Signal integrity in reflection-limited channels, 2008

 J. F. Buckwalter, "Signal integrity in reflection-limited channels," 2008 IEEE MTT-S International Microwave Symposium Digest, Atlanta, GA, USA, 2008, pp. 1565-1568, doi: 10.1109/MWSYM.2008.4633081.

• This paper analyzes multiple reflections where the channel is a lossy transmission line and the source and load impedance are the main sources of impedance discontinuity.  The paper aims to find an analytic way of quantifying the total ISI. 
• "This work aims to find worst case bounds on the ISI and DDJ caused by reflections" They handle attenuation as a simple factor.
• Did not finish reading paper.  The focus seems to be on finding some simplified equations to estimate the jitter and noise from a simplified channel model.  Interesting but I don't think it is useful to me at this time.

Electrical interconnect potential and limits

B. Casper, "Electrical interconnect potential and limits," 2014 Optical Interconnects Conference, San Diego, CA, USA, 2014, pp. 110-112

• "For system implementations with a fixed power or thermal density budget, power may be the dominant constraint to maximizing bandwidth
• Interesting observation about reported electrical link power consumption vs. optical link power consumption: 
• "A notable aspect of published electrical interconnect energy efficiency calculations is that almost all quotes include the entire power required to transmit and receive data to and from the processor or SoC and tend to include the entire clocking, biases, clock recovery, control, output stage, equalizers, amplifiers, self-test logic, etc. In contrast, many published optical energy efficiencies only include a subset of the overall power required to operate a full link, in some cases only including the output modulation power. 
• "Even with the inclusion of all necessary building blocks, electrical links have demonstrated the ability to achieve better than 1pJ/bit for meter level cable distances"

SI/PI-Database of PCB-Based Interconnects for Machine Learning Applications

 M. Schierholz et al., "SI/PI-Database of PCB-Based Interconnects for Machine Learning Applications," in IEEE Access, vol. 9, pp. 34423-34432, 2021

• A repository of data! What a magnanimous thing to do!
• "Overall 78,961 variations of interconnects are presented. By making this database available we invite other researchers to apply and customize their ML techniques using our results. This provides the possibility to accelerate ML research in EMC engineering without the need to generate expensive data
• "However, [Machine Learning techniques] cannot be easily applied to EMC engineering problems and an adaption to the specific requirements of SI and PI is usually needed [26]–[29]. Mostly this is due to the complex electromagnetic behavior that SI, PI, and EMC problems show, and the difficulty to categorize and describe their three dimensional nature consisting of a wide variety of different components and structures.

Demystifying Machine Learning for Signal and Power Integrity Problems in Packaging

M. Swaminathan, H. M. Torun, H. Yu, J. A. Hejase and W. D. Becker, "Demystifying Machine Learning for Signal and Power Integrity Problems in Packaging," in IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 10, no. 8, pp. 1276-1295, Aug. 2020

• use CNN: convolutional neural network to model frequency responses.
• "NNs are generally overconfident models, meaning that they assume that the predictions they make are always correct. As expected, this can be dangerous. A better approach is to quantify the error in the predictions
• "The CEL uses the Hilbert transform to relate the real and imaginary parts of the S-parameters, whereas the PEL ensures that the singular values of the S-parameters are less than 1 [26], both derived from the domain knowledge on behavior of passive structures. The key to this NN architecture is the feedback loop shown in Fig. 14, where the weights are automatically adjusted as part of the learning process to ensure that the constraints are satisfied while simultaneously minimizing the error in the response.
• CEL = Causality enforcement layer
• PEL= passivity enforcement layer
• H. M. Torun, A. C. Durgun, K. Aygun and M. Swaminathan, "Enforcing causality and passivity of neural network models of broadband S-parameters", Proc. IEEE 28th Conf. Electr. Perform. Electron. Packag. Syst. (EPEPS), pp. 1-3, Oct. 2019.
• Used 550 S-parameters generated from HFSS to train a package PTH model.  Looks pretty nice.
• "A problem with BO is that it does not scale well as the dimensionality increases. In the SI and PI domain, this occurs when all the parameters have both independent and joint effect (coupling) on f (x), which causes the GP surrogate model to require lots more data to identify these effects
• BO= Bayesian optimization
• GP=Gaussian Process
• They address this issue with their proposed method
• "As mentioned earlier, deterministic NNs covered in Section II assume that the predictions made are always accurate. This can be dangerous since uncertainty of the predictions is as important as the predictions themselves and should be accounted for in the model. We call this as uncertainty quantified model development, which is the subject of this section
• I really like this point they keep making.
• " we introduce the concept of simultaneous model building and optimization. Here, the goal is to jointly derive an accurate predictive model over whole sample space while converging to the worst case scenario. 
• "To prioritize finding the worst case scenario due to its importance in SI and PI problems, we introduce a technique called dropout, as shown in Fig. 30
• 
  
  
  
• The example I was waiting for "IV.C Problem 8 - High speed channel signaling"
• Great example of using adaptive sampling to train a Gaussian Process model that predicts the eye height and width.

