Peak Distortion ISI Analysis Bryan Casper Circuits Research Lab Intel® Corporation April 15, 2017

Peak Distortion Analysis Agenda Properties of a Linear Time-invariant System (LTI) Margin calculation method (voltage and timing) Worst-case eye opening calculation methods Worst-case eye with crosstalk Complete Peak Distortion equations Compare worst-case eye w/ random data eye, lone 1 or 0 eye, sine wave eye Peak Distortion Analysis April 15, 2017

Properties of a Linear Time-invariant System FFT Impulse response Frequency response Convolution Superposition Peak Distortion Analysis April 15, 2017

LTI property: Equivalence of Time and Frequency Domain Insertion loss S parameters (complex) FFT Impulse response Insertion loss S parameters (Magnitude and phase) Peak Distortion Analysis April 15, 2017

LTI property: Convolution Tx symbol (mirror) Impulse response Pulse response Peak Distortion Analysis April 15, 2017

LTI property: Superposition In Out Pulse response Tx symbol …000010000000… Peak Distortion Analysis April 15, 2017

LTI property: Superposition of symbols In Out Tx symbol …000010011100… Response to pattern 100111 Peak Distortion Analysis April 15, 2017

LTI property: Superposition of coupled symbols In Out FEXT Pulse response Tx symbol …000010000000… Peak Distortion Analysis April 15, 2017

LTI property: Superposition of coupled symbols In Out Tx symbol …000011111100… FEXT response Peak Distortion Analysis April 15, 2017

LTI property: Superposition of coupled symbols Tx symbol …000011111100… Out FEXT response Peak Distortion Analysis April 15, 2017

LTI property: Superposition of coupled symbols Out Tx symbol …000010011100… Insertion loss response Peak Distortion Analysis April 15, 2017

LTI property: Superposition of coupled symbols Tx symbol …000011111100… Out Tx symbol …000010011100… FEXT response Insertion loss response Composite response Peak Distortion Analysis April 15, 2017

Max data rate calculation method Determine maximum value of all sample timing uncertainty (not including ISI) Transmitter and receiver sampling jitter Clock vs. Data skew Determine maximum value of all voltage uncertainty (not including ISI) Power supply noise*PSRR Common mode noise*CMRR Thermal noise Comparator sensitivity Comparator offset Determine worst-case eye 1. Most noise sources can be characterized as being bounded. However, thermal noise is gaussian and has an infinite peak amplitude. However, gaussian noise peak amplitude can be considered as bounded within a certain probability. For example, a gaussian source with 1mV of rms noise will exceed 10mV with a probability of 10E-21 (practically speaking, this is an infinitely small chance) Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Margin Calculation Ideal sampling position Timing skew Jitter Voltage Noise and required comparator input Voltage offset Ideal reference point Peak Distortion Analysis April 15, 2017

Margin Calculation (zoomed) Ideal sampling position Timing skew Jitter Voltage offset Voltage Noise and required comparator input Voltage margin Time margin 1. To determine the maximum data rate, increase the symbol rate until the margins approach 0. Peak Distortion Analysis April 15, 2017

Worst-case eye calculation Eye diagrams are generally calculated empirically Convolve random data with pulse response of channel Pulse response is derived by convolving the impulse reponse with the transmitted symbol For eye diagrams to represent the worst-case, a large set of random data must be used Low probability of hitting worst case data transitions Computationally inefficient An analytical method of producing the worst-case eye diagram exists Computationally efficient algorithm Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Reference Peak distortion analysis of ISI has been used for many years J. G. Proakis, Digital Communications, 3rd ed., Singapore: McGraw-Hill, 1995, pp. 602-603 (not much detailed info here) Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Interconnect Model Point to point differential desktop topology 10” μstrip Differential, edge-coupled microstrip (10” @ 55Ω) socket 2 Sockets pkg 2 Packages (2” @ 45Ω) 1pF pad capacitance 50Ω single-ended termination Peak Distortion Analysis April 15, 2017

Differential S Parameters Peak Distortion Analysis April 15, 2017

Eye diagram (100 bits @5Gb/s) This eye is a single-ended representation of a differential eye. Explain the process of constructing eye (S->IFFT>H(t)>random data Peak Distortion Analysis April 15, 2017

Eye diagram (1000 bits @5Gb/s) Random data eye (100 bits) --- Random data eye (1000 bits) --- This eye is a single-ended representation of a differential eye. The problem with generating an empirical eye diagram is that it doesn’t accurately represent the worst-case eye without running millions (or billions) of bits of random data. This is computationally difficult. Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Sample pulse response ISI+ ISI- Precursor is previous bit time Postcursor is next bit time after cursor precursor cursor postcursor Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Step response 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Worst-case 0 0 1 1 0 1 0 0 1 0 0 0 0 0 Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Worst-case 1 0 1 0 1 1 0 0 0 0 0 Peak Distortion Analysis April 15, 2017

How to find worst-case patterns 1 1 0 1 0 0 1 Worst-case 1  0 0 1 0 1 1 0 Peak Distortion Analysis April 15, 2017

