Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
ECEN720: High-Speed Links Circuits and Systems
Spring 2021
Lecture 4: Channel Pulse Model & Modulation Schemes
Announcements• Lab 1 Report and Prelab 2 due Feb. 3
• For Prelab 2 Question 2, look ahead to Lecture 5 Slide 8
• Lab 2 Report and Prelab 3 due Feb. 10
• Reference material• Peak distortion analysis paper by Casper• Notes from H. Song, Arizona State• Papers posted on PAM-2/4 transceivers
2
Agenda• ISI and channel pulse model
• Peak distortion analysis
• Compare NRZ (PAM-2) and PAM-4 modulation
3
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
4
tc 1 th tc 1 ty 1
thtcty 11
NRZ Data Modeling• An NRZ data stream can be modeled as a
superposition of isolated “1”s and “0”s
5
Data = “1000101”
“1” Symbol
“0” Symbol
TktukTtutck 11
tctc kk 10
0001
wherett
tu[Song]
NRZ Data Modeling• An NRZ data stream can be modeled as a
superposition of isolated “1”s and “0”s
6
k
dki tctV k
[Song]
Channel Response to NRZ Data• Channel response to NRZ data stream is
equivalent to superposition of isolated pulse responses
7
k
d
k
dkio kTtytcHtVHtV kk
[Song]
Channel Pulse Response
8
thtcty kk dd
y(1)(t) sampled relative to pulse peak:[… 0.003 0.036 0.540 0.165 0.065 0.033 0.020 0.012 0.009 …]
k =[ … -2 1 0 1 2 3 4 5 6 …]By Linearity: y(0)(t) =-1*y(1)(t)
cursor
post-cursor ISI
pre-cursor ISI
…
Channel Data Stream Response
9
Input Data Stream
Pulse Responses
Channel Response
a-1
a0
a1a2 a3
Channel “FIR” Model
10
tc 10
tc 10
tytcH 1010
tytcH 1010
y(1)(t) sampled relative to pulse peak:[… 0.003 0.036 0.540 0.165 0.065 0.033 0.020 0.012 0.009 …]
a =[ … a-2 a-1 a0 a1 a2 a3 a4 a5 a6 …]
D is the delay from the channel input to the output pulse peak
Agenda• ISI and channel pulse model
• Peak distortion analysis
• Compare NRZ (PAM-2) and PAM-4 modulation
11
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=0 pulse responses
12
0
0
)1(01
kk kTty
d kTtytyts k
• Worst-case “0” is summation of a “0” pulse with all positive non k=0 pulse responses
0
0
)0(00
kk kTty
d kTtytyts k
Peak Distortion Analysis• Worst-case eye height is s1(t)-s0(t)
13
0
0
0
0
)0(0
)1(001
kk kTty
d
kk kTty
d kTtykTtytytytststs kk
• If symmetric “1” and “0” pulses (linearity), then only positive pulse response is needed
0
0
1
0
0
1)1(02
kk kTty
kk kTty
kTtykTtytyts
tyty )1(0)0(0 1 Because
“1” pulse worst-case “1” edge
“1” pulse worst-case “0” edge
Peak Distortion Analysis Example 1
14
288.0389.0007.0540.02
389.0
007.0
540.0
0
0
1
0
0
1
)1(0
ts
kTty
kTty
ty
kk kTty
kk kTty
Worst-Case Bit Pattern• Pulse response can be used to find the worst-case bit pattern
15
... ...a Pulse 654321012 aaaaaaaaa
... )()(1)()()()()(- ... 21123456 asignasignasignasignasignasignasignasign
• Flip pulse matrix about cursor a0 and the bits are the inverted sign of the pulse ISI
Worst-Case Bit Pattern Eye 10kbits Eye
Peak Distortion Analysis Example 2
16
338.0542.0053.0426.02
542.0
053.0
426.0
0
0
1
0
0
1
)1(0
ts
kTty
kTty
ty
kk kTty
kk kTty
Agenda• ISI and channel pulse model
• Peak distortion analysis
• Compare NRZ (PAM-2) and PAM-4 modulation
17
PAM-2 (NRZ) vs PAM-4 Modulation
18
• Binary, NRZ, PAM-2• Simplest, most common modulation format
• PAM-4• Transmit 2 bits/symbol• Less channel equalization and circuits run ½ speed
0
1
00
01
11
10
Modulation Frequency Spectrum
19
Majority of signal power in 1GHz bandwidth
Majority of signal power in 0.5GHz bandwidth
0
1
00
01
11
10
Nyquist Frequency• Nyquist bandwidth constraint:
• The theoretical minimum required system bandwidth to detect RS (symbols/s) without ISI is RS/2 (Hz)
• Thus, a system with bandwidth W=1/2T=RS/2 (Hz) can support a maximum transmission rate of 2W=1/T=RS (symbols/s) without ISI
20
/Hz)(symbols/s 222
1
WRWR
TSS
• For ideal Nyquist pulses (sinc), the required bandwidth is only RS/2 to support an RS symbol rate
Modulation Bits/Symbol Nyquist FrequencyNRZ 1 Rs/2=1/2Tb
PAM-4 2 Rs/2=1/4Tb
NRZ vs PAM-4
• PAM-4 should be considered when• Slope of channel insertion loss (S21) exceeds reduction in PAM-4
eye height• Insertion loss over an octave is greater than 20*log10(1/3)=-9.54dB
• On-chip clock speed limitations21
PAM-4 Receiver
• 3x the comparators of NRZ RX
22
[Stojanovic JSSC 2005]
NRZ vs PAM-4 – Desktop Channel
• 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
23
Loss at 2.5GHz = -4.8dB
Loss at 5GHz = -7.5dB
NRZ vs PAM-4 – T20 Server Channel
• 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
24
Loss at 2.5GHz = -11.1dB
Loss at 5GHz = -26.9dB
PAM-4 Peak Distortion Analysis
25• PAM4 modulation is more sensitive to residual ISI
PAM4 eye height= 2(𝟏
𝟑A –
NRZ eye height= 2(A –
A c1 c2 c3 c4 c5 c5C-1
𝑦 𝑡 𝑐 𝑡 ∗ 𝑝 𝑡
Tb
Channel pulse response
Tb
𝑐 𝑡
Transmitter symbol
response
Channel impulse response
𝑝 𝑡
a
-a
2a
PAM2 Eye Diagram a
a/3
-a/3
-a
2a/3 2a/3
-2a/3
0
PAM4 Eye Diagram
Multi-Level PAM Challenges• Receiver complexity increases considerably
• 3x input comparators (2-bit ADC)• Input signal is no longer self-referenced at 0V 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
26
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
27
Next Time• Link Circuits
• Termination structures• Drivers• Receivers
28
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