APPENDIX
Communications questions
Amplitude modulation
Q1
A signal can be described by the following equation:
Vc(t) = 5[1 + 0.5cos2π103t]cos2π106t volts.
State the frequencies contained in this signal and hence calculate the bandwidth. Calculate
the total signal power if this signal is applied across a 50 Ω resistive load.
Solution
Vc(t) = 5[1 + 0.5cos2π103t]cos2π106t
Expand this equation.
Vc(t) = 5cos2π106 + 0.5/2cos2π(106-103)t + 0.5/2cos2π(106-103)t
The frequencies contained in this signal are
Carrier = 106 Hz, LSF = 999 kHz, USF = 1001 kHz
The bandwidth is:
BW = USF -LSF = 2 kHz.
The power developed in the 50 Ω resistive load is
Pt = Pc[1 + m2/2] watts.
Where Pt and Pc are the total power and the unmodulated carrier powers respectively.
P = 52/100[1 +0.52/2] = 282mW
Q2
(a) Describe with the aid of a block diagram how two AM modulators can be combined
to generate a DSBSC signal.
[9 marks]
(b) For the AM signal described in part (a) derive equations for the carrier power, the
sideband power and the total power. An AM transmitter has an output power of 24 kW
when 100% modulated. What is the unmodulated output power? What is the output
power at 60% modulation and one sideband is suppressed fully while the carrier
component is reduced by 26 dB?
[7 marks]
Q3
The DSBSC signal Accos(2πfct)cos(2πfmt) is applied to the input of a coherent detector.
The local oscillator used in the coherent detector is defined by
e(t) = cos(2πfct + φ).
Derive an expression for the output signal. What is the significance of the φ term?
[6 marks]
Q4
For the AM signal described in part (a) derive equations for:
(i) The carrier power
(ii) The sideband power, and
(iii)The total power
An AM transmitter has an output power of 18 kW when modulated to a depth of 100%
What is the carrier output power? What is the total output power at 50% modulation and
one sideband is suppressed and the carrier component is reduced by 26 dB?
[10 marks]
Q5
(a) An AM signal is defined v(t ) = Ac [1 + ma m(t )]cos(2πf c t )
If m(t) = Am cos(2πfct), derive an expression for the AM signal where each frequency
component is individually identified. Sketch the AM signal in the time and frequency
domains. Specify the minimum and maximum envelope values. How can the AM
modulation index be determined from these extreme values?
[7 marks]
Q6
(a)Draw a block diagram and explain how FDM is applied in a telecommunications
environment. In particular give brief details of the 12-channel FDM system.
[8 marks]
(b)
Show how Quadrature Amplitude Modulation is used to facilitate the transmission of
two different signals in the same frequency band. Describe the difference between this
system and independent sideband transmission. In your description of QAM, include a
brief discussion of the demodulation process.
[12 marks]
Q7
Draw a block diagram of an AM superhetrodyne receiver. Explain the function of each
block. Include the following terms in you description: selectivity, sensitivity, AGC and
image frequency rejection. Indicate where the receiver adjacent channel selectivity
takes place. Calculate the image frequency for a receiver whose intermediate frequency
is 455 kHz and the desired carrier frequency is 1 MHz. With the aid of suitable
diagrams, explain how the am receiver could be implemented using digital signalling
techniques.
Q8
(a) Draw a block diagram for a system, which will produce an SSBSC signal using the
phase shift method. Explain, with the aid of suitable mathematical expressions, the
operation of the system.
(b) The Hilbert transform is defined: Use This transform to explain how a wideband
phase shift on the message signal is produced.
Q9
a)
What is the difference between Signal Distortion and Signal Attenuation? Which
causes greater difficulties in Communications Systems?
Briefly describe the FOUR major sources of Signal Distortion.
[8 marks ]
(b)A digital communications link is to be used to simultaneously to carry a number of
telephone calls. Describe with the aid of diagrams how the link could be shared using:
(i) Time Division Multiplexing;
(ii) Frequency Division Multiplexing
[ 8 marks ]
(c)Use a diagram to distinguish between Frequency Modulated (FM) signals and
Amplitude Modulated (AM) signals.
[ 4 marks ]
Q10
(a)Describe one technique for producing a DSBSC signal. Include in your answer a
circuit diagram and relevant time domain diagrams
(b)Explain how the modulating signal may be recovered from a DSBSC signal whose
carrier frequency is vc (t ) = 2 cos(2π 10 6 t ) volts and modulating signal. Choose suitable
component values for a low-pass filter so that the modulating signal is recovered with
minimum distortion.
(c) Describe the effects of using a non-coherent local oscillator in the circuit described
in part (b).In particular show how frequency and phase errors in the injected carrier
leads can lead to problems in the message signal
Q11
(a)Explain the operation of an AM superhetrodyne receiver. Include in your answer a
block diagram showing the main receiver operations. Explain the main disadvantage of
superhetrodyning.
[10 marks]
(b)Show that the normalised current in a series-tuned LCR circuit is:
i
1
=
io 1 + jQ ( ω − ω 0 )
ω0 ω
[5 marks]
A superhetrodyne receiver is tuned to a desired station located at f =10000 kHz. If the
intermediate frequency is 455kHz, use the normalised current expression in (b) to
calculate a value for the Q factor if the image frequency is to be attenuated by 40 dB.
[5 marks]
Q12
(b) A DSB-SC and SSB-SC transmission are each sent at a carrier frequency of 20
MHz in the presence of additive white noise. In each case, the information signal
bandwidth is 3.5 kHz, and the received signal power is 0.3 mW. The noise is assumed to
be white with a constant power spectral density of 10-3 W/Hz. The receiver consists of
a band-pass filter whose bandwidth matches the bandwidth of each transmitted signal,
followed by a synchronous demodulator.
(i) Calculate the signal-to-noise ratio of each transmission at the input to the
demodulator.
(ii) Calculate the signal-to-noise-ratios at the output of the demodulator.
[12 marks]
Q13
(a) Describe the envelope detection method for demodulation of large-carrier AM
signals. Assuming sinusoidal modulation, derive an expression for the maximum value
of the time constant of the detector.
[10 marks]
(b) Derive an expression for the output signal of a synchronous DSB-SC
demodulator when:
(i) the frequency of the local oscillator at the demodulator differs from the
carrier frequency by
an amount
;
(ii) there is a phase shift φ between the received carrier signal and the output
of the local oscillator.
[10 marks]
Q14
(a) With the aid of suitable diagrams, describe the principles of operation of (i) the
chopper modulator, and (ii) the double balanced modulator.
[8 marks]
(b) A double-sideband, suppressed-carrier system with a carrier frequency of 1
MHz is used to transmit a modulating signal which consists of two tones at 500
Hz and 1.25 kHz. The signal is to be demodulated coherently. If the frequency
of the carrier at the receiver is 1.003 MHz, calculate the frequencies of the
components in the output of the coherent demodulator. If there is no frequency
offset, but there is a phase shift of 10o between the carriers at the transmitter and
receiver, what is the effect on the output signal from the demodulator ?
[12 marks]
Q15
(a)
Sketch the spectrum of the signal which results when an 800 kHz carrier is
amplitude modulated (AM) with a speech signal whose spectrum extends from 300 Hz
to 3.4 kHz, with a modulation
index less than 1. What is the total transmitted
bandwidth of the AM signal, if a guard band of 600 Hz is included on either side of the
actual AM spectrum ? How many such speech channels could be transmitted in a 100
kHz portion of the AM spectrum ?
