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UNIVERSITY OF ZIMBABWE

~BScELECTRICAL ENG. (HONOURS) PART I I I

TELECOMMUNICATIONS EE3 10

MAIN EXAMINATION MAY/JUNE 2001

Time allowed: Three Hours

There are seven questions ofequal value.

You may attempt Question 1 and any four other questions

PLEASE NOTE

All answers must be written in ink.(Except where they are explicitly required, pencils may only be used for

drawIng, sketching or graphical work.)

Marks will only be awarded for answers that relate directly to the questionsasked.

Full marks will not be awarded ifanswers are not accompanied by adequatesupporting explanations.

Show your working and state any assumptions that you make.

You may use a non-programmable electronic calculator.Pocket computers and programmable calculators are not allowed in this

examination.

You may retain this paper at the end ofthe examination.

All the relevant tables are supplied

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Question 1 (Compulsory)

a) Explain how co-channel interference can effectively be reduced in mobilecommunications. [4]

b) Explain why it is desirable for music to have a greater bandwidth than speech in

commercial telecommunications systems. [4]

c) Whatare benefits ofdigital terrestrial transmission (broadcasting) and what would bethe major problems faced ifZimbabwe was to introduce it at this time. [4]

d) A telephone transmission system is required to transmit a minimum of10 channelsover thebandwidth 1264 KHz. State whether an amplitude modulated orfrequencymodulated system would be suitable and give reasons for youranswer. Calculate thenumber ofchannels that can be transmitted with the system you choose. [8]

Question 2

a) Determine whether the following signal fits into any ofthetwo classifications: powertype and energy type. t12]

t>0

t0

b). Determine the Coefficient; in the complex Fourier series ofthe

following waveform. [8]

1 0 1 2

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Question 3

) State and Prove The Parseval Theorem. [8]

b) Ifan impulse v,(t) 5(t) is applied to the input ofa system whose transfer function is

H0wH(w) = find the output signal v0(t). [8]

wc +

Jw

c) Distinguish between Time-Invariant and Time-Vaiying systems. [4]

Question 4

a) The BBC VHF- FM sound broadcast system has a rated system deviation of75KHzand a maximum modulating frequency of15KHz. Calculate the required bandwidthfor the system. What would the required bandwidth ifDSB AM where to be used.Comment on your answers. [6]

b) In a frequency modulation system, explain why the higher modulation index, thegreater the number ofsignificant sidebands. [5]

c) Calculate the noise voltage at the input ofthe television R.F. amplifier using anamplifier device having equivalent noise resistance of1 80~and input resistance of400~).The bandwidth ofthe amplifier is 7 MHz and the temperature is 3 05K. [9]

Question 5

a) . Derive the general equation ofan amplitude modulated wave and sketchits frequency spectrum. [6]

b). What are the advantages and disadvantages ofSSB-SC over DSB-FC[4]

). Show that the total power P~contained in an AM wave is given by

p

where P~is the carrier power and m is the modulation index

The power dissipated by an AM wave is 80W when the depth ofmodulation is 25%.What modulation depth is necessary to increase the power to 100W. [10]

Question 6

a) Explain the principle ofQuadrature Amplitude Modulation as applied in

Television transmission. [5]

b) Draw a simplified signal television flow diagram showing how video and audio

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Question 3

) State and Prove The Parseval Theorem. [8]

b) ifan impulse v1(t) =5(t) is applied to the input ofa system whose transfer function is

H0wH(w) = find the outputsignal v0(t). [8]

W~.+3W

) Distinguish between Time-Invariantand Time-Varying systems. [4]

Question 4

) The BBC VHF- FM sound broadcast system has a rated system deviation of75KHzand a maximum modulating frequency of15KHz. Calculate the required bandwidthfor the system. What would the required bandwidth ifDSB AM where to be used.Comment on your answers. [6]

b) In a frequency modulation system, explain why the higher modulation index, the

greater the number ofsignificant sidebands. [5]

) Calculate the noise voltage at the input ofthe television R.F. amplifier using anamplifier device having equivalent noise resistance of1 80~and input resistance of400~).The bandwidth ofthe amplifier is 7 MHz and the temperature is 305K. [9]

Question 5

) . Derive the general equation ofan amplitude modulated wave and sketch

its frequency spectrum. [6]). What are the advantages and disadvantages ofSSB-SC over DSB-FC[4]

