Vakkursus EMS310/311 Course EMS310/311 - Electrical, Electronic ...

Departement Elektriese,
Elektroniese en Rekenaar-
Ingenieurswese
Klastoets 2
Kopiereg voorbehou
Vakkursus EMS310/311
19 April 2007
Toetsinligting / Test information:
Maksimum punte:
Maximum marks:
Duur van vraestel:
Duration of paper:
MODULASIESTELSELS
MODULATION SYSTEMS
30 Volpunte:
Full marks:
30 minute
30 minutes
Department of Electrical, Electronic
and Computer Engineering
Oopboek / toeboek:
Open / closed book:
BELANGRIK- IMPORTANT
Class Test 2
Copyright reserved
Course EMS310/311
19 April 2007
EMS310_Klastoets2_07.wpd LPL/04/07 1 / 7
30
Toeboek
Closed book
1 Die eksamenregulasies van die Universiteit van Pretoria geld.
2 Hierdie is ‘n toeboektoets. GEEN notas of los papiere word toegelaat nie.
3 Beantwoord al die vrae. Doen asb Deel I en Deel II in aparte antwoordskrifte- hulle sal afsonderlik gemerk
word.
4 Antwoorde in potlood sal nie gemerk word nie.
5 Nommer die antwoorde presies soos dit in die vraestel voorkom.
6 Alle vrae moet in die toetsantwoordboek(e) wat verskaf word beantwoord word.
7 Toon alle aannames, stappe en berekenings.
8 Verwys ook na die Engelse bewoording indien daar onduidelikheid oor ‘n vraag is.
1 The examination regulations of the University of Pretoria apply.
2 This is a closed book test. NO notes or loose papers are allowed.
3 Answer all questions. Please do Part I and Part II in separate answer books - they will be marked
separately.
4 Work in pencil will not be marked.
5 Number your answers exactly as they appear in the question paper.
6 All questions must be answered in the supplied answer book(s) or sheets.
7 Show all assumption, steps and calculations.
8 Also refer to the Afrikaans question if there is any uncertainty with a question.
Dosent(e):
Lecturer(s):
1 Prof L.P. Linde
2
NAAM / NAME: Reg. No.
Vraag /Quest 1 [6] 2 [6] 3 [6] 4 [6] 5 [6] TOTA(A)L [30]
Punt / Mark
DEEL I VRAAG 1 VOLG / PART I QUESTION 1 FOLLOWS . . .

1.
1.1 Skets die blokdiagram van ‘n FSL en identifiseer die basiese substelsels of subelemente. Gee kortliks
die funksie van elke boublok/substelsel. Toon alle seine en spesifiseer die ekwivalente Laplace
oordragfunksie van elke element in u blokdiagram.
Sketch the block diagram of a PLL and identify the basic subsystems or building blocks. Give a
concise description of the function of each building block / subsystem. Show all signals and specify the
equivalent Laplace transfer function of each building block in your block diagram.
Fig. 1-1 FSL-blokdiagram / PLL block diagram (3)
1.2 Funksie/beskrywing van elke FSL-substelsel / Function/description of each PLL subsystem:
1.2.1
1.2.2
1.2.3
EMS310_Klastoets2_07.wpd LPL/04/07 2 / 7
[6]
(1)
(1)
(1)

2 Identifiseer en skets die boublokke wat tesame die FSL fasedetektor vorm. Watter wiskundige funksie beskryf
die werking van die fasedetektor? Gee ‘n uitdrukking in terme van die groothede in u fsl blokdiagram in 1.1
hierbo. Skets die fasedetektor-oordragfunksie en toon aan hoe die fasedetektor-konstante bepaal word
(spesifiseer eenhede!)
Identify and sketch the building blocks which together form the PLL phase detector. What mathematical function
best describes the operation of the phase detector? Write down an expression in terms of the quantities specified
in your PLL block diagram in 1.1 above. Sketch the phase detector transfer function and show
how the phase detector constant is determined (specify units!)
[6]
2.1 Skets fasedetektor / Sketch Phase detector (2) | Fasedetektoroordragfunksie / Phase detector transfer function (2)
2.1.1 Fasedetektor ekwivalente wiskundige funksie / Phase detector equivalent mathematical function:
2.1.2 Herlei fasedetektorkonstante, K D [Eenhede?] / Derive phase detector constant, K D [Units?]
EMS310_Klastoets2_07.wpd LPL/04/07 3 / 7
(1)
(1)

3.
3.1 Teken die blokdiagram van ‘n ideale basisband verwysingstelsel (sonder modulasie), met m(t) die intree-
(informasie-)sein met drywing P m=S i [Watt]. Die SWGR-kanaal tel with Gauss-ruis met tweesydige
DrywingsDigtheidSpektrum (DDS) N/2 [W/Hz] by. Aanvaar ‘n perfekte LDF in die ontvanger met bandwydte
B$f m [Hz], waar f m die maksimum informasiefrekwensie voorstel.
Draw the block diagram of an ideal reference baseband communication system (without modulation), with m(t)
the input (information) signal with power P m=S i [Watt]. The AWGN channel adds white Gaussian noise with
two-sided Power-Spectral-Density (PSD) N/2 [W/Hz]. Assume a perfect LPF in the receiver with bandwidth
B$f m [Hz], where f m denotes the maximum information frequency.
Fig. 3-1 Blokdiagram van ideale basisband verwysing-kommunikasiestelsel
Block diagram of ideal reference baseband communication system. (3)
3.2 Bereken die ontvangde informasie-seindrywing S i en die ruisdrywing N o by die uitgang van die
basisbandontvanger, en bepaal ‘n uitdrukking vir die uitgang sein-tot-ruis-verhouding, (SNR) b.
Calculate the received information signal power S i and the noise power N o at the output of the baseband
receiver, and determine an expression for the output signal-to-noise-ratio, (SNR) b.
Bereken P m= S i=S o [W] en N o [W], en gevolglik `n uitdrukking vir (SNR) b.
Calculate P m= S i=S o [W] and N o [W], and hence an expression for (SNR) b:
(SNR) b =
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[6]
(3)

