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Equalization/Compensation of Transmission Media
Channel
(copper or fiber)
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
1
Optical Receiver Block Diagram
OE
TIA
≈ -18 dBm
≈ 10 µA
EECS 270C / Winter 2016
LA
≈ 10 mV p-p
EQ
CDR
DMUX
≈ 400 mV p-p
Prof. M. Green / UC Irvine
2
Copper Cable Model
4-foot cable
Copper Cable
( )
H w » e -La
w
15-foot cable
Where: L is the cable length
a is a cable-dependent
characteristic
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
2
Effect of Copper on Broadband Data
waveform
EECS 270C / Winter 2016
eye diagram
Prof. M. Green / UC Irvine
3
Adaptive Analog Equalizer for Copper
Implemented in Jazz Semiconductor SiGe BiCMOS process:
• 120 GHz fT npn
• 0.35 µm CMOS
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
4
Equalizer Block Diagram
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
5
Analog Equalizer Concept (1)
Simple linear circuit (normalized to 1Hz):
1
V2
V1
V3
+0.5
-0.5
C1
1s
simple channel model
EECS 270C / Winter 2016
1
1
1
1×V1
bandpass filter
Prof. M. Green / UC Irvine
a ×V1
(
)
1- a ×V2
1
combined flat response
+ peaked response
6
Analog Equalizer Concept (2)
1
V2
V1
V3
+0.5
-0.5
1s
V1
EECS 270C / Winter 2016
C1
1
1
1×V1
1
a ×V1
(1- a) ×V
1
2
V2
Prof. M. Green / UC Irvine
7
Analog Equalizer Concept (3)
Equalized output pulses:
Rise time = voltage swing/slew rate
V3
Rise time nearly constant over different channels!
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
8
Feedforward Path
Vout
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
9
Equalizer Frequency Response
Veq
Vin
(dB)
Vcontrol
f (Hz)
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
10
ISI & Transition Time
VFFE
teq = 45ps
PW = 108ps
0.3
teq = 60ps
PW = 100ps
0
-0.3
2.4
teq = 75ps
PW = 86ps
2.5
2.6
2.7
2.8
t (ns)
• Simulations indicate that ISI correlates strongly with FFE transition time teq.
• Optimum teq is observed to be 60 ps.
• Nonlinearities affect pulse shape, but not location of zero crossings.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
11
Slicer
Restores full logic levels
EECS 270C / Winter 2016
Exhibits controlled
transition time
Prof. M. Green / UC Irvine
12
Feedback Path
ò
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
13
Transition Time Detector
DC characteristic:
V+
VS
VVS
Transient Characteristic:
ISS
V+ -V-
V+ -V-
CSS
(b)
(a)
VS
Rectification & filtering done
in a single stage.
(b)
(a)
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
14
t
Integrator
A0
1
H(s) =
»
1+ st int A0 st int
(
A0 = gm 1 ro1 || ro2
t int =
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
)
CL
gm 1
15
Detector + Integrator
From
FFE
tFFE
From
Slicer
tslicer= 60ps
FFE transition
Time tFFE
Vcontrol (mV)
90ps
60
slope
detector
slope
detector
40
75ps
20
60ps
0
ò
-20
-40
45ps
-60
15ps
0
10
_
+
Vcontrol
EECS 270C / Winter 2016
20
30
40
50
t (ns)
Prof. M. Green / UC Irvine
16
System Analysis
tslicer
detector
+
Kd
å
Vcontrol
_
integrator
feedforward
equalizer
H(s)
Keq
teq
detector
Kd
t eq
t slicer
=
H (s ) »
Keq = 1.5 ps/mV
Kd = 2.5 mV/ps
K d K eq H (s )
1 + K d K eq H (s )
1
st int
EECS 270C / Winter 2016
t eq
t slicer
=
1
1+ s
t int
K d K eq
Prof. M. Green / UC Irvine
int = 75ns
tadapt =
tint
= 20ns
Kd Keq
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Measurement Setup
EQ inputs
Die under test
231 PRBS signal
applied to cable
EECS 270C / Winter 2016
EQ outputs
Prof. M. Green / UC Irvine
18
Measured Eye Diagrams
EQ input
EQ output
4-foot
RU256 cable
(-5 dB atten. @ 5 GHz)
4.0 ps rms jitter
15-foot
RU256 cable
(-15 dB atten. @ 5 GHz)
3.9 ps rms jitter
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
19
Summary of Measured Performance
Supply voltage
3.3 V
Power Dissipation
350 mW
(155 mW not including output driver)
Die Size
0.81mm X 0.87mm
Output Swing
490 mV single-ended p-p
Random Jitter
4.0 ps rms (4-foot cable)
3.9 ps rms (15-foot cable)
Presented at ISSCC Feb. 2004
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
20
Equalization vs. Compensation
Equalization is accomplished by inverting the transfer function of the channel.
Compensation is accomplished only by canceling the ISI at each unit interval.
Electronic Dispersion Compensation (EDC) refers to the electronics that
accomplishes compensation of copper or optical transmission media.
EDC is becoming especially critical as bit rates increase on legacy equipment
(e.g., backplane, optical connectors, optical fiber).
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
21
Pre-Cursor/Post-Cursor ISI
Input pulse (no ISI):
0
T
cursor
pre-cursor ISI
post-cursor ISI
Output pulse:
0
T
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
22
Feedforward Equalization (FFE)
Idea: To cancel ISI, subtract a weighted & delayed version of the pulse:
output pulse
delayed by T:
d-1
d0
output pulse:
æ d ö
Xç- -1 ÷
è d0 ø
Result with 0
pre-cursor ISI:
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
23
Feedforward Equalization (2)
Din (t)
T
Din (t -T)
Time domain:
Dout (t) = Din (t) - a1 ×Din (t -T )
a1
a1 =
_
+

