Department of Electrical and Electronic Engineering

EIE First Year Tutorial Book

2015

Tutorials

You may have met your personal tutor during Week 1. You will now meet your tutor on alternate weeks throughout the autumn and spring terms. In tutorials you will be with two fellow students and the purpose of these meetings is to reinforce learning and understanding through discussion and problem sheets. Copies of the problem sheets are included in this booklet and each sheet has a problem to relate to the lecture module. You are expected to work independently on the problems and bring your ideas and workings for discussion in tutorial. You can use the blank pages in the booklet to show your work.

Schedule for problem sheets. Problem Sheet 1 – for discussion Weeks 4 or 5 Problem Sheet 2 – for discussion Weeks 6 or 7 Problem Sheet 3 – for discussion Weeks 8 or 9 Problem Sheet 4 – for discussion Weeks 10 or 11

Your personal tutor is the person who knows you best and who may be asked to write references to support your applications for scholarships, internships and future job applications. He/She is also the person who is asked to comment on your performance at the end of each term and at the end of year. It is important to maintain good attendance and participation in tutorials in order to get the most out of this valuable contact time. Towards the end of the Autumn Term you will be asked to complete a self-evaluation pro-forma in which you are asked to reflect on your first term at Imperial College. Please take time to complete this form as it will form the basis of a one-to-one progress discussion with your personal tutor. A copy of the form will also be kept on file. A copy of this questionnaire is at the back of this booklet. There is also a form requesting information about you which might be useful when completing references.

Student self-evaluation questionnaire

These forms are available to guide you through a self-evaluation exercise. The questions are not obligatory but might help you to find the solution to the problem if you experience difficulties with the course. You can always use this as a starting point for further evaluation with your tutor.

1. How confident are you in your capabilities/knowledge on the main courses taught this term?

Technical course Very confident Confident Neutral Not so confident

Not confident

EE1-01 Analysis of Circuits

EE1-02 Digital Electronics 1

EE1-10 Mathematics

EE1-03 Semiconductor Devices (EEE only)

EE1-07 Software Engineering

2. Study approaches

Always Often Occasionally Only when asked to by the lecturer

Never

Do you have your lecture notes/hand-outs open and ready to use during lectures?

Do you stop talking when the lecture begins?

Do you ask for clarification if you don’t understand?

Do you retain any information from the lecture?

Do you attend study groups? Do you take the self-assessed tests in the study groups?

Do you benefit from these self-assessed tests?

Do you answer the additional questions?

Do you hand in your coursework on time?

Do you revise every day? Do you only study when exams are imminent?

Do you organise your time in order to keep up with revisions and coursework?

Now consider whether you are using your time effectively. Are you spending enough time understanding the subject, solving problems and finding help if and when necessary.?

Information for Student File and to be used in references

You might want to consider filling in these questions for your tutor, to help them write reference letters for you. These can be put in your personal file that is kept in the Department for this purpose. You can pull out this sheet and give it to your tutor.

Name: Favourite subjects. What are your favourite subjects and how well do you think you are

performing in them. Are you a member of any student societies or take part in any extra curricula activities? Please

describe any positions of responsibility. Aims for the future. Please give a brief description of what you would like to do in the future

and how your study choices will be influenced by this.

EIE1 Autumn Term 2015– Problem Sheet 1 Please attempt these before your week 4 or 5 tutorial and bring your work for discussion with your tutor. Analysis of Circuits For the following circuit:

75V 50Ω

20Ω

20Ω

88Ω

5.9A

A B C40Ω

a) How many nodes, sources and resistors are there? b) Use nodal analysis to write the nodal equations for the nodes whose voltage is unknown: c) Hence solve the equations to find all nodal voltages relative to a suitable reference node. [65, 97] d) Finally, find the branch voltage, BCV , across the Ω40 resistor. Digital Electronics a) Why are data usually represented in binary form in digital electronics?

b) How many discrete values can be represented with 12 bits?

c) Convert the hexadecimal number (D17A)16 to decimal and to BCD format.

d) Convert (101011.01)2 to decimal. Question 3: Introduction to Computer Systems Convert the following decimal numbers into binary:

1. 48729 2. –666 (using two’s complement) 3. 0.625

Convert the following binary numbers into decimal. For each number, perform the conversion assuming (a) the number is unsigned (b) the number is in two’s complement representation.

1. 11000 2. 01010 3. 0.00111

Convert the following binary numbers into hexadecimal:

1. 101010101010 2. 11011

0

Tutorial Sheet 1 Mathematics

1. Find the real part of (1

sin θ + i cos θ

)4

in terms of cos 2θ.

2. Find all roots of

z4 + 2z2 + 2 = 0 .

Give your answers in complex exponential form and display them on an Argand

diagram...

EIE1 Autumn Term 2015 – Problem Sheet 2 Please attempt these before your week 6 or 7 tutorial and bring your work for discussion with your tutor. Analysis of Circuits In the following circuit you may assume the op-amp is ideal with infinite gain.

U1 U2

10k 20k30k

5k

XY

a) Give an expression for the voltage at node Y in terms of the voltages 1U and 2U . b) Hence, give an expression for the voltage at node X in terms of the voltages 1U and 2U .