[10 marks]
Q16
(a)
A full AM (i.e. sidebands plus carrier) transmitter develops a power output of 1
kW when no modulating signal is present. The transmitting aerial can be assumed to
present a resistive load of 50 Ω.When a sinusoidal modulating signal with peak
amplitude 5 V is applied to the modulator, it is found, using a spectrum analyser, that
the spectral component representing each sideband has an amplitude which is 40% of
the carrier amplitude. Calculate the following quantities:
(i)
the modulation index;
(ii)
the peak amplitude of each of the sidebands;
(iii) the ratio of total sideband power to carrier power;
(iv)
the total power output;
(v)
the total average power in the output if the peak
amplitude of the modulating signal is reduced to 4 V.
[10 marks]
(b) An envelope detector is used to demodulate a large-carrier AM waveform,
where the meansquared value of the information signal is 0.28 V2, and the carrier
amplitude is 2 V. Calculate
the Signal-toNoise Ratio (SNR) in dB at the detector output, in the presence of white noise with a
two-sided power spectral density of 3 W/Hz, if the bandwidth is 10 kHz. Hence,
calculate the SNR (in dB) at the output of the detector. What is the SNR if sinusoidal
modulation is used, with an information signal amplitude of 0.17 V ?
[10 marks]
Q17
(a) Describe the envelope detection method for demodulation of large-carrier AM
signals. Assuming sinusoidal modulation, derive an expression for the maximum value
of the time constant of the detector.
[8 marks]
(b) A DSB-SC and SSB-SC transmission are each sent at a carrier frequency of
10 MHz in the presence of additive white noise. In each case, the information signal
bandwidth is 3 kHz, and the received signal power is 0.4 mW. The noise is assumed to
be white with a constant power spectral density of 10-3 W/Hz. The receiver consists of
a band-pass filter whose bandwidth matches the bandwidth of each transmitted signal,
followed by a synchronous demodulator.
(i) Calculate the signal-to-noise ratio of each transmission at the input to the
demodulator.
(ii) Calculate the signal-to-noise-ratios at the output of the demodulator.
(iii) Repeat part (i) for DSB transmission only where the noise power spectral
density has the form 103/|f| W/Hz. How does this value of SNR compare to that
calculated under the assumption of purely “white” noise ?
[12 marks]
(b) Derive an expression for the power in a large carrier AM signal, in terms of the
modulation index m.
[6 marks]
Q18
(a)
With the aid of suitable diagrams, describe the principles of operation of (i) the
chopper modulator, and (ii) the double balanced modulator.
[8 marks]
(b) Derive an expression for the output signal of a synchronous DSB-SC
demodulator when:
(i) The frequency of the local oscillator at the demodulator differs from the
carrier frequency by an amount
.
(ii) There is a phase shift φ between the received carrier signal and the output
of the local oscillator.
[6 marks]
(c) A double-sideband, suppressed-carrier system with a carrier frequency of 1 MHz
is used to transmit a modulating signal which consists of two tones at 300 Hz
and 1 kHz. The signal is to be demodulated coherently. If the frequency of the
carrier at the receiver is 1.002 MHz, calculate the frequencies of the components
in the output of the coherent demodulator.
If there is no frequency offset, but there is a phase shift of 10o between the
carriers at the transmitter and receiver, what is the effect on the output signal
from the demodulator ?
[6 marks]
Frequency modulation
Q19
(a) With the aid of a block diagram, describe the indirect method of narrow-band
FM generation. Outline a scheme by which narrow-band FM may be converted into
wide-band FM for broadcast
purposes.
[7 marks]
(b) A discriminator is used to demodulate an FM waveform which has an
unmodulated carrier amplitude of 1.2 V, and an information signal mean-squared value
of 0.78 V2. The value of kf is 3.5, and the information signal bandwidth is 15 kHz.
Calculate the SNR at the output of the discriminator, in the presence of white
noise with double-sided power spectral density of 2.92 W/Hz.
[7 marks]
(c) Calculate the improvement in SNR over that obtained in part (b), if a preemphasis/de-emphasis network with a lower frequency of 2.5 kHz is used.
[6 marks]
(b) With the aid of suitable diagrams, describe how pre-emphasis and deemphasis may improve the quality of FM broadcasts.
[10 marks]
Q20
(b)
Describe briefly the operation of an FM demodulator using a phase-lock loop.
[10 marks]
Q21
(a) For a sinusoidal modulating signal, derive an expression for the Fourier series of
the corresponding
frequency-modulated signal (assuming wideband FM).
[10 marks]
(b)
Describe briefly the operation of the following FM demodulators (i)
detuned resonator (ii) phase-lock loop.
[10 marks]
Q22
(a) Outline a method by which the carrier frequency and deviation of a narrowband FM
signal may be increased to produce wideband FM for broadcast (i.e. with carrier
frequency in the range from 88 MHz to 108 MHz).
[8 marks]
(b) State Carson’s Rule for the bandwidth of an FM signal. A 10 MHz carrier is
frequency modulated by a sinusoidal baseband signal such that the frequency deviation
is 50 kHz. Estimate the bandwidth of the FM signal if the frequency of the modulating
signal is (i) 500 kHz, (ii) 500 Hz. In each case, state whether narrowband or wideband
FM is being used.
[6 marks]
Q23
(a) For a modulating signal of the form f(t) = A cos ( mt), derive an expression for the
Fourier series of the corresponding wideband frequency-modulated (FM) signal.
[8 marks]
5. (a) With the aid of a suitable block diagram, describe the process by which stereo
FM signals are generated and demodulated. You should include plots of the spectra
of the various signals as appropriate.
[10 marks]
(b) The sinusoidal signal Acos(2 ft) is applied to the input of an FM transmitter.
The corresponding FM output signal (in volts) for A = 1V and fm = 1 kHz is given
by vFM(t) = 100cos(2x107t + 4sin(2000 t))
across a 50 resistive load.
(i) What is the carrier frequency ?
(ii) What is the peak frequency deviation from the carrier ?
(iii)What is the total average power developed by vFM(t)?
(iv)What is the approximate bandwidth, using Carson’s Rule?
Repeat (i) to (iv) with the following parameters: A = 0.75V, fm = 2 kHz.
[10 marks]
Q24
(a) With the aid of a suitable example, describe the principles of operation of the
superheterodyne receiver. Indicate clearly the function of each of the components.
[10 marks]
(b) With the aid of suitable plots, describe how a varactor diode may be used as part of
a (direct) FM generation system.
Such a generator has a centre frequency of 10 MHz for a total capacitance of 100 pF. If
the voltage-capacitance characteristic is assumed linear about the operating point, with a
slope of -34 pF/V, calculate the frequency deviation if the modulating voltage causes a
±45 mV swing about the
quiescent reverse bias voltage.
[10 marks]
Q25
Draw a block diagram of a phase-locked loop and briefly explain how the PLL can be
used for demodulating an FM wave.
[10 marks]
A carrier signal of frequency 100 MHz and of amplitude 10 V is frequency modulated
by a sinusoidal signal of amplitude 1.2 V and of frequency 10 kHz. Sketch the spectrum
of the modulated signal if the modulator frequency sensitivity is 25 kHz/V.
[6 marks]
Q26
Determine with the aid of Carson's rule the bandwidth of the FM signal and find the
signal power contained inside this bandwidth. What is the FM signal total power?