d-1
d0
Dou t (t)
1+ a12
Frequency domain:
H(s) = 1- a1 × e -sT
H( jw ) = 1- a1 × e - jwT
(
= 1- a1 × cos wT - j sin wT
1- a1
)
Þ| H( jw ) |2 = (1+ a12 ) - 2a1 ×cos wT
EECS 270C / Winter 2016
p
Prof. M. Green / UC Irvine
T

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Feedforward Equalization (3)
N-tap FFE structure:
Din (t)
T
a0
T
a1
T
a2
an

Dou t (t)
FFE can cancel both pre- and post-cursor distortion.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
25
Feedforward Equalization (4)
3-tap summing circuit:
negative coefficient
R
_
R
Vout +
Din+ (k)
Din- (k)
V0
Din+ (k -1)
Din- (k -1) Din+ (k - 2)
V1
Din- (k - 2)
V2
ISS
Coefficients set by gm of each differential pair.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
26
Feedforward Equalization (5)
Fractional spacing:

p
T
1-tap T-spaced FFE frequency response
2p

T
1-tap T/2-spaced FFE frequency response
EECS 270C / Winter 2016
5-tap T-spaced FFE eye diagram
5-tap T/2-spaced FFE eye diagram
Prof. M. Green / UC Irvine
27
Adaptation (1)
Assume original sequence Din(k) is known.
Define error signal e(k) as:
^
^
e(k) º Dout (k) - Dout (k) where Dout(k) is an appropriately delayed version of Din(k).
Steepest Descent Algorithm:
e2
a2
step size
a1
optimum
setting
• Algorithm moves coefficients in direction of decreasing mean-square error.
• Step size µ should be made sufficiently small to guarantee convergence.
• Requires knowledge of properties of mean-square error; usually not available.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
28
Adaptation (2)
Least mean-square (LMS) algorithm:
FFE output signal: Dout (k) = a0 ×Din (k) + a1 ×Din (k -1) + ×××+ an ×Din (k - n)
e 2 (k) = [Dout (k) - Dout (k)]
^
[
] = -2 D^
d e 2 (k)
dai
(
out
)
- Dout ×
2
dDout
dai
= -2 × e(k) ×Din (k - i)
Analog version of LMS:
1
ai (t) =
e(t) ×Din (t - iT )dt
t
both signals are
available on chip.
ò
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
29
Adaptation (3)
Types of adaptation:
1. Training Sequence
A training sequence with known properties is sent through the channel +
equalizer. The equalizer output is compared to the original sequence and an
error signal is generated.
2. Blind Adapation
Adaptation is continually performed while system is running. Only limited
properties of the signal are known. An error signal must somehow be
generated without having the original sequence.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
30
Adaptation (4)
Generation of error signal:
Din
FFE
^
Dout
Dout
_

