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Module title and code: Sensors, ES2F5
Assessment setter (module tutor): Dr Christos Mias and Dr Jose Ortiz Gonzalez
Assignment Weighting and typical hours work: 30% of module (45 hours)
Learning outcomes assessed:
 Analyse signal propagation in transmission lines.
 Solve problems, including basic design problems, involving sensors or sensor interfaces.
Context/Introduction/Background to the assignment: Based on material of the module with further research
required for some sections of the assignment.
Requirements/Task: Complete all tasks.
Formatting requirements: The assignment should be submitted as single pdf file in Tabula. No Mac file
formats should be submitted. Answers must be typed. Schematics, diagrams and equations can be written by
hand as long as they are legible. No introduction, table of contents, summary/abstract are expected; simply
provide the answers to the questions. You don’t have to type the question again, just identify in a heading the
question number that you are answering. Indicative assignment length is 10 pages.
Assessment criteria/mark scheme: Marking is out of 100 marks. Marks for each question stated at the start of
the question. Marks will be awarded based on the completeness and conciseness of answer. If answers are not
legible, marks will not be awarded.
Submission date/deadline: 12 noon Tuesday 29th August 2023 via Tabula. All submissions that miss this
deadline will be subject to 5 marks per day penalty, starting at 12 noon on Tuesday.
Additional Useful Resources: Books, instrument manuals, journal/magazines/conference articles, online
information.
Feedback format: Your submitted report will be marked electronically. A mark will be provided for each
question as well as comments in the marked report.
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PART 1
In practice, transmission lines produced by a manufacturer and specified as 50 Ω or 75 Ω lines, are lossy and
their characteristic impedance at a given frequency (in the phasor domain) is not exactly 50 Ω or 75 Ω. Assume,
in your calculations in the following questions, that for the 75 Ω coaxial transmission line the following
approximate values apply for the per unit length resistance, conductance, inductance and capacitance,
respectively: R = 0.39 Ω/m, G = 2.96  105 S/m, L = 3.92  107 H/m, C = 6.75  1011 F/m. Also assume
that for the 50 Ω coaxial transmission line the following approximate values apply for the per unit length
resistance, conductance, inductance and capacitance, respectively: R = 0.20 Ω/m, G = 1.35  105 S/m,
L = 3.03  107 H/m, C = 0.98  1010 F/m. These R, G, L, C values are approximations hence results
obtained from calculations based on these values are not expected to exactly match experimental results.
Question 1 (Total: 36 marks)
An experiment is conducted based on Figure 1. The Arbitrary Function Generator (AFG) AFG3022C
(Zg = 50 ) is set to generate a sinusoidal signal varying between -2.1 V and +2.1 V. The frequency of the
signal is 0.5 MHz. The output of the generator is connected to the input end of the 50 Ω coaxial transmission
line (its characteristic impedance is denoted as Z01) as shown in Figure 1. The length of the line is 100 m. The
output end of the line is terminated by a load of impedance ZL = 50 . Channels 1 and 2 of the Tektronix
TBS1064 oscilloscope are connected at the input (i.e. at x = 0 m) and output (i.e. at x = 100 m, across ZL ) ends
of the transmission line as shown in Figure 1.
Figure 1
The Channel 1 and 2 experimental results are provided in the zipped folder Q1sinusoidal. The AFG is
subsequently set to generate a periodic pulse train (a periodic signal) of period 8 s. Each pulse width is 0.5 s
Channel 1 Channel 2
Zg
Z01
transmission line
x = 100 m x = 0 m
AFG
ZLvg
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and each pulse amplitude is 4.2 V (i.e. the generator signal varies from 0 to 4.2 V). Channels 1 and 2 of the
oscilloscope are again connected at the input and output ends of the transmission line. The Channel 1 and 2
experimental results are provided in the zipped folder Q1pulse.
Each zipped folder above has an image of the oscilloscope screen showing the Channel 1 and Channel 2
experimental results. Each folder also has excel files containing the values of the Channel 1 and 2 results shown
in the oscilloscope screen. Plot the experimental Channel 1 and 2 experimental values for both inputs. With the
aid of the R, G, L, and C  values provided, predict the four experimental results (i.e. the Channel 1 and 2
results for the sinusoidal input and the Channel 1 and 2 results for the pulse input). State any assumptions you
made. Show your calculation steps (see assessment criteria on the front page) otherwise marks will be lost.
