ECEN689: Special Topics in High-Speed Links Circuits and ...
Transcript of ECEN689: Special Topics in High-Speed Links Circuits and ...
Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
ECEN689: Special Topics in High-Speed Links Circuits and Systems
Spring 2010
Lecture 8: Channel Pulse Model
Announcements
• Reading• Will post some papers of link examples with
different modulation techniques
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Agenda
• ISI
• Channel Pulse Model
• Peak Distortion Analysis
• Modulation Schemes
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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
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( )( )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
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Data = “1000101”
“1” Symbol
“0” Symbol
( )( ) ( ) ( )( )TktukTtutck 11 +−−−≡
( )( ) ( )( )tctc kk10 −=
( )
<≥
≡0001
wherett
tu
NRZ Data Modeling
• An NRZ data stream can be modeled as a superposition of isolated “1”s and “0”s
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( ) ( )( )∑∞
−∞=
=k
dki tctV k
Channel Response to NRZ Data
• Channel response to NRZ data stream is equivalent to superposition of isolated pulse responses
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( ) ( )( ) ( )( )( ) ( )( )∑∑∞
−∞=
∞
−∞=
−===k
d
k
dkio kTtytcHtVHtV kk
Channel Pulse Response
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( )( ) ( )( ) ( )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
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Input Data Stream
Pulse Responses
Channel Response
Channel “FIR” Model
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( )( )tc 10
( )( )tc 10
( )( )( ) ( )( )tytcH 10
10 =
( )( )( ) ( )( )tytcH 10
10 =
a-1
a0
a1
a2 a3
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 …]
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
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( ) ( ) ( )( )( )∑
∞
≠−∞= <−
−+=
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)
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( ) ( ) ( ) ( ) ( )( ) ( )( )( )
( )( )( )
−−−+−=−= ∑∑∞
≠−∞= >−
∞
≠−∞= <−
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
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( )( )( )
( )
( )( )( )
( ) ( ) 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
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[ ]... ...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
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( )( )( )
( )
( )( )( )
( ) ( ) 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
Modulation Schemes
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• Binary, NRZ, PAM-2• Simplest, most common modulation format
• PAM-4• Transmit 2 bits/symbol• Less channel equalization and circuits run ½ speed
• Duo-binary• Allows for controlled ISI, symbol at RX is current bit plus preceding bit• Results in less channel equalization
[ ] [ ] [ ]1−+= nxnxnw
0
1
00
01
11
10
0, if x[n-1]=0
1, if x[n-1]=0 OR
0, if x[n-1]=1
1, if x[n-1]=1
No Pre-Coding Case
Modulation Frequency Spectrum
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Majority of signal power in 1GHz bandwidth
Majority of signal power in 0.5GHz bandwidth
Majority of signal power in 0.5GHz bandwidth
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
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/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 Frequency
NRZ 1 Rs/2=1/2Tb
PAM-4 2 Rs/2=1/4Tb
Duobinary 1 (or 1.5) ?? Rs/2=1/2Tb (or 1/3Tb) ??
Next Time
• Modulation scheme comparison
• Link Circuits• Termination structures• Drivers• Receivers
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