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UNSW Sydney
SCHOOL OF ELECTRICAL ENGINEERING & TELECOMMUNICATIONS
ELEC3115 – ELECTROMAGNETIC
ENGINEERING
Part B assignment – T1 2025
Assignment due date: Monday 28
th
April by 11:55 pm
Assignments submitted after the due date but before the cutoff date will lose 10% of
the marks for the whole assignment activity.
Assignment cutoff date: Tuesday 29
th
April by 11:55 pm
Assignments submitted after the cutoff date will not be considered and will be
given zero marks. This is necessary to ensure that all assignments are submitted
and peer-marked before the final exam, so students can get timely feedback on their
work.
Upload your solution on Moodle in the form of a single pdf file (the system will accept
only 1 file as submission). You can either scan your hand-written pages or prepare the
assignment report in a text editor. Please ensure your writing and drawings are as
clear and legible as possible. If possible, please use a proper scanner, or a phone
scanner app like Microsoft Lens (or equivalent), rather than just taking photos.
Peer review due date: Monday 5
th
May by 11:55 pm
The assignments will be marked through anonymous, random peer-assessment.
Therefore, please ensure that the document you upload is anonymous. Do not write
your name or zID on it (don’t worry, the Moodle system knows who you are.)
The peer assessment activity is compulsory. Failure to upload to Moodle your
assessment of the 3 assignments delivered to you by the peer review due date
will result in a mark of zero for the whole assignment activity.
If you do not submit your assignment by the cutoff date, you will not participate in the
peer-assessment activity and therefore receive no marks for it.
The assignment consists of 3 questions and gives a total of 100 marks. These 100
marks will constitute 85% of the assignment value. The remaining 15% is given for the
quality and accuracy of the assessment.
Altogether, this activity counts for 15 marks in the overall course assessment.
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Question 1 – Reflections in the time domain [35 Marks]
Consider the circuit shown in Figure 1 below. It consists of a generator with internal
resistance R
G
= 100 Ω that produces a voltage step of amplitude V
G
= 1 V starting at time t =
0. That generator voltage stays constant at 1 V for t > 0. It is connected to a 2 m long
lossless coaxial cable with characteristic impedance Z
0
= 75 Ω which contains a non-
magnetic dielectric with relative dielectric constant ε
r
= 3. On the right hand side, the cable is
terminated by a load resistance R
L
= 300 Ω.
Figure 1
(i) Calculate the total capacitance C
cable
and the total inductance L
cable
of the cable.
[5 marks]
(ii) For the time interval t = 0 – 70 ns, draw the general reflection diagram and calculate
the individual values of currents and voltages propagating forward and backward.
[6 marks]
(iii) From the reflection diagram constructed at point (ii), draw in four different plots the
voltages and the currents at the generator (where it connects to the cable) and at the load,
푉푉
퐺퐺
,퐼퐼
퐺퐺
,푉푉
퐿퐿
,퐼퐼
퐿퐿
, also in the time interval t = 0 – 70 ns. [1 6 marks]
(iv) Consider the lumped-elements circuit drawn in Figure 2 below, which contains the
same generator and load as the circuit in Figure 2, and replaces the coaxial cable with a
capacitor of the same value C
cable
as that of the coaxial cable described before. Draw the
voltage V
L
(t) for t = 0 – 70 ns.
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Figure 2
Note: you should have learned the time evolution of RC circuits in 2
nd
year electronics. As a
reminder, the general formula is of the form:
푣푣
(
푡푡
)
=푣푣
(
∞
)
+
[
푣푣
(
0
)
−푣푣(∞)
]
exp(− 푡푡/푅푅푅푅)
You may use a plotting software (Matlab, Excel, etc.) to produce the graph, or calculate a
few points and hand-draw a line that goes smoothly through them. [6 marks]
(v) Comment on the similarity between 푣푣
퐿퐿
(푡푡) obtained with the lumped-elements model
above, and the graph of 푣푣
퐿퐿
(푡푡) you have obtained at point (iii) when properly describing the
propagation through the cable.
Are the two graphs approximately similar? Why? Clearly explain your reasoning.
