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ELEC3115 – ELECTROMAGNETIC ENGINEERING

创建日期：2024-05-24 16:30:26

所属分类：电气工程electric engineering

标签： ELEC3115

ELECTROMAGNETIC ENGINEERING

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ELEC3115 – ELECTROMAGNETIC

ENGINEERING

Assignments submitted after the Cutoff Date will not be considered, and will
be given zero marks.
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 rather than
taking photos with a phone.
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 assess the 3 assignments
delivered to each person will result in a mark of zero for this assignment.
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 4 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.
2
Question 1 – Reflections in the time domain [30 Marks]
Consider the circuit shown in Figure 1 below. It consists of a voltage generator with zero
internal resistance, that produces a voltage step of amplitude VG = 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 coaxial
cable with characteristic impedance Z0 = 50  which contains a non-magnetic dielectric with
relative dielectric constant r = 2. On the right hand side, the cable is terminated by a load
resistance RL = 20 .
(i) Calculate the total capacitance Ccable and the total inductance Lcable of the cable.
[4 marks]
(ii) For the time interval t = 0 – 40 ns, draw the general reflection diagram and calculate
the individual values of currents and voltages propagating forward and backward. You can
draw a “generic” diagram and calculate the numerical values separately, or you can put the
values along the lines in the diagram – whatever you find most convenient, as long as there
is a diagram in the report. [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,
, , , , also in the time interval t = 0 – 40 ns. [12 marks]
(iv) Construct and draw a lumped-element circuit that approximately describes the
behaviour of the extended circuit in Figure 1. Clearly justify the choice you make for the
lumped element that replaces the coaxial cable (see Problem 4 in Tutorial 1).
With this lumped elements circuit, calculate and draw the voltage ,() at the load, for t
= 0 – 40 ns, and superimpose it with the “true” voltage at the load () you calculated at
point (iii) above. That is, redraw () in a new graph, and draw ,() over it. You may
use a plotting software like Matlab to help yourself, or calculate a few points for ,()
and draw a line that goes smoothly through them.
Comment on the similarity and differences between () and ,() [8 marks]
3
Question 2 – Impedance matching [35 Marks]
Consider a coaxial cable, filled with a non-magnetic dielectric with relative dielectric constant
r = 3. The cable has a characteristic impedance Z0 = 75 . The cable is 80 cm long. It is
terminated to the right by a resistor = 150 Ω in parallel with a capacitor = 10 pF, and
connected on the left to a generator with internal resistance = 75 Ω. The generator
produces a steady-state sinusoidal signal of amplitude VG = 1 V at frequency f = 500 MHz.
The circuit is depicted in Figure 2 below.
(i) The diameter of the inner conductor of the coaxial cable is d = 1 mm. Calculate the
diameter D of the outer conductor. [4 marks]
(ii) Using the Smith chart, calculate the reflection coefficient Γ at the load. [3 marks]
(iii) Imagine you can insert a slotted line between the cable and the load. What is the
maximum voltage you expect to measure? [6 marks]
(iv) Calculate the distance between maxima of the standing wave along the cable.
[2 marks]
(v) Using the Smith chart, design an open-circuited stub in parallel to the line, that
matches the load to the characteristic impedance of the cable (you may assume that you
can cut the coaxial cable at any point and insert a perfect T-piece to connect the stub). The
circuit should look like in Figure 3 below.
Explain clearly 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 the load. Quote these
lengths in absolute values, i.e. in units of meters. (Note: the stub is made of the same type of
cable as the one that connects to the load). Provide l and d for both possible solutions to the
matching problem. Scan and attach the detailed Smith chart you have used to arrive at the
solutions. [20 marks]
4
Question 3 – Waveguides [25 Marks]
Consider a rectangular waveguide, with transverse dimensions a = 22.86 mm and b = 10.13
mm. The waveguide is filled with air.
We wish to use this waveguide to propagate a wave at frequency f = 18 GHz.
(i) Calculate the cutoff frequencies of all the propagation modes (TEmn, TMmn) that can
be sustained by this waveguide at 18 GHz. Explain in detail how you choose the allowable
modes and calculate their cutoff. [10 marks]
(ii) For all the allowed modes at f = 18 GHz, calculate the propagation constant  and
the distance between the peaks of the electric field along the longitudinal direction (z).
[9 marks]
(iii) Assume that the 18 GHz signal along this waveguide is used to transmit digital data,
which means it is modulated by short pulses. Which propagation mode would you choose to
obtain the fastest possible speed of data transmission? How fast can the digital pulses travel
in this waveguide, when they modulate a 18 GHz signal? Explain your answer. [6 marks]
5
Question 4 – DC protection of RF amplifier [10 Marks]
(Note: this question pertains a topic we have not explicitly discussed during the lectures.
However, the course has given you all the knowledge you need to answer this question. The
answer is actually quite simple, but requires you to think.)
Consider a circuit that contains a signal generator at frequency = 1 GHz with internal
resistance = 50 Ω, connected to a 1 m long coaxial cable with characteristic impedance
0 = 50 Ω and propagation velocity = 2 × 10
8 m/s. This cable connects to the input of a
radiofrequency (RF) amplifier that presents a = 50 Ω input impedance. Therefore, the
whole circuit is appropriately matched.
Often, RF amplifiers are very sensitive to DC (zero-frequency) voltages, and can be
damaged by an accidental DC bias applied to their input. This is usually resolved by AC-
coupling the amplifier, for example by adding a capacitor in series. However, sometimes this
solution is undesirable.
Design a stub, to be placed in parallel to the cable, that protects the amplifier from DC
voltages. The stub must be made using the same type of cable as the one that carries the
signal. You may place the stub using a T-piece at any point along the cable, and you may
choose arbitrarily the termination of the stub. The protection stub must have no effect on the
signal at 1 GHz, although it is allowable for it to affect signals at other frequencies.
Here, “design the stub” means provide the length , distance from the load, and specify the
admittance of its termination, as per the Figure 4 below.

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