(9 marks for each experimental result that is plotted and predicted)
Question 2 (Total: 14 marks)
The experimental setup of this question is shown in Figure 2. Between the output of the AFG generator and the
input of the 50  coaxial transmission line (its characteristic impedance is denoted as Z01), there is a series
resistance of value Rs = 27 . The length of the Z01 transmission line is 100 m. The Z01 line is followed by a
75  line (its characteristic impedance is denoted as Z02). Between the two lines there is a series resistance of
value R12 = 27  as shown in Figure 2. The Z02 line is of length 50 m and it is terminated by a 75  load
(denoted as ZL). L1 = 100 m and L2 = 50 m in Figure 2. Assume that the lengths of the resistances (Rs and R12 )
can be ignored.
Figure 2
Assume that the channel 1 of the oscilloscope (TBS1064) is connected at the input end of the 50  transmission
line (see Figure 2). The signal produced by the generator (AFG3022C, Zg = 50 ) is a periodic pulse train of
period 8 s and pulse amplitude 4.2 V (i.e. the generator signal varies from 0 to 4.2 V). The pulse width is 500
Zg
Z01
Section 1
L1
AFG
vg
Rs
ZL Z02
Section 2
L2
R12
Channel 1
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ns. Predict the experimental results that one is expected to observe in Channel 1 of the oscilloscope. State any
assumptions you made. Show your calculation steps (see assessment criteria on the front page) otherwise marks
will be lost.
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PART 2
Question 3 (Total: 15 marks)
A company has requested you to select a suitable sensor for measuring the volume of a substance inside
a tank. The tank has a diameter of 10 metres and height of 10 metres. The substance is a liquid that can
foam.
a) Discuss the challenges of measuring the level of the substance in the tank and select a suitable
commercial sensor (10 marks)
You can use any commercial sensor and information from the options available at:
https://new.abb.com/products/measurement-products/level/a-dozen-ways-to-measure-fluid-level
https://www.vega.com/en-uk/products/product-catalog/level
https://www.omega.co.uk/section/level-measurement.html
https://fortop.co.uk/solutions/products/level-sensors-level-measurement-level-detection/
b) Is there any potential hazard that you should consider when selecting the sensor? (5 marks)
In the answers of both a) and b), use references to identify the source of information.
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Question 4 (Total: 35 marks)
In some cases, instead of installing a sensor that measures the fluid level and provides a directly measurable
signal, you will have to design the sensor and the conditioning circuit that will convert the physical variable
affected by the level of fluid to a measurable value. In Lab 1 and Lab 2, you designed and tested circuits that are
used for measuring the value of a capacitor that represented the level of liquid in a tank. In this section of the
assignment, you will have to design a capacitive liquid level sensor and its associated conditioning circuits.
The dimensions of the tank are 1 m x 1m x 1m and the maximum level to be measured (h max) is 1 metre. The
liquid is an oil with dielectric constant εr_oil= 30. The capacitive sensor is a parallel plate capacitor, as shown in
Fig. 1. Consider dielectric constant of air εr_air= 1.0005
Figure 1: Parallel plate capacitor used as liquid level sensor
a) Provide a design of the sensor (i.e. specify the dimensions) with a minimum capacitance range between
200 pF and 6 nF. This is an approximate range and deviations are allowed (~ 20%). Provide the equation
that determines the capacitance as function of the oil level and plot the calibration of the sensor
(capacitance) as function the level of fluid. What is the sensitivity of the sensor?
Hint: Fix the capacitor plate size and adjust the distance between plates to achieve the desired
capacitance range.
(8 marks)
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b) Determine the electrical circuit that will generate a digital signal, with constant duty cycle (around 50%)
and frequency dependent on the level of fluid in the sensor. The maximum frequency will be determined
by the last digit of your student number using the formula:
Frequency = [9000 + (last digit) *100] Hz
Describe the calculations and plot the theoretical calibration of the circuit (frequency vs capacitance and
frequency vs liquid level)
(10 marks)
c) Describe the circuit that you will use for connecting the frequency variable signal in (b) to the analogue
input of a microcontroller with an input range of 3 V. Plot the theoretical calibration of the circuit (liquid
level vs analogue voltage signal).
(7 marks)
d) Briefly discuss how the viscosity of the oil, capillarity, condensation and temperature can affect the
operation and calibration of the designed sensor
(10 marks)
Additional information about the electrical circuits is provided in the briefing sheets of Lab 1 and Lab 2.