of the link under test. The differential losses for the two pairs (in Figure 2) for the three meter, 30 AWG cable assembly are plotted in Figure 4.

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Figure 4. Differential insertion loss – 3 meter 30 AWG

The S-parameter behavioral data of the channel is stored in a standard Touchstone 1.0 format, which is available on all high-end VNA’s and easily imported into channel simulation tools. The Touchstone file format is an ASCII text file for documenting N-port network parameters of linear devices, such as passive cable assemblies. The exported data file is an s8p file that includes the far-end crosstalk aggressor data. However, for initial validation tests, only a single through channel with all aggressors turned off and paths terminated in 50 ohms is considered. As a result, the file has been reduced to an s4p file for use in the channel simulations.

Simulating PAM-4 Signals

For PAM-4 link simulations, the AMI models used are created to represent Tx and Rx behaviors. Each model consists of analog and algorithmic portions. In the Tx model, the analog part captures the output impedance, and the algorithmic part the Tx equalization. In the Rx model, the analog part captures the input load, and the algorithmic part the Rx equalizations and CDR. For this application, the Tx equalizer is a 3-tap FFE, while the Rx model implements a CTLE, DFE and CDR to represent data processing performed by the oscilloscope.

The Tx analog model, physical channel and Rx analog model are all assumed to be linear, time-independent and can be represented by a combined analog channel impulse response, denoted as hAC. During the simulation, a four-level square wave that represents the PAM-4 stimulus is passed into the Tx algorithmic model. The Tx output signal is convolved with hAC to generate the input to the Rx algorithmic model. The Rx model returns both the equalized signal and the CDR output, which are used to construct the PAM-4 eye and to calculate symbol error rates (SERs). This simulation flow is illustrated in Figure 5.

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Figure 5. PAM-4 IBIS-AMI channel simulation flow

To analyze PAM-4 link performance at different signal levels, SER is calculated for each of the three eyes. For the upper, middle and lower eyes, SER is measured between symbols 3 and 2, 2 and 1, and 1 and 0, respectively. One set of bathtub curves and SER contours is generated for each eye.

Measuring PAM-4 Signals

Now that we understand the measurement setup, the next step is to look at the characterization of a channel component for use in a PAM-4 signaling application. The intent is to validate a measurement set-up that can also be correlated with simulation. This may sound simple, yet all too often the lack of calibration and selection of reference planes makes this task quite challenging at multi-Gigabit data rates. The solution is to leverage both simulations and measurements to cross-check and ensure that both measurement and simulations can be trusted.

The measurement process is illustrated in Figure 6. The first thing to consider is the connection to the DUT, which for our example is the QSFP28 cable assembly including MCBs. A PAM-4 channel will have significant loss at the higher data rates, on top of the lower SNR that comes with the multi-level signals for the same voltage swing. Also, the loss of coaxial cable fixturing to the DUT must be calibrated out. The instrument calibration techniques are utilized to calibrate out the losses of the fixture cables. This eliminates any embedding/de-embedding steps on the simulation side and minimizes the number of variables between simulation and measurement. Mathematically there are robust methods for “de-embedding” the effects of the measurement fixture, but in practice, there are a number of basic sampling theory, domain transformations and tolerance issues that can add to the error terms when comparing simulation with measurement.

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Figure 6. Measurement flow

The next challenge is to verify that the Tx signal used in simulation matches the one used in measurement. Here again, simplicity has significant value. Ideally, one would like a model of the transmitter for use in simulation, however, for PAM-4 this is not a trivial task. PAM-4 is a new technology with proprietary designs and no standardized method of generation. Consequently, few models of actual hardware exist. If a proprietary PAM-4 vendor model is used, there is no guarantee that the channel will behave the same for a different vendor’s model. The PAM-4 Tx signal must also include complex equalization such as a feed forward equalizer (FFE) to compensate for the high losses at Nyquist frequency of PAM-4 signaling and open up the eye at the Rx. Opening the eye at the Rx allows the CDR to lock onto the signal for measurement.

To ensure consistency and flexibility in measurement-simulation correlation for the application in question, the Tx output waveform generated in simulation is saved into a file, loaded onto the AWG and transmitted into the channel for measurement. Using the AWG, this approach not only guarantees the exact same channel input signal as used in measurement and simulation, but also allows the simulation to define a simple IBIS AMI PAM-4 Tx model with a 3 tap FFE applied to the rising and falling edges of the bit pattern. The actual edges of the model can be ideal since this is not an actual device. An external lumped capacitor at the output of the Tx AMI model provides an adjustable rise time.