4 Herlei ‘n noubandmodel (tyd-uitdrukking) vir ideale bandlaatgefilterde SWGR, n(t), met tweesydige DDS N/2
[W/Hz]. Gee ook `n skets van die fasordiagram van die komplekse omhulling van die ekwivalente
nt ~ ()
nouband basisband ruis en herlei uitdrukkings vir die infasige, nc(t), en haaksfasige, ns(t), komponente van die
ruis in terme van (itv) die reële omhulling |n(t)|=| | en hoek θn [rad] van die bandlaatruis, n(t). Stel die
nt ~ ()
voorwaarde(s)/benadering(s) wat gemaak word om die noubandmodel vir die kanaal bandlaatruis af te lei.
Derive a narrowband model (time expression) for ideal band-pass-filtered AWGN, n(t), with two-sided PSD N/2
[W/Hz]. Also give a plot of the phasor diagram of the complex envelope nt ~ () of the equivalent narrowband
baseband noise and derive expressions for the in-phase, nc(t), and quadrature, ns(t), components of the noise in
terms of (ito) the real envelope |n(t)|=| nt ~ () | and angle θn [rad] of the band-pass noise, n(t). State the
assumption/approximation(s) made to derive this (narrowband) model for the channel band-pass
noise, n(t).
[6]
EMS310_Klastoets2_07.wpd LPL/04/07 5 / 7

5 Herlei uitdrukkings vir die ontvanger intree S/R (na die ontvanger-BDF) en die ontvanger uitgang S/R, (SNR) i
and (SNR) 0 repektiewelik, in die geval van AM-DSB-OD met moduleersein m(t) en Tx en Rx draers van
%2cos(ωct) en %2cos(ωct+θ), onderskeidelik, met θ=π/4 [rad]. Aanvaar `n perfekte BDF by die ontvanger en `n
SWG- kanaal met tweesydige DDS N/2 [W/Hz]. Beskryf die volledige demodulasieproses analities. Hoe
vergelyk die S/R-werkverrigting van hierdie AM-DSB-OD stelsel met die ideale basisband-verwysingstelsel in
4 hierbo? Verklaar enige verskille.
Derive expressions for the receiver input (after the Rx BPF) and the receiver output SNRs, (SNR) i and (SNR) 0,
respectively, in the case of AM-DSB-SC with modulating signal m(t) and Tx and Rx carriers of %2cos(ωct) and
%2cos(ωct+θ), respectively, with θ=π/4 [rad]. Assume a perfect BPF at the receiver and an AWGN channel with
two-sided PSD N/2 [W/Hz]. Show the complete demodulation process analytically. How does the SNR
performance of this AM-DSB-SC system compare with the ideal reference baseband system in 4 above? Explain
any differences.
EINDE
END
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[6]

T
F
ω
n
ξ =
APPENDIX A
PLL IDENTITIES
The following formulas are relevant to a second order PLL with passive loop filter, F(ω), with components (R 1, R 2, C). The natural
angular frequency of the PLL is described by:
K′ = K
N
⎡ K′
⎤
= ⎢ ⎥
⎣τ
T ⎦
1 ⎡ K ′ ⎤
⎢ ⎥
2 ⎣ τ T ⎦
1 2
( ∆ ω )
= 3
2ξωn
[sec]
2
4( ∆ f )
= 3 ;
B
ξ = 1 = 0707 .
2
L
2
1 2
[ rad / s]
(1)
where is the total loop gain, with N the loop division factor. The total loop filter constant is given by τT = ( R1 + R2) C .
The damping constant of the PLL is given by:
The -3dB bandwidth of the closed-loop transfer function, H(ω), is:
[ τ + 1
2 ]
EMS310_Klastoets2_07.wpd LPL/04/07 7 / 7
K ′
2 2 2
[ 2 1 2 1 1]
ω− 3 = ω ξ + + ξ + +
The closed-loop noise bandwidth, BL, of the PLL is given by:
∞ 2
dB n ( ) [ rad / s ]
ω n ⎡ 1 ⎤
BL= ∫ H( ω ) . df = ⎢ξ
+ ⎥ [ Hz ]
0
2 ⎣ 4ξ
⎦
If the input signal frequency and phase falls within the bandwidth of the loop filter, locking will occur without cycle slipping, for a
angular frequency difference of:
∆ω
K′
. τ 2
=
τ + τ
L n
1 2
≈ 2ξω [ rad/s] if K′
>>
The maximum angular frequency difference which the PLL will be able to Pull-In (with or without cycle slipping) is approximately
equal to:
[ K ]
1 2
2
∆ ω = 2 2ξω
′ − ω
1 2
. [rad/s] (6)
PI n n
The maximum frequency-offset, ∆ωHI [rad/s], from the nominal VCO-frequency of ωo [rad/s], which the PLL will be able to track
without cycle slipping, after it has already locked onto the input signal, is given by:
∆ω HI = K′
[rad / s] (7)
The time it takes for a PLL to lock onto a frequency component ∆ω [rad/s] away from the nominal VCO frequency, is:
(2)
(3)
(4)
(5)
(8)