). Show that the total power P~contained in an AM wave is given by

P~= ~ ~ [ i ~ Jwhere P~is the carrier power and m is the modulation index

The power dissipated by an AM wave is 80W when the depth ofmodulation is 25%.What modulation depth is necessary to increase the power to 100W. [10]

Question 6

) Explain the principle ofQuadrature A mplitude M odulation as applied in

Television transmission. [5]

b) Draw a simplified signal television flow diagram showing how video and audioinformation is captured at source, transmitted and reproduced at destination. [7]

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) In TV broadcasting a method ofovercoming the constant luminance problem wouldbe to use a linear system at the transmitter and to place a gamma correcting amplifier

in the receiver so that the overall characteristics ofthe receiver is linear. Brieflyexplain why this is not a practical proposition. [8]

Question 7

) Define the following terms, Failure Rate , Availability, Reliability [6]

) For an electronic instrument the total failure rate is estimated to be 2.5x106 per hour.Calculate the MTBF and the reliability for a 10 000 hour operating period. [6]

) The forecasts ofroutes leading to three possible telephone exchange sitesA, B an Care shown in the figure below. Indicate which is the practical centre ofthe proposed

exchange and why. [8]

K~n~1Kin

Ic fot~cas1Ti~ur~sFirst fl~ure~upp9r) ir~iC~t~S~J~stirIgsze

f~ut~(n~ddI~)Irdloales 1C-yuarlcrYcastThird ligure (lewer) inrkale3 20-yeor corece~t

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USEFUL TRIGONOMETRIC FUNCTIONSUSEFULTRIGONOMETRIC IDENTiTIES

cos(xy) =cos(x) cos(y) F sin(x)sin(y)

sin(xy) =sin(x) cos(y)cos(x)sin(y)

f ~ J=~ sin(x)

=cos(x)

A cos(x) B sin(x) =R cos(x+0)

whereR =~JA2B2, ~ ~ (% )A R cos(0), B=Rsin(0)

2cos(x)=e~+e~

2isin(x~=e~e~

Indefinite Integrals

J cos(x) dx =sin(x)

J x cos(x) dx =cos(x) +x sin(x)

Jx2 cos(x) dx =2x cos(x) +(x2 2) sin(x)

fsin(x) dx = cos(x)

5 x sin(x) dx =sin(x) x cos(x)

5 x2 sin(x) dx =2x sin(x) (x2 2) cos(x)

Exponential functions

Jxe~dx=e~[~i...I]

Jx2e~dx=e~[~__~__~]

Definite Inte2rals

Je~2xZdx=

1fr~,~

ix2e~2dx=ij~2~

SSa2@~)dx=~2

cos(2x)=cos2 (x) sin2 (x)

sin(2x)=2 sin(x) cos(x)

2 cos(x) cos(y)=cos(x y)+cos(x+y)

2 sin(x)sin(y) =cos(x y) cos(x y)

2 sin(x)cos(y)=sin(x y) +sin(x +y)

2 cos2 (x) =1 + cos(2x)

2 sin2 (x) =1 cos(2x)

4 cos3 (x) =3 cos(x)+ cos(3x)

4 sin3 (x)=3sin(x)+sin(3x)

8 cos4 (x) =3 +4 cos(2x)+ cos(4x)

8 sin4 (x) =3 4 cos(2x)+ cos(4x)

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EE31O Tables and Constants

Constants

BolttzmannsConstant k=1.38x1O~J/K

Electroncharge q=1.6x109 C

Velocityoflight c=3x108 rn/s

TABLE OF FOUR I ER T R ANS FORMS

Time Domain Frequency Domain

1

CJ~1~OIcos(2irfoI)

sin(2xfot)

fl(t)sinc(:)

A(4sinc (t)e~u_j(t)~a> 0

te~u.....,(r),a> 0

sgn(t)

u_t(t)

8(t)8(* ) (:)

I

Et8(t nlo)

1

(a-I-f

a2-f(2xf)2

I/(jirf)

j2xrf(j2icfY fir sgn(f)

_ i . . %fl=+0O8(f_ S

18(f)

S(ffo)

a ~8(ffo)~~It5(f+fo)

*8(f+fo)+ ~y8(ffo)sinc(f)11(f)

sinc2(f)

A4)

a+j2zf

1

Jlxf