Senior Project Proposal Micron Contact Tim Hollis thollismicron

What would Micron like? Windows/Unix compatible tool for implementing Worst-Case and Statistical Link Analysis.

Market Driven Trends SPEED, CAPACITY, FORM-FACTOR, POWER, COST ⇔ SIGNAL INTEGRITY 11/27/2020 © 2008

Digital Chip-to-Chip Communication 11/27/2020 Micron Confidential

Typical High-Speed Memory Interface Controller Data Serializer Channel Driver Memory Capture De-serializer Data[0: 7]

The Eye Diagram Bit-stream Voltage Time Bits Superimposed 1 Unit Interval (UI) 11/27/2020 ©

The Eye Diagram (Noise) Bit-stream Voltage Noise Time Voltage Time Bits Superimposed 1 Unit

The Eye Diagram (Jitter) Bit-stream Voltage Time Jitter Voltage Time Bits Superimposed 1 Unit

The “Real” Eye Diagram Data Jitter Clock Jitter Signal Noise Vref Noise + Receiver

Signals are Still Analog • Understanding the analog nature of the digital signals being

Digital Signals contain Many Analog Signals (Fourier Series) First Harmonic Triangle Wave Construction Square

Digital Signals contain Many Analog Signals (Fourier Series) First + Third Harmonics Triangle Wave

Digital Signals contain Many Analog Signals (Fourier Series) First + Third + Fifth Harmonics

Digital Signals contain Many Analog Signals (Fourier Series) 50 Accumulated Harmonics Triangle Wave Construction

Components of a Single Digital Signal Amplitude Distortion Components of a Single Digital Signal

Chip-to-Chip Signal Degradation 6 inches 2 Gbps Gb/s 1 5 Gb/s 10 Gb/s 11/27/2020

Chip-to-Chip Signal Degradation T 1 T 2 P 3 P 1 P 2 Inter-symbol

Signal Degradation leads to Communication Errors M i c r o n 11/27/2020 ©

Handling Communication Errors • Because it’s theoretically impossible to communicate without errors indefinitely, a

Pulse-Response-based Link Analysis Methods 11/27/2020 Micron Confidential

Pulse Response Analysis • Most emerging analysis methods are based on the information contained

Worst-Case Link Verification 11/27/2020 Micron Confidential

Worst Case Eye (Peak Distortion Analysis) 1 UI J. G. Proakis, “Digital Communication”, Mc.

Worst Case Eye WC 1 WC 2 WC 3 ISI Only x. Talk DBI

Statistical Link Verification 11/27/2020 Micron Confidential

What is a PDF (probability density function)? If Gaussian Distribution: µ = mean s

Calculating Probability from the PDF voltage/time a b • Describes the probability of encountering

Error due to Voltage Uncertainty Ideal ONE Ideal ZERO 11/27/2020 © 2008 Micron Technology,

Error due to Voltage Uncertainty 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved.

Error due to Timing Uncertainty 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved.

Error due to Timing Uncertainty * Complete * integration leads to Bathtub curves 11/27/2020

Bathtub Curves Eye Height 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. Eye

Statistical Analysis (Deriving a 3 D Bathtub) Recursively convolve 1 UI sample terms assuming

Error due to simultaneous Voltage and Timing Uncertainty Probabilistic Data Eye VREF Sample Voltage

Computing Bit Error Ratio Sampling Uncertainty Distribution Sam Vo lt ag e e Tim

Statistical Eye built from Step Statistical Eye built from Transient 10 x All figures

Correct Jitter Modeling Bit transitions convolved with channel step response = received transitions, no

Who’s working on this? • Intel: First to publish • AMD: Has an internally

What would Micron like? Project Deliverables 11/27/2020 Micron Confidential

Resources B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis

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Senior Project Proposal Micron Contact: Tim Hollis thollis@micron. com 11/27/2020 208 -363 -3944 Micron Confidential © 2008 Micron Technology, Inc. All rights reserved. Products are warranted only to meet Micron’s production data sheet specifications. Information, products and/or specifications are subject to change without notice. All information is provided on an “AS IS” basis without warranties of any kind. Dates are estimates only. Drawings not to scale. Micron and the Micron logo are trademarks of Micron Technology, Inc. All other trademarks are the property of their respective owners.

