ECEN72: High-Speed Links Circuits and Systems Spring 217 Lecture 4: Channel Pulse Model & Modulation Schemes Sam Palermo Analog & Mixed-Signal Center Texas A&M University
Announcements & Agenda Lab 1 Report and Prelab 2 due Feb. 6 ISI Channel pulse model Peak distortion analysis Compare NRZ, PAM-4, and Duobinary modulation Reference material for this lecture Peak distortion analysis paper by Casper (posted on web) Notes from H. Song, Arizona State Papers posted on PAM-4 and duobinary modulation 2
Inter-Symbol Interference (ISI) Previous bits residual state can distort the current bit, resulting in inter-symbol interference (ISI) ISI is caused by Reflections, Channel resonances, Channel loss (dispersion) Pulse Response y 1 t c 1 t ht c 1 t ht c 1 t y 1 t 3
NRZ Data Modeling An NRZ data stream can be modeled as a superposition of isolated 1 s and s Data = 111 1 Symbol 1 t ut kt ut k c k 1 T Symbol c t k c 1 t k [Song] where u t 1 t t 4
NRZ Data Modeling An NRZ data stream can be modeled as a superposition of isolated 1 s and s V i dk t c t k k [Song] 5
Channel Response to NRZ Data Channel response to NRZ data stream is equivalent to superposition of isolated pulse responses [Song] V o t dk t H c t H V i k dk k y t kt k 6
Channel Pulse Response cursor y d k t c d t ht k post-cursor ISI pre-cursor ISI y (1) (t) sampled relative to pulse peak: [.3.36.54.165.65.33.2.12.9 ] k =[ -2 1 1 2 3 4 5 6 ] By Linearity: y () (t) =-1*y (1) (t) 7
Channel Data Stream Response Input Data Stream Pulse Responses Channel Response 8
Channel FIR Model t c 1 H 1 1 c t y t t c 1 a D is the delay from the channel input to the output pulse peak H 1 1 c t y t a -1 a 1 a 2 a3 y (1) (t) sampled relative to pulse peak: [.3.36.54.165.65.33.2.12.9 ] a =[ a -2 a -1 a a 1 a 2 a 3 a 4 a 5 a 6 ] 9
Peak Distortion Analysis Can estimate worst-case eye height and data pattern from pulse response Worst-case 1 is summation of a 1 pulse with all negative non k= pulse responses s 1 (1) dk t y t y t kt y tkt k k Worst-case is summation of a pulse with all positive non k= pulse responses s () dk t y t y t kt y tkt k k 1
Peak Distortion Analysis s Worst-case eye height is s 1 (t)-s (t) (1) () t s t s t y t y t 1 s dk dk y t kt y t kt y tkt y tkt k k k k () (1) Because y t y t 1 (1) 1 1 t 2 y t y t kt y t kt y tkt y tkt k k k k 1 pulse worstcase 1 edge 1 pulse worstcase edge If symmetric 1 and pulses (linearity), then only positive pulse response is needed 11
Peak Distortion Analysis Example 1 s k k k k y (1) t.54 1 t kt y tkt y y 1 t kt y tkt.7.389 t 2.54.7.389. 288 12
Worst-Case Bit Pattern Pulse response can be used to find the worst-case bit pattern Pulse a... a 2 a 1 a a1 a2 a3 a4 a5 a6... Flip pulse matrix about cursor a and the bits are the inverted sign of the pulse ISI - sign a sign( a ) sign( a ) sign( a ) sign( a ) sign( a ) 1 sign( a ) sign( a )...... 6 5 4 3 2 1 1 2 Worst-Case Bit Pattern Eye 1kbits Eye 13
Peak Distortion Analysis Example 2 s k k k k y (1) t.426 1 t kt y tkt y y 1 t kt y tkt.53.542 t 2.426.53.542. 338 14
Modulation Schemes Binary, NRZ, PAM-2 Simplest, most common modulation format PAM-4 Transmit 2 bits/symbol Less channel equalization and circuits run ½ speed Duobinary xnxn1 w n Allows for controlled ISI, symbol at RX is current bit plus preceding bit Results in less channel equalization No Pre-Coding Case 1 1 11 1 1, if x[n-1]=1 1, if x[n-1]= OR, if x[n-1]=1, if x[n-1]= 15
