Assignment 2 - Summer 2022
Due: July 10, 2022 at 11:59pm via CrowdMark.
Unless otherwise stated, you must show your work.
Question 1. Quadric surfaces:
(a) Sketch the cross-sections of the surface x2 + 3y2 = 1 + z2 parallel to the xy-plane, the xz-plane, and the
yz-plane. Identify the shapes of these cross-sections.
(b) The parametric curve r(t) = ?1 + cos(t), sin(t), 2 sin( 12 t)? parametrizes the intersection of two quadric surfaces.
Identify the two quadric surfaces by equation (and by name) and explain how you know that your answer is
correct.
Question 2. Computing partial derivatives:
(a) Let f(x, y) be a function of two variables such that fx(5, 3) = 4 and fy(5, 3) = ?1. Let g(x, y) = f(2x+3, 3y2).
Find gx(1, 1) and gy(1, 1).
Evaluate fx(1, π) and fy(1, π).
Question 3. Finding tangent planes through certain “anchors” and certain directions:
(a) Find all planes which (i) are tangent to the elliptic paraboloid z = x2 + y2, and (ii) pass through both points
P = (0, 0,?1) and Q = (2, 0, 3). How many such planes are there?
(b) Find all planes which (i) are tangent to the surface z = x+xy2? y3, (ii) are parallel to the vector v? = ?3, 1, 1?,
and (iii) pass through the point P = (?1,?2, 3). How many such planes are there?
(c) Find all planes which (i) are tangent to the surface z = x2 + sin y, (ii) are parallel to the x-axis, and (iii) pass
through the point P = (0, 0,?5). How many such planes are there?
ELEC2133
Analogue Electronics
This midterm contributes to 10% of the total assessment of this course
The due date is on Monday July 18, 2022 (11:59pm). Your submissions are to
be submitted on Moodle before the due date and time. Assignments submitted
after this date will attract a penalty of 5% per day.
The take home midterm contains two problems with four parts. The first problem
is the continuation of assignment II. The parts which deal with frequency
response and simulation are included here. The second problem is the modified
version of assignment I. Each problem contains one or more parts. Each part has
been labelled with P, C, D or HD that indicates the level of difficulty. P means
that the question could be attempted by all students and students who answer the
question correctly are at the level of “pass”. C means the question could be
attempted by students who are at the level of “credit” in the course. D and HD
indicate the question could be attempted by students who are at the level of
“Distinction” and “High Distinction”, respectively.
What does this mean?
If you are targeting to pass or get credit in the course, you may only attempt those
P or C types of questions.
If you are happy or targeting to get a distinction, you can attempt those P, C, and
D types of questions.
If you are targeting a to get high distinction, you should attempt all the questions
including HD type of questions.
2
QUESTION 1 [60 Marks]
In the assignment I, you analyzed and designed the charge readout circuit for PZT actuator
shown in Fig 1(a). One of the problems that is encountered in the readout circuit is that the last
stage of the amplifier, which is the non-inverting amplifier, amplifies low-frequency noise from
power supply or the vibration of the actuator due to environmental factors. It also amplifies
any of DC imperfections contributed from the previous stages. Reducing the noise at the output
is important while ensuring the readout signal is amplified. Although there are other
modifications that may be applied to the non-inverting amplifier in order to achieve high signal-
to-noise ratio, the non-inverting amplifier will be replaced by a three-stage transistor amplifier
shown in Fig. 2(a) in this assessment. Your task will be to calculate its bandwidth.
Fig. 1: PZT actuator self-sensing readout circuit
The three-stage amplifier consists of one n-channel MOSFET transistor M1 in depletion
mode with W/L = 1 and two BJT transistors Q1 and Q2. The transistors have the model
parameters as provided in the Table below
Transistor Parameters
M1 Kn = 10mA/V
2 VTN = -2V λ=0.02V-1 Cgs = 3.5pf, Cgd = 0.1pf
Q2 β=150 VA = 80V VBE = 0.7V fT = 2GHz, Cμ= 0.2pf
Q3 β=80 VA = 60V VBE = 0.7V fT = 2GHz, Cμ= 0.2pf
Fig. 2: A three-stage transistor amplifier
PART I (Calculating bandwidth)
a) [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for
low frequency. [5 marks]
b) [P,C] Calculate the lower 3dB frequency, fL, of the amplifier using the appropriate
time constant method. [15 Marks]
c) [P,C] Draw small-signal equivalent circuit of the amplifier in the form suitable for
high-frequency analysis. [5 Marks]
d) [DN]*Calculate the higher 3dB frequency, fH, of the amplifier using the appropriate
time constant method. [15 Marks]
PART II (LTSpice or Pspice Simulation)
a) [DN] *Simulate Fig. 2 and compare the results with your calculation in assignment II
and Part I. The Spice transistor models will be uploaded on Moodle.
[20 marks]
4
QUESTION 2 [40 Marks]
The Opamp readout circuit you dealt with in assignment I and shown in Fig. 1 is modified to
output voltage, Vo.
[15 marks]
b) [P,C] In the non-ideal case, all op-amps in Fig. 3 have the following DC
imperfections
Input bias current: IB = 40nA at room temperature
Input offset current: Iio = ±2nA at room temperature
Input offset voltage: Vio = ±2mV at room temperature
Calculate the worst-case output offset voltage at room temperature assuming R5 =
0.5M?, R4 = 280K?, R3 = 1K?, R1=1K?, R2=1K?, C1 = C2 = CPZT = 10nf.
[25 marks]