Digital Signal Processing Reference
In-Depth Information
PD
d[k]
Fiber
Fiber
Tx
FA
TIA
n
e
(t)
n
o
(t)
FA: Fiber Amplifier
PD: Photo Detector
Fig. 8
Block diagram of an optical link model showing primary sources of noise
It can be shown that the sampled received signal in the presence of jitter and ISI is
given by:
]=
∑
k
]
−
k
]
k
y
[
n
d
[
k
]
h
g
[
n
−
k
v
[
k
]
q
[
k
]
h
t
0
[
n
−
k
]
−
s
[
n
v
[
k
]
h
t
0
[
n
−
k
]
(14)
where
h
g
[
k
]
is the sampled pulse-response (composite of transmit shaping
g
(
t
)
and
channel impulse response
h
(
t
)
),
h
t
0
[
k
]=
h
(
t
0
+
nT
)
is the sampled channel impulse
response with a sampling offset of
t
0,
v
[
k
]=
d
[
k
]
−
d
[
k
−
1
]
is the data transition,
q
is the jitter in the recovered clock.
impact of jitter. Note: jitter appears as additional noise source in the received signal,
and that jitter appears only when there is a data transition (non-zero
v
[
k
]
is the jitter in the transmit clock, and
s
[
n
]
).
Thermal noise in back-plane links are generated by the termination resistors (
R
T
[
k
]
/
Hz
)
is given by:
R
sw
+
g
m
)
N
o
=
4
kT
(
R
T
+
(15)
where
R
T
,
R
sw
,
g
m
and
are the termination resistance, sampler resistance,
input stage transconductance, and a technology dependent parameter, respectively.
Assuming typical values of
R
T
=
α
50
Ω
,
R
sw
=
200
Ω
,
g
m
=
1
mA
/
V
and
α
=
1, we
10
−
17
V
2
get
N
o
=
Hz
.
In addition, the slicer imposes a minimum input voltage requirement referred to
as
slicer resolution
, needed to resolve the input signal. The slicer resolution is a
function of static offsets that occur in differential circuit structures due to transistor
mismatch. Typical values of uncorrected offsets are in the range of 10 mV.
2
×
/
2.4.2
Optical Fiber Noise Models
In amplified links, the dominant source of noise as observed at the receiver is ampli-
fied spontaneous emission noise
n
o
(
t
)
