Q.1
12v
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0.1ms 0.4ms
12v
0v
The periodic pulse waveform shown above is measured across a 4 ohm
resistor.
(a) Using the Fourier series evaluate and sketch its amplitude spectrum
from 0Hz to 11kHz showing each step in the calculation.
10 marks
(b) Calculate what percentage of the total power in this waveform is
contained in the component at 4kHz.
5 marks
(c) This waveform is now multiplied by a sinusoid of peak amplitude 1
volt and frequency 100kHz. Explain what you would expect to see at the output
of this multiplier when viewed on a spectrum analyser covering the frequency
range 90kHz to 110kHz.
5 marks
Q.2
An amplitude modulator with a conversion characteristic of 1volt/volt
produces a full AM wave defined in the time domain by the following formula.
a(t) = [15
+ 6cos(18849.6t)]cos(3141592.7t) volts
(a) Identify and write down the formula
for the unmodulated carrier, evaluate its peak amplitude and frequency in Hz.
2 marks
(b) Identify and write down the formula for the message being carried,
evaluate its peak amplitude and frequency in Hz.
2 marks
(c) Sketch this AM waveform in the
frequency domain labelling the amplitude and frequency of each component,
explaining how it was derived. State its bandwidth.
4 marks
(d) Define and calculate the modulation index of this AM wave.
3 marks
(e) If a(t) is measured across an 8 ohm resistance calculate its total
average power, explaining how this is obtained.
4 marks
(f) Using this example show why full AM is regarded as an inefficient
modulation system. State briefly why, despite this inefficiency, it is still
used in broadcasting.
5 marks
|
Q.3
|
FM TRANSFER CHARACTERISTIC
|
|
230kHz
220kHz
210kHz
CARRIER
200kHz FREQUENCY OUT
190kHz
180kHz
170kHz
-15v -10v -5v 0v 5v 10v 15v
MESSAGE VOLTAGE IN
A carrier wave of peak amplitude 25 volts is frequency modulated by a
sinusoidal message of peak amplitude 10 volts and frequency 10kHz using an FM
modulator with the transfer characteristic shown above.
(a) Using this transfer characteristic determine the maximum frequency
deviation ( FC), then evaluate the
modulation index ( ) of this FM wave.
4 marks
(b) Use the Bessel Tables below to sketch the amplitude spectrum of
this FM wave, labelling the amplitude and frequency of each component. Explain
clearly and fully how each value was obtained. State the bandwidth of the FM
wave and indicate this on the spectrum.
7 marks
(c) Calculate what percentage of the
total power in this FM wave is contained in the component at the carrier
frequency.
5 marks
(d) Explain how the bandwidth of this FM wave would alter if the
frequency of the message was now increased to 20kHz.
4 marks
Bessel Tables
J0
|
J1
|
J2
|
J3
|
J4
|
J5
|
J6
|
J7
|
J8
|
J9
|
|
1.0
|
0.77
|
0.44
|
0.11
|
0.02
|
||||||
1.5
|
0.51
|
0.56
|
0.23
|
0.06
|
0.01
|
|||||
2.0
|
0.22
|
0.58
|
0.35
|
0.13
|
0.03
|
0.01
|
||||
3.0
|
0.26
|
0.34
|
0.49
|
0.31
|
0.13
|
0.04
|
0.01
|
|||
4.0
|
0.40
|
0.07
|
0.36
|
0.43
|
0.28
|
0.13
|
0.05
|
0.02
|
||
Q.4
(a) Explain what is meant by the characteristic impedance, Z0, of a
transmission line.
4 marks
(b) 25 metres of loss-free, air-spaced, 75 ohm coaxial cable is
terminated at its receiving end by a load of impedance 115 + j100 ohms. A
sinusoidal generator of internal resistance 75 ohms which, on open circuit
gives an output of 24 volts r.m.s., is now connected to the sending end of this
line.
(i) Calculate the voltage reflection coefficient, V, at the load expressed in polar form correct to two decimal places.
3 marks
(ii) Calculate the voltage standing wave ratio on the line.
3 marks
(iii) With the aid of a phasor diagram evaluate the resultant steady
state voltage at the load.
7 marks
4 | P
a g e
(iv) This load is now removed, leaving an
open circuit at the load end of the line. State and explain the impedance at
the generator when its frequency is set to 3 MHz.
3 marks
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