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May 2012 Page 1 of 9

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SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS

SEMESTER-TWO EXAMINATIONS, 2011/2012

ANALOGUE ELECTRONICS – PART B

EO127

DR. D.S. GILL

Time allowed: THREE hours

Answer: FOUR questions from SIX questions

Each question carries 25 marks

Items permitted: Any approved calculator

Items supplied: Linear-linear graph paper

Blank oscilloscope screen diagrams (pp. 8-9)

Marks for whole and part questions are indicated in brackets ( )

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Question 1

(a) Draw a simple block diagram for a general-purpose cathode-ray oscilloscope

(CRO) showing the major elements that are necessary for successful operation.

Marks will also be given for a simple explanation of how the oscilloscope works.

(6 marks)

(b) A general-purpose dual-channel oscilloscope is used to display two sinusoidal

signals. Figure Q1 shows a blank screen of a typical oscilloscope. You are

now required to sketch the following two sinusoidal waveforms on Figure Q1

such that an engineer observing the waveforms would be able to sensibly

measure the amplitude, frequency and phase.

The parameters for each signal are as follows:

Signal A: 1 kHz,1 Vrms. Signal B: 1 kHz, 2 Vrms, lags Signal A by 90º.

You may choose your own setting of the timebase control and the Y-sensitivity.

However, it is essential that you state what settings you have chosen in your

answer. Marks will also be given for an explanation with your answer as to how

you arrive at the necessary calculations.

Figure Q1

(10 marks)

(c) Repeat the above, but this time for two triangular waves, one with a peak-to-

peak voltage of 4 V, and the other with a peak to peak voltage of 2 V. The

signal with the larger amplitude is leading the smaller signal by 45º. The

frequency of both waveforms is 20 kHz.

(9 marks)

Please use the copies of Figure Q1 provided in Appendix One (page 8) for your

answer for parts (b) and (c) above. Ensure that you write your student number on

the sheet and attach your answer to your script – spare blank copies are also

provided (page 9).

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Question 2

The circuit shown in Figure Q2 is one way to configure an operational amplifier (op-

amp).

0V

- + Vin

A Vout

Vd +V

-V

Rin Rf

Figure Q2

(a) Explain what is meant by the ‘open-loop-gain’, “ A”, of the op-amp. Your answer

will include a typical numerical value of “ A” for a typical general purpose op-

amp such as a 741 or equivalent.

(4 marks)

(b) Derive, from first principles, the expression for the closed-loop gain, “G”, of the

circuit illustrated in Figure Q2.

(10 marks)

(c) (i) A temperature sensor produces a voltage in the range of 100 mV to

200 mV for a temperature range of 22ºC to 42ºC.

You are required to design a circuit that uses an op-amp and two resistors

that will give an output in the range of 3 V to 6 V. Sketch the configuration

of the required circuit. Calculate the value of the resistor, Rf, if Rin is

1 kΩ.

(6 marks)

(ii) Now choose the nearest preferred values (using the E12 series) for the

resistors, assuming a tolerance of 5%. Estimate the possible variation in

the gain as a result of your choice of resistors. You are still limited to

using only two resistors in total.

(5 marks)

Note: the following numbers are used in the E12 series:

1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2 and 10.0

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Question 3

(a) Transducers are used frequently in industrial applications. Describe what is

meant by a transducer and why it is used. Your answer will include a

description of at least four different parameters that can be measured by

transducers (excluding the LVDT).

(8 marks)

(b) Another type of transducer is an “LVDT”. Discuss the operation of the LVDT

with the aid of suitable diagrams. Your answer will include a typical application

of this transducer.

(10 marks)

(c) Instrumentation systems often require the use of an operational amplifier

configured as a voltage follower.

(i) Determine the value of the closed-loop gain for the voltage follower, giving

reasons for your answer.

(4 marks)

(ii) Explain why this configuration of the op-amp is selected. Your answer will

focus on the input and output impedances.

(3 marks)

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Question 4

(a) A 1 kHz analogue signal of amplitude 1 V is to be converted to a digital signal,

where each sample is represented by three bits.

(i) Explain the process required. Your answer will include a discussion ofthe following: minimum sampling rate, sampling process, pulse code

modulation and quantisation. Diagrams should be used to support your

answer.

(10 marks)

(ii) Hence suggest why the system would be improved if the analogue-to-

digital process produces four bits per sample instead of three.

(3 marks)

(b) State briefly why the configuration for a ladder digital-to-analogue converter is

preferable to that of a binary-weighted digital-to-analogue converter.

(3 marks)

(c) Explain how the ‘successive approximation’ algorithm can be used to perform

conversion of an analogue voltage to an 8-bit digital word. You should illustrate

your answer by converting an analogue voltage of 1.9 V. The significance of

the ‘Least Significant Bit (LSB)’ should be 10 mV. Use an appropriate table to

structure your answer.

(9 marks)

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Question 5

(a) The spectrum of a single audio signal was found to contain the following

frequency components (all in kHz):

1, 2, 3, 4, 8, 10 and 15 kHz

The sound engineer would like to design a filter circuit so that when the above

audio signal is fed to the circuit, the spectrum of the signal at the output will

have NO frequency components above 5 kHz.

Suggest what type of filter circuit is required and sketch the frequency response

of that circuit. You may use the graph paper provided if you wish. You should

also show where the above frequency components are in the same sketch.

Marks will be given for an explanation of how you arrived at your sketch.

(5 marks)

(b) Study carefully the circuit shown in Figure Q5 below:

Figure Q5

Taking care to include every step, determine an expression for the voltage gain

Vout/Vin. Hence indicate, with reference to your expression, what type of filter

this circuit represents.

(8 marks)

(c) (i) Explain the significance of the 'cut-off frequency', 'ωc', for the circuit shown

in Figure Q5 above. Calculate the gain and the phase difference at the

cut-off frequency.

(7 marks)

(ii) Calculate the cut-off frequency for the circuit shown in Figure Q5. Your

answer should be in rad.s

-1

as well as in Hz.(5 marks)

R C Vout Vin

2F

100

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Question 6

(a) A friend has asked you to design a simple circuit to fulfil the following task. He

needs to combine the signals from two electric guitars and one microphone into

one signal as he only has a single input amplifier. Show how this can be

achieved using just one operational amplifier (op-amp) and several resistors.Your answer will include a sketch of the required circuit configuration.

Assume that each of the input signals is to be mixed equally to create the single

output signal. Derive an expression for the output signal of your circuit in terms

of the input signals and the passive components used. Please label your input

signals as V1, V2 and V3 and your output signal as V4.

Your answer should include all working and assumptions made.

(15 marks)

(b) For Figure Q6, derive from first principles, the mathematical expression for

V2/V1, showing all working and stating any assumptions made. Hence state its

purpose.

R 2

C1

-

+

i1

i2

Node X

V1 V2

Figure Q6

(10 marks)

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Appendix 1 – Oscilloscope screen for Question 1 (b) and (c)

Attach to your answer script if used.Student Registration number: ___________________

FIG Q1 for Question 1 (b)

FIG Q1 for Question 1 (c)

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Attach to your answer script if used.Student Registration number: ___________________

Appendix 2 – Oscilloscope screen for Question 1 (b) and (c)

SPARE COPIES

Version 120525.2 dsg

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