Solutions to ECE 565 MidTerm Examination, 3/23/2005
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View Full DocumentProblem 1.
A receiver operating at 1.55
µ
m and
T
=300 Kelvin uses a highspeed InGaAsInP
PIN detector with a quantum efficiency of 0.7. Assume that the receiver bandwidth is limited by
the
RC
time constant, where
R
is the load resistor and
C
is the junction capacitance of the PIN
diode,
C
= 0.8 pf. Moreover, assume that depending on the transmission speed, the load
resistance is judiciously selected to that the receiver bandwidth exactly matches that of the
transmitted digital signal.
a.
Calculate the responsivity of this PIN detector.
The responsivity,
R
, is
q
η
/
h
ν
=
ηλ /1.24,
with
λ
expressed in
µ
m
.
For
λ
=1.55
µ
m,
R
=
0.8739A/W.
b.
Write the expression for the receiver SNR and comment on the relative significance of
Johnson noise and shot noise as a function of the load resistance.
SNR
=
i
p
2
/ (
σ
s
2
+
σ
T
2
) = (
R
P
)
2
/{(4
k
B
TB/R
) + 2
qi
p
B
}.
If the bit duration is
T
b
s, then the bandwidth required to support the corresponding
transmission is
B
= 1/2
T
b
. On the other hand, since the load resistance
R
is selected so that
the receiver bandwidth exactly matches that of the transmitted digital signal, we have
(2
π
RC
)
1
= 1/2
T
b
, or
R
=
T
b
/
π
C
.
Thus, we obtain
SNR
= (8.739 x 10
7
)
2
/{(4
k
B
T
π
C/
2
T
b
2
) + 2
q
x8.75 x 10
7
x 1/2
T
b
}
= 7.6372 x 10
13
/{(2.0820x10
32
/
T
b
2
) + 1.3983 x 10
25
/
T
b
}.
At high transmission speeds (when
T
b
becomes small), Johnson noise will dominate shot
noise because of the
T
b

2
dependence in the Johnsonnoise term as opposed to the
T
b

1
dependence in the shotnoise term.
c.
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 Spring '11
 Rahmir
 Bit rate, SNR, Phonon, Data rate units, Nonlinear optics, transmission speed

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