[10 marks]
(b) Show how both channels of a stereo FM multiplexed signal are extracted. Use
appropriate diagrams to illustrate your answer.
[12 marks]
Q27
Explain with the aid of appropriate diagrams the principle of baseband voice scrambling
based on a simple frequency inversion process.
[8 marks]
Determine the change in bandwidth if the modulating signal amplitude is halved.
[4 marks]
(c) Show how both channels of a stereo FM multiplexed signal are extracted. Use
appropriate diagrams to illustrate your answer.
[12 marks]
(d) A frequency synthesiser capable of generating frequencies in the range from 1 kHz
to 999.9 kHz in 100 Hz steps is required. Draw a block diagram of a system based
on direct frequency synthesis that will provide this specification. Assume that a 1
MHz reference oscillator is provided.
[12 marks]
Q28
A carrier signal of frequency 100 MHz and of amplitude 10 V is frequency modulated
by a sinusoidal signal of amplitude 1.2 V and of frequency 10 kHz. Sketch the spectrum
of the modulated signal if the modulator frequency sensitivity is 25 kHz/V.
[6 marks]
Determine with the aid of Carson's rule the bandwidth of the FM signal and find the
signal power contained inside this bandwidth. What is the FM signal total power?
[10 marks]
Determine the change in bandwidth if the modulating signal amplitude is halved.
[4 marks]
Q29
Sketch the spectrum of an FM signal (up to the 7 th side-frequency pair) which has a
centre frequency of 110 MHz and is modulated with a 20kHz sinusoidal signal. The
amplitude of the modulation has been slowly increased until the frequency component
at 110.04 MHz is zero. Determine the percentage of total power contained within:
(i) A 100 kHz bandwidth,
(ii) A 180 kHz bandwidth.
Both bandwidths are centred about 110 MHz.
[19 marks]
If the FM signal is restricted in bandwidth according to (i) above, draw the phasor
diagram of the resultant FM signal and determine the maximum and minimum values of
the envelope of the signal.
[6 marks]
Q30
The instantaneous voltage of an FM signal, developed across a resistive 75 Ω load, can
be expressed as
v(t) = 100cos[2π103 t+ 2. 4cos2π106 t] volts
State the value of the modulation index and hence calculate the frequency-deviation,
and the modulator sensitivity if the modulating signal has a peak amplitude of 500 mV.
What is the significance of this modulation index value? Calculate the bandwidth of the
FM signal.
[10marks]
Q31
Draw a block diagram representing the Armstrong indirect frequency modulation
system and derive an expression for the output signal from the modulator. Discuss the
term residual AM.
[12 marks]
A modulating signal with an amplitude and frequency of 12 V and 1200 Hz respectively
is applied to the input of a modulation system of this type. It utilises a 20 MHz carrier
signal. If the product modulator being used in the system has a sensitivity of 100,
determine the frequency multiplication required to produce the following FM signal:
v(t)=12sin[(2π.20.10 6 t)+5sin(2π1200t)]
[13 marks]
Q32
(a) Explain in detail using an appropriate block diagram how each audio channel is
recovered from a stereo FM multiplexed signal.
[12 marks]
(b) If a 10 MΗz reference sinusoidal oscillator is available, draw the block diagram of a
direct frequency synthesiser, which will generate frequencies in the range from 100 Hz
to 2 MΗz with a resolution of 10 Hz using the reference provided.
[13 marks]
Q33
A modulating signal with an amplitude and frequency of 12 V and 1200 Hz respectively
is applied to the input of a modulation system of this type. It utilises a 20 MHz carrier
signal. If the product modulator being used in the system has a sensitivity of 100,
determine the frequency multiplication required to produce the following FM signal:
v(t)=12sin[(2π.20.10 6 t)+5sin(2π1200t)]
[13 marks]
Show how both channels of a stereo FM multiplexed signal are extracted. Use
appropriate diagrams to illustrate your answer.
[12 marks]
Q34
(e) A frequency synthesiser capable of generating frequencies in the range from 1 kHz
to 999.9 kHz in 100 Hz steps is required. Draw a block diagram of a system based
on direct frequency synthesis that will provide this specification. Assume that a 1
MHz reference oscillator is provided.
[12 marks]
(b)
Explain with the aid of appropriate diagrams the principle of baseband voice scrambling
based on a simple frequency inversion process.
[8 marks]
Q35
A carrier signal of frequency 100 MHz and of amplitude 10 V is frequency modulated
by a sinusoidal signal of amplitude 1.2 V and of frequency 10 kHz. Sketch the spectrum
of the modulated signal if the modulator frequency sensitivity is 25 kHz/V.
[6 marks]
Determine with the aid of Carson's rule the bandwidth of the FM signal and find the
signal power contained inside this bandwidth. What is the FM signal total power?
[10 marks]
Determine the change in bandwidth if the modulating signal amplitude is halved.
[4 marks]
Q36
Draw a block diagram of a phase-locked loop and briefly explain how the PLL can be
used for demodulating an FM wave.
[10 marks]
The system parameters for the fundamental components of a PLL are defined for the
phase detector, amplifier, loop filter and VCO as
kθ = 0.2 V /rad, ka = 5 V/V, kf = 1 V/V, ko = 20 kHz/V.
If the free-running frequency of the VCO is 500 kHz and the input frequency to the PLL
is 510 kHz determine
(a) The open-loop gain kv,
(b) The change in frequency to achieve lock,
(c) The output voltage Vo,
(d) The error voltage Vd, and
(e) The static phase error θ
(i) The loop gain is given as
kv =2π kθ .ka .kf .ko = (0.2v/rad).(5v/v).(1v/v).(20 kHz/v)
kv = 1256 ks-1
(b) The change in the frequency for lock
∆f = (510 - 500) kHz. = 10 kHz
(c) The output voltage Vo is obtained by considering the definition for the modulator
sensitivity ko as
ko = ∆f/ Vo
Or
Vo = ∆f/ko = 10 kHz/20 kHz = 0.5V
(d) The error voltage Vd is obtained as
Vd = V0/ka.kf = 0.5v/1.5 = 0.1V
(e) Again knowing the value for Vd, we can calculate the value for the static phase error θ:
θ = Vd/kd = 0.1/0.2v/rad = 0.5 rad.
2π∆f i
If the input is a step input θ i =
s
Vo
2πk v / k o
=
∆f i
s + kv
The transfer function for a first order RC is
1 / CR
ωC
H ( s) = k f =
=
s + 1 / CR s + ω C
ωC
Vo
s + ωC
2πk v / k oω C
=
= 2
ωC
∆f i
s + sω C + k v ω C
s + kv
s + ωC
2πk v / k o
Q37
The bandwidth of an FM signal is given by Carson's modified rule as
BW = 30 [2 + 5] kHz
State the value of the modulating frequency and modulation index and hence calculate
the following:
(a) The peak amplitude of the modulating signal if the modulator sensitivity is 30 kHz /
volt, and
(b) The power in the first sideband, if the unmodulated carrier power is 20 kW.
Data Transmission
Q38
Calculate the transmission bit rate for a 30 channel TDM PCM telephone system. The
input signal to one channel of such a system has an amplitude Vp volts at a frequency
limited to 3.4 kHZ. Calculate the maximum permitted value for Vp and the dynamic range
if the minimum step size is 10 mV.