[ 314 , 3

7 ]

Digital Electronics

a) Draw a logic circuit to implement the function CBAf )( += directly with basic logic gates (AND, OR, NOT). Using DeMorgan’s Theorem, show that the function can also be implemented with one OR gate and two inverters.

b) Simplify the equation DBCABCDCABDBAg +++= using a Karnaugh Map.

c) Use a MUX to implement: BAABCBAf ++= .

d) Explain the following symbol and describe the operation of the device. How would the symbol and the operation of the device be modified if the G1 input was active low?

MUX

11

SELECT

ENABLE ENG174LS157

23

4

56 7

1110 9

1413 12

Introduction to Computer Systems

There are 8 MU0 instructions listed in your notes. How many could there be? What other instructions may be useful? What does the following series of MU0 machine code instructions do?

0000 0000 0000 0000 0010 0000 0000 0100 0001 0000 0000 0000

What does the memory contain after execution?

0

Tutorial Sheet 2 Mathematics

1. Evaluate the limit

limx→∞

√x(√

1 + x−√x).

Do not use l’Hopital’s rule.

2. Differentiate

(sinx)sinx .

EIE1Autumn Term 2015 – Problem Sheet 3 Please attempt these before your week 8 or 9 tutorial and bring your work for discussion with your tutor. Analysis of Circuits For the following circuit:

V R LC VC

VLVR

(a) If V is the phasor j−1 and the impedances of the components (in Ω ) are 10=R , jL 50=

and jC 40−= , calculate the values of the phasors CV , LV and RV . Sketch a phasor diagram that demonstrates the phasor equation shows RLC VVVV ++= .

(b) If the frequency of V is 1kHz, calculate the values of L and C (in Henries and Farads). Also, give expressions for the waveforms )(tv and )(tvC .

(c) At what frequency will the impedances of L and C have the same magnitude? Calculate the magnitude of CV at this frequency. [4.47]

Digital Electronics

a) Subtract 98 from 49 using 8-bit 2’s complement representation of the numbers. How would the answer be written in sign-magnitude form?

b) A 64x4 bit ROM is to be used to implement the following functions:

BAABCBAf ++=

DBABg +=

Complete the following table showing the contents of the ROM at each address:

Address Data 00 0 01 0 02 0 03 0 04 3 05 2 06 … 07 08 09 0A …

Draw the symbol for the ROM showing how the inputs and outputs are connected, making sure there are no floating inputs, and labelling unused outputs.

Introduction to Computer Systems a) What does the following ARM code do?

LDR r0, NUMA LDR r1, NUMB MOV r2, r0 Loop SUBS r1, r1, #1 ADDNE r2, r2, r0 BNE Loop STR r2, NUMA SWI 0x11 NUMA DCD 0x00000025 NUMB DCD 0x00000004 b) What is the difference between the ASR and LSR instructions?

0

Tutorial Sheet 3 Mathematics

1. Obtain the indefinite integral ∫dx√

3 + 2x− x2.

[HINT: beginning by completing the square!]

2. Integrate ∫dx

2 + cos x

EIE1 Autumn Term 2015– Problem Sheet 4 Please attempt these before your week 10 or 11 tutorial and bring your work for discussion with your tutor. Analysis of Circuits For the following circuit:

v(t)

1k

4k1.25µF

x(t)

(a) If ttv ωcos)( = , find )(tx in the form of a phasor X . Sketch a graph showing the magnitude

of X in decibels as a function of ω using a logarithmic frequency axis. (b) Calculate the time constant of the circuit. [1ms] (c) Suppose that

≥+<−

=ms 5for 10ms 5for 10

)(tt

tv

(i) Find the steady state value of )(tx for ms 5<t . (ii) Find the steady state value of )(tx for ∞=t . (iii) Find the value of )(tx for ms )5( +=t , that is, immediately after )(tv changes to +10V. (iv) Find a formula for )(tx for ms 5≥t . (v) Sketch a graph of )(tx for ms 100 ≤≤ t .

Digital Electronics

a) Design a 4-bit synchronous binary down counter using D-type flip-flops and appropriate logic. Show working, including the state transition table, and Karnaugh Maps for each state variable.

Introduction to Computer Systems a) What does the ARM STMED instruction do?

Consider the following subroutine code: BL SUB1 . . . SUB1 STMED r13!, r0-r2,r14 . . . BL SUB2 . . . LDMED r13!, r0-r2,r14 MOV pc, r14

1. Which registers does the BL instruction affect and why? 2. Why is r14 pushed onto the stack?

b) Here is a series of address references given in decimal: 1, 4, 8, 5, 20, 17, 19, 56, 9, 11, 4, 43, 5, 6, 9,

17. Assuming a direct-mapped cache with 16 one-word blocks which are initially empty, label each reference in the list as a hit or a miss and show the final contents of the cache. [P & H, Ex. 7.7]

Mathematics 4. The waveform , shown below, is periodic with period .

For , it is given by for and otherwise.

-4 -2 0 2 4024

Time (s)

v(t)

a) What is the frequency of ?

b) Say whether the function is“odd”, “even”, or neither.

c) The Fourier series of is given by

Find expressions for the coefficients and .

d) Give numerical values for the coefficients , , and .