H6109
THE UNIVERSITY OF SUSSEX
RADIO TO OPTICAL FREQUENCY ENGINEERING
Candidates must attempt THREE out of FOUR questions
If all four questions are attempted, all will be marked, but the lowest mark will
not be counted in the total for the paper.
Exam Session: 2 hours and 30 minutes
You should spend 2 hours answering the exam questions and allow 30
minutes for scanning, uploading, and checking your submission.
Examination handout: Formula Sheet and Smith Chart (available to download
from Canvas)
Read Academic Integrity Statement
You MAY access online materials, notes etc. during this examination. You
must complete this assessment on your own and in your own words. By
submitting this assessment, you confirm that your assessment includes no
instances of academic misconduct, for example plagiarism or collusion. Any
instance of academic misconduct will be thoroughly investigated in
accordance with our academic misconduct regulations
Briefing:
For questions requiring a Smith Chart: print off a hard copy, draw your
solutions on the hardcopy and include the page with the rest of your exam
pages when you scan and upload them as a single PDF file.
Alternatively, you can draw your solutions directly on the soft copy provided
and include the page with the rest of your exam pages when you scan and
upload them as a single PDF file.
H6109 RADIO TO OPTICAL FREQUENCY ENGINEERING
2
Q1. The input impedance of a preamplifier is measured to be 25 – j50 . It is
to be connected to a 4 GHz signal source using a 50 transmission line.
(a) Assume that the phase velocity of the signal on the line is 1.5 x 108 m/s.
Calculate the wavelength of the signal. [2 marks]
(b) Calculate the normalised impedance of the preamplifier. [2 marks]
(c) Clearly indicate the normalized load and the circle corresponding to r=1
on the Smith chart. [4 marks]
(d) With reference to Figure Q1, use the Smith chart provided to design
the matching network consisting of a length, l1 of the transmission line
and short circuited stub of a length l2 . Show your constructions on the
Smith chart. Specify the lengths l1 and l2.
[12 marks]
Figure Q1
H6109 RADIO TO OPTICAL FREQUENCY ENGINEERING
3
Q2. (a) The scattering (s) parameters of a high frequency transistor may be
specified as s11, s21, s12 and s22. What transistor operating
parameters must be stated in order to specify particular values of the
s-parameters [2 marks]
(b) Express the forward gain, reverse gain, input reflection coefficient
and output reflection coefficient of the device in terms of its
s-parameters. Under what condi
tions do these definitions apply
[4 marks]
(c) The following transistor s-parameters are to be used in the design
of a high frequency amplifier:
s11 = 0.7, -57o
;
s21 = 10.5, 36o
;
s12 = 0.04, 47o
;
s22 = 0.79, -33o
Calculate the parameter and Rollett stability factor and hence
specify the stability condition of the transistor. [8 marks]
(d) Using the above s-parameters calculate the center and radius of
the input stability circle. Subsequently, plot the input stability circle
on a Smith chart, and indicate the input stability region of this
transistor on the chart. [6 marks]
Q3. (a) The dielectric substrate of a microstrip transmission line has a
relative dielectric constant = 3.4 Find the effective dielectric
constant of the microstrip if the filling factor is given by = 0.7 and
q=1, respectively. [5 marks]
(b) Design a copper microstrip transmission line with a 100Ω
characteristic impedance, to be fabricated on a substrate 0.51 mm
thick with a relative dielectric constant of = 2.2 . Use the
equations provided in the formula sheet and specify the width
required. [9 marks]
(c) Consider the transmission of a 600 MHz signal on this line. If the
effective dielectric constant of such a microstrip line is 4.6, calculate
the % difference between the guided wavelength and the
wavelength in an infinite slab of this substrate. What are the
implications of using the wrong wavelength in the design of
microstrip circuits (Take the speed of signal propagation as 1.5
x108 m/s). [6 marks]
H6109 RADIO TO OPTICAL FREQUENCY ENGINEERING
4
Q4. (a) Briefly describe and sketch the principle of operation of a circular
optical fibre which allows for the propagation of optical frequency
signals. How does its construction differ fundamentally from a lower
frequency transmission line such as a waveguide or coaxial cable
[4 marks]
(b) An optical fibre has a core refractive index of 1.540. Calculate a
suitable value of cladding refractive index so that it may be used for
weakly guided optical propagation. [5 marks]
(c) If, in addition, the fibre is to be used for single-mode propagation of
1.1 m wavelength signals, choose a suitable value for the core
radius, a, and find the associated value of the V number. [6 marks]
(d) An optical fibre has a core refractive index of 1.550 and a cladding
refractive index of 1.530. Calculate the time delay between the
arrival of the signals travelling on the fastest versus the slowest
mode in the fibre, assuming the length of the fibre to be 1km. Take
the speed of light as 3 x108
m/s. [5 marks]
End of paper