Question 1: (50 marks)
Dispersion, expressed in terms of the symbol ∆?, is defined as pulse spreading in an optical fiber. As
a pulse of light propagates through a fiber, elements such as numerical aperture, core diameter,
refractive index profile, wavelength, and laser linewidth cause the pulse to broaden. Dispersion is
generally divided into two categories: modal (or multimode) dispersion and chromatic dispersion.
a) Define modal dispersion and chromatic dispersion. (10 marks)
b) When considering the total dispersion from different causes, how can we approximate the
total dispersion (denoted by ∆????)? (10 marks)
c) A 2-km-length multimode fiber has a modal dispersion of 1 ns/km and a chromatic dispersion
of 100 ps/km nm. This fiber is used with an LED of linewidth 40 nm.
i. What is the total dispersion? (12 marks)
ii. If the approximate bandwidth (BW) of a fiber can be related to the total dispersion by the
following relationship: BW = 0.35/∆????, calculate the bandwidth of the fiber.
(4 marks)
iii. Find the transmission capacity of the fiber is expressed in terms of bandwidth×distance.
(6 marks)
d) In building a network it is often useful to add together the signals from two or more fibers, or
to send the signal from a single fiber out onto a number of fibers. How can this be done
optically, without the need for intermediate electronics? Draw a simple sketch for this device.
(8 marks)
TM355/ STMA 3 of 3 Spring 2019-20
Question 2: (50 marks)
Cyclic Redundancy Check (CRC) is a method of detecting accidental changes/errors in
communication channel. In implementing this method, a transmitter sends an encoded data that
consists of n bits constructed in the following way:
 Step 1: Obtain a binary number from a generator polynomial consisting of k bits (as you have
learned during the course)
 Step 2: For the m bits binary data message, augment the message by adding k-1 zeros at the
end of the data message
 Step 3: Use modulo-2 binary division to divide binary data obtained from Step 2 by the key
obtained from Step 1, and store remainder of division.
 Step 4: Append the remainder at the end of the binary message data m to form the encoded
data of length n, and send it to the receiver
Now, assume that a standard for some system specifies the use of CRC with the following generator
polynomial: x
3
+ x
2
+ 1.
a) What binary number does this generator represent? (10 marks)
b) If the transmitter is to send the following data message: 100100. Follow up the procedure
explained above to find the remainder, and the encoded data to be sent. (20 marks)
c) Suppose the receiver receives the following data: 100000001. To check if there is an error in
the received data, the receiver performs modulo-2 division again and if the remainder is 0,
then there are no errors. Check if there are errors in the received encoded data message.
(20 marks)