PROBLEMS 511
used in a 140-Mb/s system experiment, intended mainly for video distribution [165].
A balanced heterodyne OEIC receiver with a 9-GHz bandwidth was fabricated in 1996
by integrating a local oscillator and two photodiodes with a 3-dB coupler [168]. The
coherent techniques may turn out to be more suitable for multichannel access networks
for which bit rates per channel are relatively low but number of channels can be quite
large [161]. An integrated transceiver suitable for bidirectional access networks has
been developed for such applications [170].
Problems
10.1Prove the 3-dB advantage of homodyne detection by showing that the average
electrical power generated by a coherent receiver is twice as large for homodyne
detection as for heterodyne detection under identical operating conditions.
10.2Derive an expression for the SNR of a homodyne receiver by taking into account
both the shot noise and the thermal noise.
10.3Consider a 1.55-μm heterodyne receiver with ap–i–nphotodiode of 90% quan-
tum efficiency connected to a 50-Ωload resistance. How much local-oscillator
power is needed to operate in the shot-noise limit? Assume that shot-noise limit
is achieved when the thermal-noise contribution at room temperature to the noise
power is below 1%.
10.4Prove that the SNR of an ideal PSK homodyne receiver (perfect phase locking
and 100% quantum efficiency) approaches 4N ̄p, whereN ̄pis the average number
of photons/bit. Assume that the receiver bandwidth equals half the bit rate and
that the receiver operates in the shot-noise limit.
10.5Show how an electro-optic material such as LiNbO 3 can be used for generating
optical bit streams with ASK, PSK, and FSK modulation formats. Use diagrams
as necessary.
10.6A 1.55-μm DFB laser is used for the FSK modulation at 100 Mb/s with a tone
spacing of 300 MHz. The modulation efficiency is 500 MHz/mA and the dif-
ferential quantum efficiency equals 50% at the bias level of 3 mW. Estimate the
power change associated with FSK by assuming that the two facets emit equal
powers.
10.7Derive an expression for the BER of a synchronous heterodyne ASK receiver by
assuming that the in-phase noise componentichas a probability density functionp(ic)=1
σ√
2
exp(
−
√
2
σ|ic|)
.
Determine the SNR required to achieve a BER of 10−^9.
10.8Calculate the sensitivity (in dBm units) of a homodyne ASK receiver operating at
1.55μm in the shot-noise limit by using the SNR expression obtained in Problem
10.2. Assume thatη= 0 .8 and∆f=1 GHz. What is the receiver sensitivity
when the PSK format is used in place of ASK?