BER vs. SNR plot

 M. N. Sakib and O. Liboiron-Ladouceur, "A Study of Error Correction Codes for PAM Signals in Data Center Applications," in IEEE Photonics Technology Letters, vol. 25, no. 23, pp. 2274-2277, Dec.1, 2013

• "Using Monte-Carlo and semi-analytical simulations the signal to noise ratio (SNR) requirement of PAM-N is obtained
• The paper is really about exploring the FEC coding gain of optical systems, it would be very interesting to reproduce these results.

Notes from Jitter Methodology OIF-CEI

https://www.oiforum.com/wp-content/uploads/2019/01/OIF-CEI-04.0.pdf

• Method A: interfaces with no Tx or Rx equalization required for an open eye
• CID (Consecutive Identical Digits) jitter tolerance test pattern
• specify a very specific data pattern that tries to "exercise possible weakness in rise and fall time symmetry"
• [72 zeros + 10328 bits from PRBS31 + 72 ones + 10328 bits from PRBS31]
• Regular JTOL test pattern is PRBS31
• Eye Measurements on compliance channel
• "The opening of the eye shall be calculated using Statistical Eye Analysis methods, as per Annex 2.C.5, and confirmed to be within the requirements at the required BER of the Implementation Agreement, usually,
• "Amplitude at the zero time offset sampling point
• "Time jitter measured at the zero amplitude sampling point
• The trouble is, the "offset sampling point" is not defined in section 2.1.2 or Annex 2.C.5, so hopefully it is defined by the standard that references this? Or maybe it is up to the user to specify the 'best' location. This ambiguity may be due to this section is just used to specify the channel compliance and not the system compliance.
• "A sampling point as defined by the reference receiver shall be used" 
• Where is the reference receiver defined?
• See 2.B.9.1 Annex - Receiver Sample Point
• Transmitter Compliance
• Ensure output jitter is within specified limits
• Measure total wander and relative wander
• Receiver Compliance
• Measure BER to be better than specified for a stressed input signal.