What would Micron like? Windows/Unix compatible tool for implementing Worst-Case and Statistical Link Analysis. Deliverables: • • Compiled GUI to run without Matlab license Tool should: 4 Read in several data formats (ADS, Hspice, etc. ) and allow the user to request Worst-Case or Statistical Analysis. 4 Provide visualization of resulting data eye 4 Allow for multiple sources of co-channel interference 4 Allow for user defined TX and RX jitter • • The worst-case tool should output a pass/fail based on a user-defined sampling window • • • Extra: The statistical tool should output a BER based on a user-defined sampling uncertainty distribution Be able to incorporate a user-defined TX FIR filter and/or RX DFE Tool could output a worst-case pattern, based on the pulse response, for use in time domain simulation Analysis of the impact of nonlinearity and driver asymmetry Consider how to add simultaneous switching output noise (SSO) Be able to justify all decisions 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 2 Micron Confidential

Digital Chip-to-Chip Communication 11/27/2020 Micron Confidential

Typical High-Speed Memory Interface Controller Data Serializer Channel Driver Memory Capture De-serializer Data[0: 7] Data Driver Capture De-serializer Serializer CLK Timing Adjustment Driver 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. Reference Clock 5 Micron Confidential

The “Real” Eye Diagram Data Jitter Clock Jitter Signal Noise Vref Noise + Receiver Sensitivity Vref Data Signal Clock Signal 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 9 Micron Confidential

Signals are Still Analog • Understanding the analog nature of the digital signals being communicated helps explain the degradation of the signals at high speeds. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 10 Micron Confidential

Digital Signals contain Many Analog Signals (Fourier Series) First Harmonic Triangle Wave Construction Square Wave Construction 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 11 Micron Confidential

Digital Signals contain Many Analog Signals (Fourier Series) First + Third Harmonics Triangle Wave Construction Square Wave Construction 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 12 Micron Confidential

Digital Signals contain Many Analog Signals (Fourier Series) First + Third + Fifth Harmonics Triangle Wave Construction Square Wave Construction 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 13 Micron Confidential

Digital Signals contain Many Analog Signals (Fourier Series) 50 Accumulated Harmonics Triangle Wave Construction Square Wave Construction 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 14 Micron Confidential

Components of a Single Digital Signal Amplitude Distortion Components of a Single Digital Signal Impact of Channel on Analog Signals Phase Distortion 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 15 Micron Confidential

Handling Communication Errors • Because it’s theoretically impossible to communicate without errors indefinitely, a certain number of errors per a given number of transmitted bits is specified: 4 Bit-Error-Rate (Ratio) = # Errors / # Bits Transmitted • Usually spec’d below 1 / 1, 000, 000 4 Requires simulating more than 1, 000, 000 cycles to verify. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 19 Micron Confidential

Pulse-Response-based Link Analysis Methods 11/27/2020 Micron Confidential

Pulse Response Analysis • Most emerging analysis methods are based on the information contained in the system pulse response(s). 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 21 Micron Confidential

Worst-Case Link Verification 11/27/2020 Micron Confidential

Worst Case Eye (Peak Distortion Analysis) 1 UI J. G. Proakis, “Digital Communication”, Mc. Graw-Hill, 3 rd Ed. , 1995. B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis method for multi-Gb/s chip-to-chip signaling schemes”, in Digest of Technical Papers from the IEEE Symposium on VLSI Circuits, June 2002, pp. 54– 57. © 2008 Micron Technology, Inc. All rights reserved. Micron Confidential 11/27/2020 23

Statistical Link Verification 11/27/2020 Micron Confidential

What is a PDF (probability density function)? If Gaussian Distribution: µ = mean s 2= variance 1 = rms value voltage/time • Describes the probability of encountering a sample (noise/jitter) at a specific voltage/time. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 27 Micron Confidential