The transmission bit rate is calculated as
Tx = Number of frames /sec x Number of time slots x Number of bits per time slot
Tx = 8000 x 32 x 8 = 2.048 Mbits/sec
The maximum input signal voltage Vm is calculated as
V = q.M
Where q is the minimum step size and M the Number of levels but M = 2n where n is the
no. of bits.
V = 10 mV x 256 = 2.56
The dynamic range DR is calculated as
DR = 20 log q
2.56
q = 20 log
= −48 dB
0.001
This can also be quoted using the 6 dB rule as as 6.02n = 48 dB
Q39
The public switched telephone network(PSTN) uses the following modulation schemes
in transmitting data over bandlimited channels:
a)FSK,
b)PSK, and
c)QAM
Explain briefly the fundamental principles of each system, using block diagram where
necessary.
[10 marks]
DPSK MODULATOR
The data signal is fed into the ex-nor gate the truth table of which is given in Table 1.The
initial value for B input is assumed to be zero Thus the output at C for the first received
pulse, which is a one, is therefore zero. The output is then fed back to the gate input,
delayed by one bit and with the second inputted bit (a zero) will produce a one. The
process continues and the logic waveforms can then be drawn as shown in Table 2. The
NRZ signal at the gate output is then transformed to an NRZ-B signal by using a
comparator.
The output of the comparator will be either +1 or -1 depending on the value of the
input i.e. if the input is +1 then the output will saturate at the plus rail voltage which is
+1.If the input is zero then the output will saturate at the -rail voltage i.e.-1 V because the
inverting input is at V/2 volts. The NRZB signal is then used to switch the pairs of
diodes D1, D3 and D2, D4 on or off depending on the polarity. Thus the signal path will
be reversed when a 1 is present and no inversion of the path signal when a -1 is present
at the point D. The phase at the output is as shown in the Table2.
DPSK DEMODULATOR:
The DPSK input signal and a delayed version of the signal id fed into the phase detector
(which is basically a multiplier). This produces an NRZ-B. Consider the following
analysis:
Let the input signal be Asinx. The delayed signal is also Asinx i.e. no inversion then
AsinxAsinx = A 2sin2 x
Assume unity amplitude A = 1 and expanding gives
sinx.sinx = 1/2(1-cos2x)
After low-pass filtering, the output is equal to 1/2. However if a phase reversal takes
place then the inputs to the phase detector are then sinx and (- sinx) so that with the
previous assumptions gives:
sinx (-sinx) = -1/2(1-cos2x) = -1/2
Again the low pass filter removes the cos 2x term. Thus the signal is in NRZ-B format
which when inputted to the comparator, will yield a TTL NRZ format.
Q40
A transmission system has an overall 30.1 dB S/N ratio and is required to transmit data
at a maximum rate of 45 M b/s . Calculate
a) the absolute minimum bandwidth,
b) the number of levels of encoding, and
c) the number of bits n required .
[10 marks]
Explain how the system shown in Fig 3 can encode a data signal 1001011 into a suitable
DPSK format. Sketch the resultant logic waveform at points A, B, C and D.
Hence determine the output sequence at E.
[10 marks]
Q41
The binary sequence 1101 1001 is transmitted using 2-phase PSK. Sketch the
modulated signal assuming that the duration of each bit is four times greater than the
carrier period.
[4 marks]
If the binary sequence is changed to an alternating 10101010.... sequence, determine the
spectrum of the PSK signal. Assume that the bit rate is 1600 bps and that the carrier
frequency is 10 times the bit rate.
[8 marks]
Draw the block diagram of a DPSK encoder and decoder and explain the operation of
the system.
[8 marks]
Q42
Give a brief description of the application an limitations of the following types of
transmission media:
(I)
2 wire open lines
(ii)
twisted pair lines
(iii)
(iv)
coaxial cable
optical fibre
[12 marks]
(b)
A modem to be used within a PSTN uses an 8-level QPSK modulation scheme. If the
PSTN bandwidth is 3100 Hz, deduce the Nyquist maximum data transfer rate.
[4 marks]
(c)
If the PSTN described in (b) has a typical signal-to-noise of 20dB, determine the
maximum theoretical information rate that can be achieved.
[4 marks]
Q43
Draw a block diagram illustrating the main processes that occur in a digital receiver.
Explain the function of each block.
[8 marks]
Q44
Show how the basic delta modulator can be modified to provide a CVSD Two types of
digital filter are shown in Fig 1. Obtain the difference equation and hence express the
system function as H(Z) = Y(Z)/X(z). State the filter type (i.e. FIR or IIR) of each
configuration.
[12 marks]
Q45
Explain the operation of a basic delta modulator.
[12 marks]
(a) modulator and briefly explain the operation of this modulator.
(b) A sinusoidal signal of amplitude 5 V and of frequency 10 kHz is applied to the input
of a delta modulator. The clock frequency of the modulator is 1 MHz. Determine
the step size of the modulator such that slope-overload will not occur. Derive any
equations used.
[12 marks]
(c) Show how the basic delta modulator can be modified to provide a CVSD modulator
and briefly explain the operation of this modulator.
Amplitude modulation receivers
Q46
Explain the terms image channel and adjacent channel applied to an AM superhetrodyne
receiver.
Explain the following terms:
Signal to noise ratio, noise factor and noise figure. How is the overall noise figure for a
receiver calculated?
[10 marks]
The noise at the input of a system has a RMS value equal to 10 uV. Determine the
signal input amplitude to this system whose noise figure is 5 dB so that the signal to
noise ratio at the output is equal to 45 dB.
[4 marks]
Q47
The sum of the local oscillator and the RF voltage is:
A mixer utilises an active device whose relationship between the output current id and
the input voltage vgs is
im ≈ 2 vgs2
Calculate the conversion transconductance gm if vgs is the sum of the local oscillator
voltage whose peak amplitude is 2 V and the RF input signal whose peak amplitude is
2mV.
Vgs = Vlosinωot + Vrfsinωrt
When this is substituted into the equation given and considering the cross -products only
when applying the trig identity gives the quantity
2sinAsinB =cos(A-B) -cos(A +B)
The difference frequency current component has a magnitude
im = Vm.V
The conversion transconductance is defined as gc = im/ Vrf = 2 mS
Explain the term SINAD RATIO.
Q48
Draw a block diagram for an AM superheterodyne receiver suitable for reception of the
medium wave band and explain the function of each block.
An AM superheterodyne receiver is tuned to an RF station whose frequency is 600 kHz.
The IF and local oscillator frequencies are 465 kHz and 1065 kHz respectively. Calculate
the image frequency and the image-channel response ratio in dB, given that the Q-factor
of the input parallel tuned circuit is 80.
Solution
The block diagram is as shown in Fig 1
Figure 1 AM superhetrodyne receiver
Q49
Explain by means of a block diagram how a composite FM stereo baseband signal is
produced. Describe the operation of an FM superheterodyne receiver. What factors
contribute to its superior noise performance above an AM receiver?
Stereo Generation
Audio signals from the left and right sources are fed to the linear matrixing network to
produce the L - R and the L + R signals. The L + R signal is required for the reception
of signals by mono receivers only. Since the two signals out of the matrix are in the
audio band then some means of separating them must be created before modulating
them. This is achieved by translating the L-R signal to a different frequency band. Using
DSBSC techniques, a balanced modulator produces two side-bands centred around 38
kHz as shown but of course the carrier is suppressed. To simplify the receiver design a
frequency and phase coherent pilot tone is derived from the 38 kHz carrier and this fits
between the lower sideband and the audio signal. The three signals i.e. the L - R, the 19
kHz pilot tone and the DSBSC signal are then added together to form the composite
signal.
