ECE-756 Design of Lightwave Communication Systems and Networks
Duration of examination: 3 hours
There are six questions. Please answer any 5 questions. Each question has a weight of 10 marks.
Good luck and have a great summer!
1a. Explain the meaning of cutoff wavelength for (a) optical fibers and (b) photodetectors. 4 marks
1b. The bit sequence launched to the fiber is given by
where is the field envelope, is the bit interval, and
Suppose the length of the fiber is L and dispersion coefficient is , find the field envelope at the output of the fiber. Sketch the field envelopes (absolute) at the input and at the output. Ignore and fiber loss. Explain briefly what happens if is not ignored. 6 marks
2a. Explain why an ultra-short pulse broadens in a step-index multi-mode fiber. Explain how the pulse broadening can be reduced by using a graded-index multi-mode fiber.
4 marks
2b.The optical power output of the transmitter shown in the figure is 0 dBm. The fiber 1 has a dispersion coefficient (β2 ) = -15 ps2 /km, loss of 0.3 dB/km and length = 80 Km. The optical wavelength = 1.55 microns, receiver bandwidth = 30 GHz (one-sided). The loss of the fiber 1 is compensated by an amplifier with gain G and excess noise factor nsp = 6. The fiber 2 is a dispersion compensating fiber of length 20 Km and its loss is 0.5 dB/km. Find (a) gain G of the amplifier so that the output of the amplifier is 0 dBm (b) dispersion coefficient (β2 ) of fiber 2 such that the pulse width of the optical signal at the receiver input is same as that at the transmitter output (i.e. there is no pulse broadening) (c) Signal to noise ratio at the receiver assuming that pulse width at the transmitter output is same as that at the receiver input, and output of the amplifier is 0 dBm. Ignore β1 of the fiber, shot noise and thermal noise of the receiver. Assume that the pulse width of the signal is very large so that there is no reduction in signal power due to the finite bandwidth of the receiver. 6 marks
3a. Explain the meaning of conduction band and valence band. Explain why the efficiency of light generation is reduced if the conduction band minimum and valence band maximum arenot aligned. 4 Marks
6 marks
4a. Prove that the quantum efficiency of a photodetector is given by
where is the absorption coefficient and W is the width of the depletion layer. 5 marks
4b. Ten photons are incident on the left side of the depletion region of a PIN photo-diode. It is found that two photons are present on the other side of the depletion region. The optical wavelength = 0.98 microns. Find the required incident optical power on this photo-diode to have a SNR of 25. The temperature is 30o C, load resistance is 1000 Ohms and one sided receiver bandwidth = 30 GHz. Ignore dark current.
5. The optical amplifier configuration used in commercial systems is shown in figure 1. The gain and noise figure of amplifier are and , respectively. The power loss coefficient of the dispersion compensating module (DCM) is and its length is The effective noise figure of this system is defined as
where and are the signal to noise ratio defined in electrical domain at the input and output of the system, respectively. Show that
10 marks
6a Draw the block diagram of a wavelength division multiplexed system and provide the functional description of each block. 5 marks
6b. Starting from the three dimensional wave equation (for free space), show that the forward propagating plane waves are given by
with
where c is velocity of light in vacuum. 5 marks
6a. An optical transmission operates at 10 Gb/s. The dispersion of the transmission fiber is -21 ps.ps/km. Determine the maximum transmission distance (to avoid inter symbol interference). 4 marks
6b. 10 Gb/s RZ bit stream consisting of random ‘1’ and ‘0’ s is launched to a fiber. Bit ‘1’ is transmitted by sending a Gaussian pulse of width 8 ps (FWHM) and a peak power of 10 mW and bit ‘0’ is transmitted by sending nothing. The fiber dispersion is -3 ps.ps/km and length 40 km. The fiber loss is 0.2 dB/km. An amplifier of gain 11 dB is placed after the fiber. Find (a) the average power (b) the pulse width (FWHM) after the amplifier. 6 marks
Useful information
Speed of light in vacuum c 2.99793m/s
Electron charge q 1.60218 C
Planck’s constant h 6.625J.s
Boltzmann’s constant k 1.38054J/K
The transfer function of an optical fiber is given by
Bit rate and transmission distance in a dispersion limited system are related by
For Gaussian pulse
=half width at 1/e-intensity point
The PSD of shot noise is
and that of thermal noise is
The PSD of ASE noise is given by
Total loss in the cavity is given by
The rate equations governing photons and electrons are given by
.