Calculating Probability from the PDF voltage/time a b • Describes the probability of encountering a sample (noise/jitter) at a specific voltage/time. • Because the total area under the PDF integrates to 1, the probability that a sample will fall between two values requires integrating the function over the range between the values of interest. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 28 Micron Confidential

Statistical Analysis (Deriving a 3 D Bathtub) Recursively convolve 1 UI sample terms assuming equal probability of a transmitted ‘ 0’ or ‘ 1’ 1 UI [0 -0. 01] [0 0. 59] [0 -0. 07] [0 0. 015] [0 0. 055] [0 0. 2] 0. 59 [0 0. 5] 0. 0 [0 0] [0 0. 7] Each step scaled by ½ to account for P(0) = P(1) 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 34 Micron Confidential y(t)

Error due to simultaneous Voltage and Timing Uncertainty Probabilistic Data Eye VREF Sample Voltage Probability of Error ts Sam ple Vo lt ag e e Tim e l p Sam 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. Sample Time 35 Micron Confidential

Computing Bit Error Ratio Sampling Uncertainty Distribution Sam Vo lt ag e e Tim e l p Sam BER EYE Sam ple Vo lta ge pl Sam e im e. T 2 D integration provides BER value Error Rate ple Sampling Probability of Error Probabilistic Data Eye Vo lta e ge m Ti B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis method for multi-Gb/s chip-to-chip signaling scheme”, in Digest of Technical Papers from the IEEE Symposium on VLSI Circuits, June 2002, pp. 54– 57. © 2008 Micron Technology, Inc. All rights reserved. Micron Confidential 11/27/2020 36

Statistical Eye built from Step Statistical Eye built from Transient 10 x All figures correspond to 350 received bits. (50 W) Results are almost identical Transient Eye Vout Linear Driver Vin © 2008 Micron Technology, Inc. All rights reserved. Micron Confidential 11/27/2020 37

Correct Jitter Modeling Bit transitions convolved with channel step response = received transitions, no jitter “Jittered” bit transitions convolved with channel impulse response = channel-effected TX jitter Bit transitions convolved with channel impulse response, then “jittered” = RX jitter * Not implemented correctly in existing tools * P. K. Hanumolu, B. K. Casper, R. Mooney, G. Y. Wei, and U. K. Moon, “Jitter in high-speed serial and parallel links”, in Proceedings of the IEEE International Symposium on Circuits and Systems, May 2004, pp. 425– 428. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 38 Micron Confidential

Who’s working on this? • Intel: First to publish • AMD: Has an internally developed tool • Stat. Eye. Org: Open-source code with several contributors • Agilent: Has wrapped Stat. Eye code into their Ptolemy tool. • Ansoft: Has wrapped Stat. Eye code (Verif. Eye) and a variant (Quick. Eye) into their Designer tool. • Mentor Graphics: Has implemented a non-convolution based approach called Fast. Eye within their Hyper. Lynx tool. • Synopsys (Hspice): Currently in development. • Tools available for purchase are limited in flexibility (multi-trace analysis, etc. ) and vendors do not completely understand the assumptions. 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 39 Micron Confidential

What would Micron like? Project Deliverables 11/27/2020 Micron Confidential

Resources B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis method for multi-Gb/s chip-to-chip signaling scheme”, in Digest of Technical Papers from the IEEE Symposium on VLSI Circuits, June 2002, pp. 54– 57. B. K. Casper , G. Balamurugan, J. E. Jaussi, J. Kennedy, M. Mansuri, “Future microprocessor interfaces: Analysis, design and optimization”, in Proceedings of the IEEE Custom Integrated Circuits Conference, Sept. 2007, pp. 479 -486. P. K. Hanumolu, B. K. Casper, R. Mooney, G. Y. Wei, and U. K. Moon, “Jitter in high-speed serial and parallel links”, in Proceedings of the IEEE International Symposium on Circuits and Systems, May 2004, pp. 425– 428. www. stateye. org 11/27/2020 © 2008 Micron Technology, Inc. All rights reserved. 42 Micron Confidential