[6marks]
OPERATION OF THE FM SUPERHETERODYNE RECEIVER
The main sections of an FM receiver are as follows:
Because the fm signal is, in general, much weaker than an am signal, the first stage is an
RF amplifier. The superheterodyne action occurs by coupling the tuning capacitor of the
tuned circuits in both the local oscillator and the RF amplifier together. The signals from
both stages are then fed to a mixer stage which can be a multi-gate FET device. The
output from the mixer produces a 10.7 MHz IF output and this is fed to several stages of if
amplification The limiting stage of the final if amp limits the amplitude of both wanted
signal and undesirable noise. This stage also ensures correct operation of the PLL.
The PLL demodulates the signal in the following manner. The VCO is set to a
free- running frequency = 10.7 MHz and the error signal out of the phase detector is a
voltage vd which is proportional to the phase difference between the incoming frequency
and the VCO frequency. This error voltage after suitable filtering is fed back to the VCO
and will force the VCO to track the incoming frequency over a limited range. Thus the
signal out of the PLL filter is the required audio signal. The de-emphasis network which is
a simple low pass filter correct the process of pre-emphasis introduced at the transmitting
stage to produce a uniform S/N ratio over the desired band. The audio signal is then fed to
the preamplifier and power amplifier.
[10marks]
The main factors that contribute to the good noise performance are the limiting action of
the limiting stage and the pre-emphasis network (LPF).
[4marks]
Q50
Draw a circuit of a simple AM diode detector. The signal to be recovered from a diode
detector can be defined as
Vm(t) = 5 sin 2π104t volts.
Calculate the optimum value of capacitance required in the circuit in order to avoid
diagonal clipping distortion. You may assume a total output resistance of 4.7 kΩ and a
modulation index of 0.5. Determine suitable CR component values for a simple low-pass
filter circuit which, when connected, will develop a signal suitable for AGC.
(a) The circuit as required is as shown in Fig.
The optimum value for the capacitor is obtained by substituting values into the equation.
1
1
−1
−1
2
0.52 2
C≤ m
= 5.68 nF
=
2πf m RL
2π 10 4 4700
The low-pass filter components are calculated from the cut-off expression
fc = 1/2πCR.
Assume a value for R to avoid any loading i.e. 47 kΩ and for a cut-off fc = 10 Hz gives a
capacitor value as
C = 1/2π10.47 kΩ = 0.338 uF
Q51
A block diagram for a superhetrodyne receiver is shown in Fig 1. Explain the function
of each block. Include the following terms in you description: selectivity, sensitivity,
AGC and image frequency rejection. Indicate where in the receiver adjacent channel
selectivity takes place. A 10 microvolt peak signal is measured at the output of a 50 Ω
aerial connected to the receiver input shown in Fig 1 Determine the power levels in
dBW and dBm at the output of the RF amplifier. How many IF amplifiers are required
if the level at the detector input is 0 dBm (you may assume each IF amplifiers has gain
of 20 dB each)? The mixer and bandpass filter have a total loss of 7 dB.
[12 marks]
With the aid of suitable diagrams, explain how the am receiver could be implemented
using digital signalling techniques.
[8 marks]
Q52
Draw a block diagram of an AM superhetrodyne receiver. Explain the function of each
block. Include the following terms in you description: selectivity, sensitivity, AGC and
image frequency rejection. Indicate where in the receiver adjacent channel selectivity
takes place. Calculate the image frequency for a receiver whose intermediate frequency
is 455 kHz and the desired carrier frequency is 1 MHz.
[12marks]
Q53
With the aid of suitable diagrams, explain how the am receiver could be implemented
using digital signalling techniques.
[8 marks]
(a)Discuss the following terms as applied to a superhetrodyne radio receiver:
(i) Delayed AGC
(ii) Band-spread
(iii) Squelch
Provide appropriate circuit diagrams in the discussion illustrating how each parameter is
typically implemented.
[15 marks]
(b) Explain the advantage of using an up-conversion process instead of the more simple
down conversion technique in a superhetrodyne receiver.
[5 marks]
Q54
A superhetrodyne receiver is required to tune over a range of input frequencies from 20
MΗz to 30 MΗz. Determine the local oscillator tuning range if the intermediate
frequency is 40 MΗz.
[5 marks]
a) Draw the circuit diagram of a single-tuned FET radio frequency amplifier. Draw an
ac equivalent circuit of the amplifier and derive an expression for its voltage gain.
[12 marks]
(b) An IF amplifier is needed for a standard broadcast AM receiver. The centre
frequency is 455 kHz and the bandwidth is 10 kHz. Choose suitable components for
such a circuit. Determine the voltage gain of the circuit at resonance. It may be assumed
that the unloaded Q-factor of the inductor to be used is 100 and that the output of the
amplifier feeds into a 10 kΩ load.
Note: The FET characteristics are g m = 10 mS, r ds = 10 kΩ , C ds = 30 pF.
[13 marks]
Q55
An RF amplifier of bandwidth 10 kHz at a centre frequency of 1 MHz is to be designed
using an FET with the following characteristics:
(i) Transconductance g m =10 mS
(ii) Drain slope resistance r ds =120 kΩ
(iii) Drain source capacitance C ds = 10 pF.
The amplifier output terminals is loaded with a 120 kΩ resistance. A coil with an
unloaded Q-factor of 150 is to be used. Sketch suitable amplifier and its ac equivalent
circuit.
[4 marks]
Derive expressions for the gain at resonance, the gain off resonance and the bandwidth
of the circuit.
[8 marks]
Determine the amplifier gain at resonance and at 1100 kHz.
[8 marks]
Q56
Explain the following terms as they apply to communications receivers:
(i) Double conversion
(ii) Up conversion
[10 marks]
Determine the image frequency of the double conversion receiver section shown in
Fig.1. If single conversion is used to produce the 1 MHz signal at the input of the IF
amplifier calculate the new image frequency. If the loaded Q factor of the IF amplifier is
100 what extra image frequency suppression does the double conversion receiver offer
above the single conversion receiver?
[15 marks]
Q57
Draw a block diagram of an AM superhetrodyne receiver and explain the function of
each block. Explain what is meant by image channel interference and adjacent channel
interference.
[10 marks]
Q57
A block diagram for a superhetrodyne receiver is shown in Fig 1. Explain the function
of each block. Include the following terms in you description: selectivity, sensitivity,
AGC and image frequency rejection. Indicate where in the receiver adjacent channel
selectivity takes place.
A 10 microvolt peak signal is measured at the output of a 50 Ω aerial connected to the
receiver input shown in Fig 1 Determine the power levels in dBW and dBm at the
output of the RF amplifier. How many IF amplifiers are required if the level at the
detector input is 0 dBm (you may assume each IF amplifiers has gain of 20 dB each)?
The mixer and bandpass filter have a total loss of 7 dB.
[12 marks]
Q58
With the aid of suitable diagrams, explain how the am receiver could be implemented
using digital signalling techniques.
Draw a block diagram of an AM superhetrodyne receiver. Explain the function of each
block. Include the following terms in you description: selectivity, sensitivity, AGC and
image frequency rejection. Indicate where in the receiver adjacent channel selectivity
takes place. Calculate the image frequency for a receiver whose intermediate frequency
is 455 kHz and the desired carrier frequency is 1 MHz.