• Method B: interfaces where Tx EQ may be used but Rx EQ not required for an open eye at the BER of interest
• Test Pattern: JTOL and Tx output jitter tests use PRBS31
• Channel Compliance the same as method A
• Transmitter Compliance
• Similar to method A but accounts for the inevitable issue of the Tx EQ alone is unable to open the eye.
• Receiver Compliance nearly the same as method A but requires Rx high probability jitter and gaussian jitter injected.
• Method C: interfaces where Tx EQ may be used and requires Rx CTLE EQ for an open eye at a BER level
• channel compliance the same as methods A and B
• Transmitter Compliance seems to be the same as method B
• Receiver Compliance seems very similar to method B but can include crosstalk and other jitter sources.
• Method D: interfaces where Tx EQ may be used and requires DFE EQ for an open eye
•  The compliance sections seem very very similar to method C.
• Method E: interfaces where "simple Rx EQ may be used to improve the margin of the link" for an open eye and "transparent applications may be used"
• What is a "transparent application"????
• Defines a CID jitter tolerance pattern (same as method A).
• Channel compliance
• Same as the others but "Any parameters that have degrees of freedom e.g. filter coefficients, shall be optimised against the amplitude, at the zero phase offset, as generated by the Statistical Eye Output. e.g. by sweeping all degrees of freedom and selecting the parameters giving the maximum amplitude."
• I wonder if this is an accommodation for COM?
• Transmitter Compliance
• discusses "transparent applications" maybe these are repeater units which transparently transfer along any jitter?
• Receiver Compliance
• "transparent application" use the SJ mask for the specific optical standard.
• Carefully calibrate the injected jitter.
• 2.A Annex - Masks
• Total Wander Masks / Relative Wander Masks
• "Total wander specifications should be considered as accumulated low frequency jitter"
• For JTOL testing, wander is considered a SJ source.
• Random Jitter Mask
• specifies a high frequency random jitter spectrum to use to stress CDR.
• 2.B Annex - Pulse Response Channel Modeling
• Generating a pulse response - how to go from frequency to time domain.
• Basic Pulse Response Definitions
• Definition of the cursor location of pulse. Initially they say this location is at the "maximum signal energy" and then later they say the "exact position of c_0 is arbitrary and is defined specifically by the various methodologies."
• Transmitter Pulse Definition
• Nice description of how to calculate how many dB of emphasis a transmitter has.
• Receiver Pulse Response
• This section seems incomplete, it says "the receiver pulse cursors are then defined as follows" but then only provides a figure without explanation.  I think they punted on this one.
• Time Continuous Transverse Filter
• FFE, FIR, Comb structure or Transverse Filter
• Time Continuous Zero-Pole Equalizer adaptation
• CTE with 3 poles and 3 zeros (not sure how this is stable) they use the "Nelder-Mead Multidimensional Unconstrained Non-Linear Minimization Method" to figure out the filter.  Would like more details here, sounds interesting.
• 2.B.9.1 Annex - Receiver Sample Point
• "A receiver shall be allowed to either position the centre sampling point fully independently to the signal transitions or exactly in between the mean crossover of the receiver signal.
• The above is the whole section and is the first definitive description of how to center the clock. 
• 2.C Annex - Jitter Modeling
• Disparages dual Dirac jitter model and instead encourages the "stateye" approach
• "Jitter is defined as the deviation of the signal transition from an origin, usually its mean.
• High Frequency jitter vs. Wander
• Jitter below the CDR bandwidth is wander, jitter above the CDR bandwidth is high frequency jitter.
• Total vs. Relative Wander
• Great description of how to generate SJ with two slightly different frequencies as they beat against each other they generate different types of jitter.  Very helpful.
• The measurements in 2.E.2 and 2.E.3 help as it shows that total wander is measured against an external reference clock and relative wander is measured against an extracted clock.
• Jitter distributions
• "The low probability part of the jitter distribution can be described by two components"
• Unbounded Gaussian distribution function
• Bounded Gaussian distribution function
• "this conversion from BER to Q [using the standard equation] is only valid given a large time offset from the optimal sampling point. . . Any accurate prediction of the BER towards the centre of the eye should be done using Marcum's Q function , and is outside the scope of this document"
• What is Marcum's Q function? https://en.wikipedia.org/wiki/Marcum_Q-function
• Annex - Statistical Eye Methodology
• Great discussion of statistical eye calculation
• 2.D Annex - Definition of CEI Test Patterns
• PRBS31 - uses taps 28 and 31, which unfortunately is not what my prbs.m function uses.
• SSPR - short stress pattern random
• designed to have a baseline wander and timing content that is as stressful as 10,000 years of random binary.  This is sounds like a version of importance sampling.
• uses PRBS28 with taps 25 and 28 with CID (Consecutive Identical Digits) segments interspersed.
• SSPS-16, short stress pattern SDH 16
• "STM-16 framed random binary" so this must be specific to some standard
• This pattern is PRBS28 + CID + various preamble frame patterns.
• SSPS-64: short stress pattern SDH-64 frame
• Hex patterns provided for
• SSPR, SSPS-16, SSPS-64
• 2.E Appendix - Lab Setups
• Define a Golden PLL as "have at maximum a bandwidth of baud rate over 1667, with a maximum of 20dB/dec rolloff, until at least baud rate over 16.67, with no peaking around the corner frequency.
• "The High Probability and Gaussian Jitter components should be extracted from the bathtub measurement using the methodology defined in Annex 2.C.4.6.
• Annex 2.C.4.6 looks very much like dual Dirac method, I wonder what the differences (if any) are.
• Discuss some jitter decomposition methods
• Total Transmit Wander Measurement
• "The peak to peak total wander of the extracted clock should be measured using a scope trigger by the reference clock. The measured peak to peak wander should be verified to be bounded by repeating the measurement for ever increasing periods of time until the measurement is constant.
• Relative Transmit Wander Measurement
• "The peak to peak relative wander between the extracted clocks should be measured using a scope trigger by one of the extracted clocks. The measured peak to peak wander should be verified to be bounded by repeating the measurement for ever increasing periods of time until the measurement is constant.
• Jitter Tolerance
• JTOL test includes injecting total and relative SJ as well as other jitter sources.
• Jitter Transfer Function
• "The peak to peak jitter for a 60 second period measured on the scope should be compared before and after the application of the sinusoidal jitter. The ratio of the difference to the jitter applied is then defined as the jitter transfer function.
• 2.F Appendix - BER Adjustment Methodology
• Extrapolation of correlated bounded Gaussian jitter to low BERs
• If possible use combined spectral and oscilloscope methods to estimate jitter flavors
• methods for determining error of BER estimation