Page 204 - Fiber Optic Communications Fund

Optical Modulators and Modulation Schemes 185

Eq. (4.143) can be written as
sin (Bt) sin (Bt)
p(t)= − . (4.145)
Bt B(t − T )
b
The first term on the right-hand side of Eq. (4.145) is in the form of a sinc function. To bring the second term
into sinc form, consider
sin [B(t − T )] = sin (Bt − )=−sin (Bt). (4.146)
b
Using Eq. (4.146) in Eq. (4.145), we find
sin (Bt) sin (Bt)
p(t)= − = sinc (Bt)+ sinc [B(t − T )]. (4.147)
b
Bt B(t − T )
b
Using the following identities:
1
[sinc (Bt)] = rect (f∕B),
B
[x(t − T )] = ̃x(f) exp (i2fT ),
b b
the Fourier transform of Eq. (4.147) is
1
̃ p(f)= rect (f∕B)[1 + exp (i2fT )]
b
B
2exp (ifT )rect (f∕B) [exp (−ifT )+ exp (ifT )]
b
b
b
=
B 2
2
= exp (if∕B)rect (f∕B) cos (f∕B). (4.148)
B

Exercises

4.1 Explain the differences between NRZ and RZ formats. Which of these formats has a wider spectrum?
4.2 Discuss the following modulation schemes: (i) ASK, (ii) PSK, and (iii) FSK.

4.3 The pulse shape of a RZ signal is described by
2
2
p(t)= exp (−t ∕2T ).
0
Find the PSD assuming (a) polar and (b) unipolar signaling.
4.4 Derive an expression for the PSD of a bipolar signal such as AMI. Assume rectangular pulses with
100% duty cycle.

4.5 Discuss the differences between binary PSK and DPSK. Does DPSK require a reference laser (local
oscillator) at the receiver?
4.6 Explain the Pockels effect. Show that the phase change is proportional to the applied voltage in an
electro-optic crystal.