Q59
Sketch a block diagram illustrating the main signalling processes, which occur in a
superhetrodyne receiver. Explain the function of each block. Include the following
terms in you description: selectivity, sensitivity, AGC and image frequency rejection.
Indicate where in the receiver adjacent channel selectivity and image channel rejection
takes place.
[10 marks]
Q60
With the aid of suitable diagrams, explain how the am receiver could be implemented
using digital signalling techniques.
[8 marks]
What is meant by image channel interference and adjacent channel interference?
[10 marks
The image frequency is defined:
fi = flo + fif
But fIo = fs + .fif
Therefore
fi = fs + 2.fif
Substituting values
fi = (1065 + 465)kHz = 1530 kHz.
The Image channel response ratio (ICRR) is given as
ICRR =
1+ Q2 ρ
Where ρ = (fi/fs - fs/fi)
ρ = (1530/600 - 600/1530) = 2.55 - 0.392 = 2.157
ICRR = 1 + 802 .2.157 = 1117.5 = 20 log 117.2
Q61
Draw a block diagram of an AM superhetrodyne receiver. Explain the function of each
block. Include the following terms in you description: selectivity, sensitivity, AGC and
image frequency rejection. Indicate where in the receiver adjacent channel selectivity
takes place. Calculate the image frequency for a receiver whose intermediate frequency
is 455 kHz and the desired carrier frequency is 1 MHz.
[12 marks]
Q62
Define the term noise figure.
[2 marks]
The noise at the input of a system has a RMS value equal to 10 uV. Determine the
signal input amplitude to this system whose noise figure is 5 dB so that the signal to
noise ratio at the output is equal to 45 dB.
[4 marks]
(c)
Three amplifiers are connected as shown in Fig.2. Calculate, using the noise figure and
power gain information as supplied, the overall system noise figure in dB and comment
briefly on the significance of the result
4c) Applying the noise and power gains, which were given in dB, are first converted to
RATIOS and then applied to Frii's formula i.e.
N −1
N R2 − 1
+ R3
+ .........
A1
A1 A2
3.981 − 1
10 − 1
NR = 1.58 +
+
+ ..... = 1.5 + 0.47 + 0.09 = 2.14
6.3
6.3.15.85
NF = 10log NR = 3.3 dB
It can be seen from the results that the first stage should have a low noise and high gain,
since its influence on the overall figure is much greater than the other stages.
NR = N R1 +
Q63
(a)A Colpitts oscillator utilises a single stage self-biased JFET operating with quiescent
conditions VGSQ = 1 V, IDSQ= 2 mA and gm = 2 mS. The total resistive loading on the
drain is 4.7 kΩ and the inductance is 470 uH. Calculate suitable component values for this
circuit to ensure sustained oscillations at a frequency of 100 kHz
Q64
(d) Explain the operation of a basic delta modulator.
(a)Show how Quadrature Amplitude Modulation is used to facilitate the transmission of
two different signals in the same frequency band. Describe the difference between this
system and independent sideband transmission. In your description of QAM, include a
brief discussion of the demodulation process.
[12 marks]
(b)Explain with the aid of appropriate diagrams the principle of baseband voice
scrambling based on a simple frequency inversion process.
[8 marks]
Q65
A modulating signal s(t) and a carrier signal Acos(2πf c t) are the two inputs to a
summing amplifier. The output from the summing amplifier is applied to the input of a
non-linear circuit whose input/output relationship is:
2
v out (t) = k1 v in (t) + k 2 v in
(t)
Derive an expression for the output signal from the non-linear circuit and sketch the
output signal spectrum given that:
S(f)=rect(f/B) cos(πf/B)
Where B is a constant.
[7 marks]
Show that this output signal contains an AM signal component. Determine the
amplitude sensitivity of this modulator if k1 = 2 and k 2 = 0.5.
[6 marks]
Show with the aid of a block diagram how you would demodulate the AM signal using
a similar non-linear circuit. Derive an expression for the signal-to-noise ratio of the
signal at the demodulator output.
[12 marks]
Q66
Give that a double sideband suppressed carrier signal m(t)cos(2πf c t ) is applied to the
input of a coherent detector whose local oscillator frequency is
f lo = cos[2π ( f c + ∆f)t + φ]
[20 marks]
Discuss the operation of the detector for the following conditions:
(i) ∆f = φ = 0
(ii) φ = 0
(iii) ∆f = 0
In case (ii) determine φ if the amplitude of the recovered signal is three quarters of its
amplitude when φ = 0.
[5 marks]
What is the minimum allowable carrier frequency if the baseband signal whose
bandwidth is 12 kHz is to be recovered without distortion?
[5 marks]
The SSB signal s(t) = x(t) cos(2πf c t ) + x(t) sin(2πf c t ) is applied to the input of a
coherent demodulator consisting of a product modulator and a low pass filter. If the
modulation x(t) whose Hilbert transform, defined as x(t), has a single sided spectrum
X(f) defined by:
X(f) = (A/B)(B-f), 0 < f < B
X(f) = (A/B)(B+f), -B < f < 0
X(f) = 0 elsewhere.
Sketch the following spectra:
(i) X(f)
(i) jX(f).
(ii) S(f).
[13 marks]
(iii) The output signal from the product modulator,
(iv) The output signal from the low-pass filter,
[8 marks]
If the input to the demodulator is a sinusoidal signal of frequency f 1 and of unit
amplitude, derive an expression for the output signal from the low-pass filter, given that
the carrier at the receiver has both a frequency error (∆f) and a phase error φ with
respect to the carrier at the transmitter.
[4 marks]
(b)
Explain with the aid of appropriate diagrams the principle of baseband voice scrambling
based on a simple frequency inversion process.
[8 marks]
(b)Describe with the aid of a block diagram how two AM modulators can be combined
to generate a DSBSC signal.
[9 marks]
(e) Explain the operation of a basic delta modulator.
[12 marks]
Sampling
Q67
Q68
(a)A linear PCM quantiser has 256 discrete levels for a maximum signal level of 10
volts. Determine the number of bits required, the smallest step size and the dynamic
range.
(b) A signal with a uniform probability density function is applied to the input of a
uniform pulse-code modulation encoder. The encoder provides 'n' binary digits per
sample. Derive an expression for the peak signal to rms output noise ratio and for the
average signal to rms output noise ratio. If n = 8, determine the difference in decibels
between the above two measurements.
[12 marks]
(a)The spectrum of a signal to be sampled, using impulse sampling, is shown in figure
1. Use this spectrum to state and prove the Sampling theorem. Show the effects of
aliasing for the case of under- sampling.
[8 marks]
(b) Explain why companding is required in the codec section of a TMD PCM system
Sketch the segmented A-law companding characteristic and relate the 8-bit allocation to
the quantised signal.
[6 marks]
Figure 2
Q69
A linear PCM quantiser has 256 discrete levels for a maximum signal level of 10 volts.
Determine the number of bits required, the smallest step size and the dynamic range.
[6 marks]
Solution
What is the number of bits needed to represent each character?
Solution:
There are 110 distinct ''messages'' (characters) produced by the digital source. We
assume that each character is represented by a unique sequence of bits and that the
number of bits b in the sequence is the same for all 110 characters. Then the minimum
number of bits required to uniquely represent the characters is:
B = dlog2110)e = log10 (110) log10(2) = 7
Where Delta e denotes the ''ceiling'' operation (i.e. round up to the next highest integer).