Modulation Frequency Spectrum Majority of signal power in 1GHz bandwidth Majority of signal power in.5ghz bandwidth Majority of signal power in.5ghz bandwidth 16
Nyquist Frequency Nyquist bandwidth constraint: The theoretical minimum required system bandwidth to detect R S (symbols/s) without ISI is R S /2 (Hz) Thus, a system with bandwidth W=1/2T=R S /2 (Hz) can support a maximum transmission rate of 2W=1/T=R S (symbols/s) without ISI 1 2T RS 2 W RS W 2 (symbols/s/hz) For ideal Nyquist pulses (sinc), the required bandwidth is only R S /2 to support an R S symbol rate Modulation Bits/Symbol Nyquist Frequency NRZ 1 R s /2=1/2T b PAM-4 2 R s /2=1/4T b Duobinary is not Nyquist signaling, as it employs controlled ISI for reduced signal bandwidth 17
NRZ vs PAM-4 PAM-4 should be considered when Slope of channel insertion loss (S 21 ) exceeds reduction in PAM-4 eye height Insertion loss over an octave is greater than 2*log1(1/3)=-9.54dB On-chip clock speed limitations 18
PAM-4 Receiver 3x the comparators of NRZ RX [Stojanovic JSSC 25] 19
NRZ vs PAM-4 Desktop Channel Loss at 5GHz = -7.5dB Loss at 2.5GHz = -4.8dB Eyes are produced with 4-tap TX FIR equalization Loss in the octave between 2.5 and 5GHz is only 2.7dB NRZ has better voltage margin 2
NRZ vs PAM-4 T2 Server Channel Loss at 2.5GHz = -11.1dB Loss at 5GHz = -26.9dB Eyes are produced with 4-tap TX FIR equalization Loss in the octave between 2.5 and 5GHz is 15.8dB PAM-4 might be a better choice 21
Multi-Level PAM Challenges Receiver complexity increases considerably 3x input comparators (2-bit ADC) Input signal is no longer self-referenced at V differential Need to generate reference threshold levels, which will be dependent on channel loss and TX equalization CDR can display extra jitter due to multiple zero crossing times Smaller eyes are more sensitive to cross-talk due to maximum transitions Advanced equalization (DFE) can allow NRZ signaling to have comparable (or better) performance even with >9.5dB loss per octave 22
Duobinary Signaling xn xn 1 w n [NEC ISSCC 25 & 29] Binary (1, -1) x n TX EQ Channel RX EQ wn Duobinary (2,, -2) 23
Duobinary Signaling w/ Precoder [Lee JSSC 28] With precoder, middle signal at the receiver maps to a 1 and high and low signal maps to a Precoder allows for binary signal out of transmitter resulting in a power gain Channel can be leveraged to aid in duobinary pulse shaping Eliminates error propagation at receiver Similar performance to using a 1-tap loopunrolled DFE at RX [NEC ISSCC 25] 24
1Gb/s Modulation Comparisons [Sinsky MTT 25] Channel input = 6mV pp 2-tap TX FIR equalization Both duobinary and PAM-4 perform better With more equalization NRZ will be more competitive 25
Modulation Take-Away Points Loss-slope guidelines are a good place to start in consideration of alternate modulation schemes More advanced modulation trades-off receiver complexity versus equalization complexity Advanced modulation challenges Peak TX power limitations Setting RX comparator thresholds and controlling offsets CDR complexity Crosstalk sensitivity (PAM-4) Need link analysis tools that consider voltage, timing, and crosstalk noise to choose best modulation scheme for a given channel 26
Next Time Link Circuits Termination structures Drivers Receivers 27