Simulation uses this simple PAM-4 Tx model to set the rising edge and FFE for the measurement of the QSFP28 cable assembly. The setting of the rise-time must consider a typical value for a given data rate and be within the control of the AWG hardware. Here again, simplicity is the key. Starting with a slow rise time that is well within the control range of the AWG reduces reflections/ringing that are not captured by the simple Tx model used in simulation. The desire is to have the AWG replicate the simulated waveform and not be at the limits of its control. The AWG calibration features are used to calibrate out the fixture cabling and provide the desired waveform at the Rx or oscilloscope in this example. A simple clock pattern can be used to correct the simulation for small differences in rising and falling edge rates, level amplitude, amplitude noise, and random timing jitter.

The next decision is whether to use a real-time oscilloscope or an equivalent time sampling oscilloscope. The real-time oscilloscope can capture the actual voltage versus time waveform at very high sampling rates. This is very helpful when turning on PAM-4 hardware for the first time to capture the waveform to see what equalization is needed, only to realize that the received eye is completely closed. However, at-speed real-time oscilloscopes can be quite expensive when compared to the same bandwidth that a sampling oscilloscope can provide. The sampling oscilloscope requires a repetitive pattern so that it can keep sampling the waveform at different time points with high fidelity to accurately recreate the full pattern. The precision of the equivalent time sampling oscilloscope with its low SNRs and focus on measuring repetitive patterns makes it ideal for characterizing passive channel components and comparing with simulation.

To simplify the correlation of the Rx on the sampling oscilloscope with the Rx in simulation it helps to take advantage of the calibration features of the instrument. Measuring oscilloscopes can be made to emulate a given bandwidth and CDR topology so that a generic Rx AMI model can be used on the simulation side. The oscilloscope can be set to emulate a simple 1st order phase locked loop (PLL) with the loop bandwidth adjusted for a given data rate. At 12.5 Gbps (6.25 GBaud), the loop bandwidth is set to 3.25 MHz. At 25 Gbps, it is set to 7.5 MHz. The receiver bandwidth on the sampling oscilloscope can be set to a 4thorder Bessel for flat group delay to avoid amplitude ripple from the instrument’s bandwidth limits.

Now that the AWG Tx, QSFP28 DUT and equivalent time sampling oscilloscope Rx have been defined, the actual measurement can be performed. Starting with a clean PAM-4 signal with no equalization, it’s determined that the eye is completely closed after the long 3-meter QSFP28 cable, even at the lower data rate of 12.5 Gbps (6.25 GBaud). As a result, equalization must be added for PAM-4 channel testing. Simulation makes it an easy task to optimize a 3 tap FFE for the loss of the QSFP28 cable. This equalized Tx waveform is then downloaded to the AWG and measured on the oscilloscope to verify that the simulated FFE equalized Tx matches the measurement Tx stimulus. Additional adjustments to amplitude settings, noise amplitude and random jitter can be added back into the simulation to account for small differences with the generated waveform.

Next, the calibrated PAM-4 FFE corrected stimulus is connected to the QSFP28 3 meter DUT, as shown in Figure 7, and the desired open eyes are observed at the receiver, both in simulation and measurement. Figure 8 shows the direct comparison of the simulated and measured eye diagrams at the Rx side. Note that simulations and measurements correspond well for this first test case at 12.5 Gbps (6.25 GBaud) with a PRBS7 pattern.

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Figure 7. The simulated Tx stimulus, top left, with a 3 Tap FFE is exported to the AWG to generate the measurement Tx stimulus, bottom left. The signal received after the DUT channel at the oscilloscope Rx on the bottom right is then compared with the simulated Rx top right.

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Figure 8. Waveform at the Rx side including the DUT with 3 tap FFE; measured on Channel 1A (top) and simulated on Channel 2A (bottom)

Finally, the best method of quantifying the correlation between measurement and simulation has to be determined. Traditionally, measured data has always been post processed in the simulation environment; however, modern day instruments now contain state of the art tools for quickly measuring and analyzing captured waveforms. Comparing measurement with simulation on the instrument can provide an instantaneous comparison of measurement with simulation, enabling simulated data to be displayed the same way a final pass/fail measurement might be in production.

From here it is a simple task to use the measurement eye width and eye height settings to compare simulation with measurement. This simulation to measurement correlation at the slower data rate verifies the methodology and ensures that it can be applied to the desired higher data rates and increasing channel losses.

The ability to simulate an FFE corrected waveform on the simulation side and then use this exact waveform generated by an AWG on the measurement side provides excellent measurement to simulation correlation for a PAM-4 SERDES channel. The key to success with this process is to start simple, ensuring that variables between simulation and measurement are minimized. Even the data rates are lowered to verify the methodology. Then, data rates can be increased and additional equalization added to compensate for the higher losses. By analyzing the generic instrument generation and measurement case for a PAM-4 end-to-end link, engineers should now have a clearer understanding of the critical elements for correlating simulations with measurements for multi-level signaling.