Thus, seven (7) bits are required to represent each character.
1.b How fast can the characters be sent (char/sec) over a telephone line channel having a
bandwidth of 3.2 kHz and a SNR of 20 dB?
Solution: Determine the SNR in absolute units:
20 dB = 10log10(S/N)
S/N = alog(2) = 100
Now substitute S/N = 100 and B = 3200 into equation 1-10:
C = B log2(1 + S/N)
C = 3200 log2(1 + 100)= 3200 log210 (101) = log10(2) = 21; 307 bits per sec
We want to know the capacity in terms of characters per second. Since there are b bits
per character, we must divide by b:
C = 21; 307 bits per sec = 7 bits per char = 3; 044 chars per sec
(a)An analogue signal with a uniform probability density function is applied to the input
of an n-bit linear PCM encoder. Derive an expression for the peak signal to rms.
quantisation noise ratio at the encoder output. Determine the magnitude of the
quantisation noise if n=16.
[12 marks]
(b) Discuss with the aid of a block diagram the operation of a delta modulator. A
sinusoidal signal of amplitude 500 mV and of frequency 1 kHz is applied to the input a
delta modulator. Determine the lowest sampling frequency such that slope overload will
be avoided if the modulator step size is 400 µV.
[13 marks]
Data
Q70
(a) Show how the system capacity C, in a ideal noiseless channel, is
C = 2 f c (min) log 2 M , where M is the number of levels per information interval and
fc(min) is the absolute minimum channel cut-off frequency (bandwidth).
[8 marks]
(b) Explain what is meant by entropy applied to a communication channel. Include an
expression for the entropy in your answer.
[5 marks]
(c) Discuss the factors, which determine the channel capacity of a telecommunications
channel. The channel capacity of a telephone channel is 29.92 kb/s and has an
available bandwidth of 3 kHz. Calculate the maximum signal to noise ratio.
Calculate how many signalling levels are required for this channel if the received
signal is decoded error free?
[7 marks]
Q71
(b) If the bandwidth of a telephone channel is 4 kHz, what is the highest information
rate that can be transmitted as binary, assuming an ideal noiseless channel?
[6 marks]
(c) What is the channel capacity for a 4-level encoded Pam transmission if the
(d)telephone channel has an SNR of 30 dB and a 4 kHz BW?
[6 marks]
Q72
Clearly describe one modern bandpass technique for modulating binary data to produce
a bandpass signal.
Differentiate between frequency division multiplexing (FDM) and time division
multiplexing (TDM) as applied in the public switched telephone network (PSTN). Give
a simple block diagram representation for each multiplex technique.
[6 marks]
Q73
Explain the following terms:
Signal to noise ratio, noise factor and noise figure. How is the overall noise figure for a
receiver calculated?
[10 marks]
A baseband transmission system whose overall S/N is 30.1 dB, is to be used for
transmitting information at a maximum rate of 45 Mbits/s. Calculate,
(i) The minimum bandwidth required,
(ii) The number of levels M, and
(iii) The value of n, in an n-bit PCM system, to be used for transmitting the information.
[10 marks]
The input signal applied at point A is a ramp signal described by the equation
v(t)=5t +1.25 volts
Where t is in ms. The staircase generator produces 10 samples/ms and 1 volt per step.
The first step starts at t = 0 s. Sketch the signal waveforms you would expect at points
A and B (over 7 clock periods). Hence determine the delta modulator output bit
sequence.
[7 marks]
Q74
Explain the term slope overload. Hence show how adaptive delta modulation techniques
minimises the difficulties associated with non-adaptive delta modulation techniques.
[8 marks]
Explain the process by which 30 bandlimited audio telephone signals are multiplexed
together and sent over a junction telephone network. The discussion should make
references to the following terms: companding, time slots, frame and multiframe.
[15 marks]
If the sampling rate is 8 kHz, calculate the transmitted bit rate for this system and state
the time period occupied by a bit, a time slot, a frame and a multiframe.
[5 marks]
Explain the following terms as applied to the transmission of data over a bandlimited
line: Bit rate and baud rate.
[4 marks]
Q75
An expression for the maximum rate at which information can be transmitted through a
system is given as C = 3.32BWlog10 [S/N + 1]. Discuss the significance of each term in
the expression.
[6 marks]
Q76
Draw a block diagram of a simple modem and describe briefly its operation.
Draw the block diagram of a DPSK encoder and decoder and explain the operation of
the system.
[8 marks]
(a)The binary sequence 1101 1001 is transmitted using 2-phase PSK. Sketch the
modulated signal assuming that the duration of each bit is four times greater than the
carrier period.
[4 marks]
If the binary sequence is changed to an alternating 10101010 sequence, determine the
spectrum of the PSK signal. Assume that the bit rate is 1600 bps and that the carrier
frequency is 10 times the bit rate.
[8 marks]
Q77
(f) Show how the basic delta modulator can be modified to provide a CVSD modulator
and briefly explain the operation of this modulator.
[9 marks]
(a) A sinusoidal signal of amplitude 5 V and of frequency 10 kHz is applied to the input
of a delta modulator. The clock frequency of the modulator is 1 MHz. Determine the
step size of the modulator such that slope-overload will not occur. Derive any equations
used.
[12 marks]
Discuss in detail the operation of a basic delta modulator. A sinusoidal signal of
amplitude 1 V and of frequency 10 kHz is applied to the input of a delta modulator. The
modulator uses a step size of 0.5 mV. Determine the minimum clock frequency of the
modulator so that slope overload will not occur.
[13 marks]
Q78
A modem to be used within a PSTN uses an 8-level QPSK modulation scheme. If the
PSTN bandwidth is 3100 Hz, deduce the Nyquist maximum data transfer rate.
[4 marks]
(c)If the PSTN described in (b) has a typical signal-to-noise of 20dB, determine the
maximum theoretical information rate that can be achieved.
[4 marks
(b)A signal with a uniform probability density function is applied to the input of a
uniform pulse-code modulation encoder. The encoder provides 'n' binary digits per
sample. Derive an expression for the peak signal to rms output noise ratio and for the
average signal to rms output noise ratio. If n = 8, determine the difference in decibels
between the above two measurements.
[12 marks]
Q79
Explain the terms FSK and QPSK.
[6 marks]
Draw a block diagram of a simple modem and describe briefly its operation.
The binary sequence 1101 1001 is being transmitted using two-phase PSK. Sketch the
modulated carrier signal assuming that the duration of each bit is four times greater than
the carrier period.
[5 marks]
If the binary sequence is changed to an alternating 101010 sequence determine the
spectrum of the PSK signal. Assume that the bit rate is 1600 b/s and that the carrier
frequency is ten times the bit rate. Fully label this diagram including the magnitudes of
the significant phasor components. State clearly any further assumptions made.
[10 marks]
Draw the block diagram of a DPSK encoder and decoder and explain the operation of
the system fully.
[10 marks]
Q80
The public switched telephone network (PSTN) uses the following modulation schemes
in transmitting data over bandlimited channels:
a) FSK,
b) PSK, and
c) QAM
Explain briefly the fundamental principles of each system, using block diagram where
necessary,
[10 marks]
Q81
Explain how the system shown in Fig 3 can encode a data signal 1001011 into a suitable
DPSK format. Sketch the resultant logic waveform at points A, B, C and D. Hence
determine the output sequence at E.