Ideal reference placement 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 Peak Distortion Analysis April 15, 2017

Worst-case Received Voltage Difference (RVD) for WC1 Reference Peak Distortion Analysis April 15, 2017

Worst-case Received Voltage Difference (RVD) for WC0 Reference Worst-case 0 Peak Distortion Analysis April 15, 2017

Worst-case Received Voltage Difference (RVD) 16 -3 4 2 -1 Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis 5Gb/s Pulse Response Differential output swing is 1V. Peak Distortion Analysis April 15, 2017

5Gb/s Response due to worst-case data pattern Differential output swing is 1V. Peak Distortion Analysis April 15, 2017

Worst-case data response Lone 1 Worst-case 1 Differential output swing is 1V. Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Worst-case data eye Differential output swing is 1V. Peak Distortion Analysis April 15, 2017

WC response vs Random response 1. This is the worst-case eye only at the cursor point. To determine the worst-case eye shape, it is best to apply the worst case RVD equation across the entire eye. WC eye for cursor point only 100 symbols random data eye 1000 symbols random data eye Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis 5Gb/s WC eye shape Precursor Cursor Postcursor Emphasize the difference in calculation Peak Distortion Analysis April 15, 2017

WC eye vs random data eye WC eye shape 100 symbols random data eye 1000 symbols random data eye Peak Distortion Analysis April 15, 2017

Co-channel Interference 1 2 3 4 5 6 12 Port 7 8 9 10 11 12 Attacking differential pairs FEXT NEXT ECHO Victim differential pair Peak Distortion Analysis April 15, 2017

Pulse responses (differential) Peak Distortion Analysis April 15, 2017

WC RVD w/ Co-channel Interference Take out N Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Random data eye w/ FEXT Peak Distortion Analysis April 15, 2017

Random data eye w/ & w/o FEXT Random data eye w/ FEXT --- Random data eye w/o FEXT --- Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis WC eye w/ & w/o FEXT Random data eye --- WC eye w/o FEXT … WC eye w FEXT … Random data eye --- WC eye w FEXT … Peak Distortion Analysis April 15, 2017

Complete Peak Distortion Equations Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Definitions y(t) is the pulse response of the interconnect T is the symbol period s1 is the eye edge due to a worst case 1 Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Example pulse response Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 1 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 0 eye edge due to ISI Remove y(t) Peak Distortion Analysis April 15, 2017

Worst-case 0 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 0 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 0 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case 0 eye edge due to ISI Peak Distortion Analysis April 15, 2017

Worst-case eye opening Peak Distortion Analysis April 15, 2017

Worst-case eye opening Peak Distortion Analysis April 15, 2017

Worst-case eye opening Peak Distortion Analysis April 15, 2017

Worst-case eye opening Peak Distortion Analysis April 15, 2017

Worst-case eye edges with ISI and CCI where ti is the relative sampling point of each cochannel pulse response. Worst-case 0 eye edge Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis How do different methods of SI analysis compare with peak distortion analysis? Random data eye Lone pulse method Frequency domain method Measure the output amplitude due to a sine wave input (sine wave freq = data rate/2) Peak Distortion Analysis April 15, 2017

SI analysis comparison w/ 10” ustrip (previous example) Peak Distortion Analysis April 15, 2017

SI analysis comparison w/ 10” ustrip (previous example) Peak Distortion Analysis April 15, 2017

SI analysis comparison w/ multi-drop channel 2.5 Gb/s Peak Distortion Analysis April 15, 2017

SI analysis comparison w/ multi-drop channel Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Conclusion Given S Parameters and the corresponding pulse response, the worst case eye shape can be determined analytically Worst-case co-channel interference can also be determined analytically Advantages – Objective, Exact, Computationally Efficient Peak Distortion Analysis April 15, 2017

Peak Distortion Analysis Backup Peak Distortion Analysis April 15, 2017

Complete equations for peak distortion analysis To determine the worst-case voltage or timing margin, the worst-case received eye shape is extracted along with the peak sampling boundary. Since sources such as intersymbol and cochannel interference have truncated distributions, the associated worst-case magnitudes can be directly calculated from the unit pulse responses of the system. The unit pulse response y(t) of a system is given by Equation 1: Unit pulse response of a communication system where c(t) is the transmitter symbol response, p(t) is the impulse response of the channel and receiver and denotes convolution. The eye edge due to the worst-case 1 is given by Equation 2: Worst-case 1 eye edge due to ISI where T is the symbol period. Peak Distortion Analysis April 15, 2017

Complete equations for peak distortion analysis If n cochannel interference sources exist and yi is the cochannel pulse response, the worst-case 1 eye edge becomes Equation 3: Worst-case 1 eye edge due to ISI and cochannel interference where ti is the relative sampling point of each cochannel pulse response. Peak Distortion Analysis April 15, 2017

Complete equations for peak distortion analysis The eye edge due to the worst-case 0 is given by Equation 4: Worst-case 0 eye edge Therefore, the worst-case eye opening, e(t), is defined as Peak Distortion Analysis April 15, 2017