代写MAT232H、Java/Python程序代写

日期：2022-07-13 07:45

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]