[10 marks]
(a)Give a brief description of the application and limitations of the following types of
transmission media:
(i) Two- wire open-lines
(ii) Twisted pair lines
(iii) Coaxial cable
(iv) Optical fibre
[12 marks]
(b)A modem to be used within a PSTN uses an 8-level QPSK modulation scheme. If the
PSTN bandwidth is 3100 Hz, deduce the Nyquist maximum data transfer rate.
[4 marks]
(c)If the PSTN described in (b) has a typical signal-to-noise of 20dB, determine the
maximum theoretical information rate that can be achieved.
[4 marks]
If the binary sequence is changed to an alternating 10101010 sequence, determine the
spectrum of the PSK signal. Assume that the bit rate is 1600 BPS and that the carrier
frequency is 10 times the bit rate.
[8 marks]
Q82
Many communications channels are unsuitable for direct digital communication.
i) Describe how inter computer communication can be achieved using a telephone line.
(8 Marks)
ii) Clearly describe three techniques for modulating binary data highlighting the
relationship between Bits/sec and Baud rate.
Draw the block diagram of a DPSK encoder and decoder and explain the operation of
the system fully.
[10 marks
(a)
Show how Quadrature Amplitude Modulation is used to facilitate the transmission of
two different signals in the same frequency band. Describe the difference between this
system and independent sideband transmission. In your description of QAM, include a
brief discussion of the demodulation process.
[12 marks]
DSP
Q84
Use the following digital filter definition to classify the FIR and IIR type structures
where y(n) is the filter output and x(n) is the input:
P
L
k =0
k =1
y (n ) = ∑ ak x(n − k ) − ∑ bk y (n − k )
(a) Determine the z-transform of the following difference equation:
y (n) = a0 x(n) + a2 x(n − 2) + b2 y (n − 2)
Q85
Obtain the system transfer function Y(z)/X(z). Draw a block diagram of the system
represented by the above difference equation. If x(n)=1 for n=0 or n=1 and x(n)=0
otherwise, determine y(2). It may be assumed that y(-1)=0 and that ao=a1=b2=0.5.
Two types of digital filter are shown in Fig 1. Obtain the difference equation and hence
express the system function as H(Z)=Y(Z)/X(z). State the filter type (i.e. FIR or IIR) of
each configuration.
[12 marks]
Q86
Draw a block diagram illustrating the main processes that occur in a digital receiver.
Explain the function of each block.
[8 marks]
(b) Use the following digital filter definition to classify the FIR and IIR type structures
where y(n) is the filter output and x(n) is the input:
P
L
k =0
k =1
y (n ) = ∑ ak x(n − k ) − ∑ bk y (n − k )
[10 marks]
(c) Obtain the system transfer function Y(z)/X(z) for each system shown in Fig.1(a) and
Fig.1(b). Which system is an IIR type filter?
[11
(d)
(e) Determine the z-transform of the following difference equation:
y (n) = a0 x(n) + a2 x(n − 2) + b2 y (n − 2)
Obtain the system transfer function Y(z)/X(z). Draw a block diagram of the system
represented by the above difference equation. If x(n)=1 for n = 0 or n = 1 and x(n) = 0
otherwise, determine y(2). It may be assumed that y(-1)=0 and that ao = a1 = b2 = 0.5.
Q87
A 7-bit linear quantiser with a voltage range 5V is used to quantise an analogue signal.
Calculate the distortion power (in mW) introduced by the quantiser.
[5 marks]
Determine the entropy of a source that transmits 5 symbols with the probabilities shown
in table 1:
[5 marks]
Q88
Single-bit error correction is used to reduce the errors in a communications channel. If
the channel bit-error probability is 5 10 6, determine the probability of an error in an 8bit byte when this error correction is applied.
[5 marks]
Q89
If the communications channel in question (3) is used without error correction, calculate
the distortion power (in mW) introduced by the errors if the 8-bit words represent
linearly-quantised analogue signals with quantising step of 10mV.
[5 marks]
Q90
A signal is transmitted through 3 stages with signal/noise ratios as shown in figure 1.
Calculate the overall signal/noise ratio in dB.
[5 marks]
out
Figure 1
Q91
Determine the maximum theoretical speed at which computer data could be transmitted
over an analogue telephone line with a bandwidth of 4 kHz and signal/noise ratio of 32
dB
[5 marks]
Explain the principles of the synchronous digital hierarchy and why it is now preferred
to the plesiochronous digital hierarchy.
[10 marks]
Q91
(b) Design a second-order digital filter, with a centre frequency of 3 kHz, and a Q-factor
of 1.5. Sketch the pole-zero map in the Z-plane, and make a rough sketch of the
frequency response. The sampling frequency is 20 kHz.[10 marks]
(b) Derive an expression for the magnitude response of the linear, time-invariant
system shown in Fig. 4. If a0 = 0.6, and T = 50 ms (the sampling period), calculate the
cut-off frequency in Hz.
[7 marks]
(c) Calculate the pole frequency in Hz, and the pole radius of the second-order system
(with a single conjugate pole-pair) whose transfer function is as follows:
H ( z) =
1 + 0.51298 z
1
−1
+ 0.6489 z
−2
The sampling frequency is 10 kHz.
[7 marks]
x(n)
y(n)
Σ
1-a0
z-1
a0
Fig.
(b) Derive an expression for the magnitude frequency response of the second-order
discrete-time system with the following transfer function:
H ( z) =
1
1 + 1.3435z
−1
+ 0.9025z
−2
What is the resonant frequency (in Hz) of the system, if the sampling frequency is 20
kHz ?
[10 marks]
Q92
(a) How many bits are needed for uniform quantisation of a signal with amplitude ±5
V, if the smallest change in analogue voltage which must be detected is 1.23 mV ?
What is the SQNR
for the resulting sampled signal ?
[8 marks]
(b) Making appropriate assumptions, derive an expression for the Equivalent Noise
Bandwidth (BN) of a linear system.
[10 marks]
Q93
With the aid of appropriate equations, describe the A-law characteristic used for nonuniform compression of speech signals for transmission, and describe how it would be
implemented in a practical telecommunications system. What are the advantages of this
method over uniform quantisation of speech signals ?
[10 marks]
(a)
What are the two methods used to achieve Bit Synchronisation in Bit-oriented
transmission systems. Show how the sequence 10110010 is encoded using:
(i) Manchester Encoding;
(ii) Differential NRZI Encoding.
[ 8 marks ]
Q94
(a) Derive an expression for the signal-to-quantisation-noise ratio (SQNR), in dB, for
uniform quantisation of a sinusoidal signal of peak amplitude 2A volts, using B bits.
How many bits are required for uniform quantisation of a signal with amplitude +/-5
volts, if the quantisation step size is to be no greater than 0.17 mV ? What is the SQNR
in this case ?
[10 marks]
Q95
(a) A satellite receiver has an antenna with an Equivalent Noise Temperature (Teq) of
30 K,
connected via a coupling network (Teq = 37 K) to a microwave receiver
(Teq=50 K). What is the equivalent noise power referred to the input over a bandwidth
of 1.5 MHz ? What is the noise figure of the receiver ? Assume a reference temperature
of 290 K. The value of k (Boltzmann’s constant) is 1.38x10-23 J/K.
[10 marks]
Q96
(a) How many bits are needed for uniform quantisation of a signal with amplitude ±2.5
V, if the smallest change in analogue voltage which must be detected is 1.23 mV ? What
is the SQNR for the resulting sampled signal ?
[6 marks]