+
e
• Slicer restores logic levels and opens eye vertically.
• Bit sequences at slicer input & input are identical.
• Slicer has no effect on placement of zero crossing.
• Slicer can be realized using CML buffers with sufficient gain and speed.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
31
Decision Feedback Equalization (DFE)
Din (t)
T
T
T
FFE structure:
a0
a1
a2
an

Dou t (t)
Noise applied to FFE input will be retained (perhaps filtered) at the output.
Din (t)
DFE structure:
Dou t (t)
+ - -
bm
b2
T
EECS 270C / Winter 2016
b1
T
Prof. M. Green / UC Irvine
T
32
Decision Feedback Equalization (2)
Din (t)
+
Dou t (t)

-
-
-
bm
b2
T
b1
T
T
• Slicer is embedded in the structure; Dout is a digital signal.
• Delay elements are digital -- commonly realized by DFFs.
• Use of slicer suppresses input noise.
• Cancels post-cursor distortion only.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
33
Decision Feedback Equalization (3)
Din (t)
Dou t (t)
+  - -
post-cursor
distortion
1-tap example:
2/3
Din (k)
1/3
1
bm
b2
Dout (k)
(desired)
consistent
with
b1
1
T
T
T
• Tap weights provide a “look-up table,” canceling
post-cursor distortion based on last m bits of output
sequence.
• DFE can sometimes “latch up” with wrong tap
weights during adaptation.
Dout (k -1)
2/3
Din (k) -
1
×Dout (k -1)
3
b1 =
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
1
3
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FFE + DFE
Din (t)
a0
T
T
a1
T
a2
an

Combined FFE and DFE can be used to
cancel both pre- and post-cursor
distortion with low noise.
Dou t (t)
+ - -
bm
b2
T
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
b1
T
T
35
Front-End Circuits for DSP-Based Receivers
from channel
Vin
PGA
VA
ADC
Dout [1:n]
ADC requires strict control
over its input amplitude VA.
VC
AGC
Automatic Gain
Control
Programmable Gain Amplifier (PGA):
VA (t) = G(VC ) ×Vin (t)
æV ö
where G(VC ) = V1 × expç C ÷
è V2 ø
EECS 270C / Winter 2016
“Linear in dB” gain characteristic
gives settling time independent of
input amplitude.
Prof. M. Green / UC Irvine
36
PGA Design
1. Differential Pair:
Iout-
2. Source Degeneration:
Iout+
Vin+
Vin-
Iout-
Iout+
Vin+
Vin-
3. Op-Amp with Feedback:
Rf
RS
+
V_in RS
+
V_out
2RS
ISS
Rf
+
VC_
For biasing in weak inversion:
ISS
2nVT
æ V -V ö
= ID0 × expç C T ÷
è nVT ø
Iout = gmVin »
ISS
Iout =
»
gm
×Vin
1+ gmRS
Vin
RS
Vout = -
Rf
×Vin
RS
for gmRS >> 1
RS varied with constant
dB per step.
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
37
PGA Example (1)
C.-C. Hsu, J.-T. Wu, “A highly linear 125-MHz
CMOS switched-resistor programmable-gain
amplifier,” JSSC, Oct. 2003, pp. 1663-1670.
Vout =
Rf
×Vin
RS
Realization of RS:
2 dB steps
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
38
PGA Example (2)
J. Cao, et al., “A 500mW digitally calibrated AFE
in 65nm CMOS for 10Gb/s links over backplane
and multimode fiber,” ISSCC 2009, pp. 370-371.
Av = gmR
= N × mnCox
W
IO × R
L
gain of single diff. pair
where N = number of diff. pairs turned on
EECS 270C / Winter 2016
Prof. M. Green / UC Irvine
39