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174 Systems
I:
Problems
7.1 An intrusion alarm uses a HgCdTe photovoltaic mode detector in an
optical system with aperture diameter of 2 cm and focal length of 20 cm.
If an intruding object suddenly fills the detector FOV, we wish to find
how small a temperature difference will yield a (S/N)y of 10, which
would assure a high detection probability and low false-alarm
rate.
The
detector has a wavelength cut-off of 5 /jm, an 7j of 1, an area of
10'^
cm^,
a zero-bias junction resistance of 10 Q, and operates at room
temperature, 300 K. Since the detected radiation is on the "tail" of the
blackbody curve, it may be approximated by
hource
=
f^e~^'''^'^
=
5.9
watts
I
m^
at
300 K
(a) Find
dHldT
in
W/n^K.
(b) What is
dPg /dT
for the detector ?
(c) Assume junction noise is dominant and find the NEP for a
bandwidth of
B
=
100
Hz.
(d) What is the minimum temperature change that will give a
reliable alarm ?
7.2 The
PINFET
amplifier sensitivity for direct detection at the end of
Section 7.2 was A3
dBm
or 5 x
10'^
W.
(a) Find the sensitivity for the same data rate using ideal
heterodyne
performance with
rj
=
0.5,
B
=
90
MHz, and the same BER =
10'^.
(b) Find the new achievable range for a fiber attenuation of 0.2
dB/km,
and P ^
1
mW
7.3 A museum exhibit is held in a large room with a ceiling height of 10
m. To supply multilingual narrative, the visitors are supplied with
earphones equipped with a PIN-FET /audio amplifier with an optical
filter tuned to one of several semiconductor laser wavelengths. In the
ceiling, various lasers transmit audio messages in the various languages.
All the lasers operate near
0.9
jjm.
1
(jum)^,
the threshold current is 20 mA, operating point, 50 mA, atl5 mW. The
maximum audio signal is thus a sinusoid with a full excursion between
Problems
175
0 and 30 mW. There are no optics at the transmitter or the detector so
that wide-angle transmission and reception is assured.
(a) For a detector area of 2 mm^, find the average or quiescent
received optical power assuming the detector is inunediately below the
laser and pointed in a vertical direction. Use R = 9m.
(b) To assure reliable operation we wish a large electrical audio
power signal-to-noise ratio at the amplifier output. For full laser
modulation what is this ratio with
]?,•
=
1
MQ, T^ = 300 K, and
7J
= OS,
The audio bandwidth is 10
kHz,
(c) Estimate the electrical power required to drive the laser trans-
mitter.
7.4 A "cat's eye" retroreflector is shown in the sketch. An incident
transmitted wave focuses onto the
diffuse
reflective surface. Part of the
reflected power returns to the lens and is propagated back in the direct-
ion of incidence as a plane wave. (The retroreflection can occur over a
broad range of incidence angles.) Find an expression for the radar cross
section a in terms of
A^,
f, and A. Assume that the lens diameter is
small compared to the focal length and that the diffuse reflectivity is
unity. Hint: See
Eq.
(1.23).
p
=
I
7,5 A photon-counting digital communication system uses on-off
coding. If the received background count in each pulse interval has an
average value of
n^
= 1, and the threshold is set at rij >4, find pll,0],
the probability of
a
"one"
being registered when a
"zero"
is transnutted.
7.6. In the America's Cup race (as seen on TV in 1992), one of the ships
was using a pulsed laser rangefinder to measure the range to its compet-

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