[2 marks]
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Question 2 – Impedance matching [35 Marks]
Consider the circuit drawn in Figure 3 below:
Figure 3
A load impedance 푍푍
퐿퐿
=120−푗푗30 Ω is connected to a lossless cable of length 푙푙
2
=1.5 m and
characteristic impedance 푍푍
02
=75 Ω. The cable has a dielectric with relative dielectric
constant 휖휖
푟푟2
=3. The 1.5 m cable with 푍푍
02
=75 Ω is an integral part of the circuit and cannot
be removed. We will call this cable “type-2”.
We wish to connect this system of “load + type-2 cable” to a distant generator, which
produces a steady-state sinusoidal signal at frequency 푓푓=500 MHz. The generator needs
to be connected to the rest of the circuit with a lossless cable having characteristic
impedance 푍푍
01
=50 Ω and a relative dielectric constant 휖휖
푟푟1
=2. We will call this cable “type-
1”.
The aim of this exercise is to design a circuit that matches the “load + type-2 cable” to the
generator, using pieces of type-1 cable.
In all the questions below, you must obtain the results using a Smith chart.
(i) Using the Smith chart, calculate the reflection coefficient Γ
퐿퐿
at the load. [4 marks]
(ii) Using the Smith chart, calculate the Voltage Standing Wave Ratio (VSWR) in the
type-2 cable. [2 marks]
(iii) Calculate the distance between maxima of the standing wave along the type-2 cable.
[3 marks]
(iv) Using the Smith chart, calculate the impedance seen at point J (see drawing above),
looking towards the load. [5 marks]
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(v) Using the Smith chart, design a single short-circuited stub that matches the load to
the characteristic impedance of the type-1 cable (you may assume that you can cut the
coaxial cable at any point and insert a perfect T-piece to connect the stub). Explain in words
each step you take to arrive at the result. Once you have obtained the result, describe the
stub in terms of its length l, and its distance d from point J. Quote these lengths relative to
the signal wavelength. (Note: the whole matching circuit is made of type-1 cable).
[16 marks]
(vi) Now assume you replace the piece of type-2 cable with a different one, that has
휖휖
푟푟2
=4, but the same characteristic impedance 푍푍
02
=75 Ω. With this new cable, is the stub
geometry you designed at point (v) still effective at matching the system? Explain clearly the
reason for your answer. [5 marks]
For all the questions that required using a Smith chart, clearly mark on the chart all the
relevant points, explain in the text of your assignment paper how you found every point, and
include a scan of the Smith chart with your submitted pdf file.
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Question 3 – Waveguides [30 Marks]
Consider a rectangular waveguide, with transverse dimensions a = 10.668 mm and b =
4.318 mm. The waveguide is uniformly filled with a non-magnetic dielectric with 휖휖
푟푟
=1.5.
We wish to use this waveguide to propagate a wave at frequency 푓푓=25 GHz.
(i) Which propagation modes can be sustained by this waveguide at 25 GHz? Explain in
detail how you arrive at the answer. [10 marks]
(ii) Calculate the propagation constant
β for the allowed modes at f = 25 GHz. [5 marks]
(iii) Again for a signal at 25 GHz, calculate the wave impedance for the TM mode with
the lowest cutoff frequency. Explain the meaning of the results. [5 marks]
(iv) Now assume that the dielectric has broken perpendicularly to the length of the
waveguide, and that the two resulting pieces of dielectric have been pulled out slightly,
leaving a 20 mm gap, as shown in Figure 4 below.
Suppose we wish to transmit a digital signal described by a set of pulses that modulate a
carrier at 푓푓=25 GHz, propagating in the TE
10
mode.
Calculate the group velocity and the wave impedance of the modulated signal, both in the
intact waveguide (with the dielectric having 휖휖
푟푟
=1.5) and in the broken section (where the
dielectric is air).
Assuming, as usual, that the dielectrics are lossless, will the amplitude of the signal output at
Port 2 be the same as the signal input at Port 1? Explain in words the reason for your
answer. [10 marks]
Figure 4
****************************** end of assignment paper ****************************
