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School of Electrical, Electronics andComputer Engineering
University of Newcastle-upon-Tyne
Baseband Digital Modulation Baseband Digital Modulation
Prof. Rolando CarrascoProf. Rolando Carrasco
Lecture Notes University of Newcastle-upon-Tyne
2007
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Baseband digital informationBaseband digital information
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Bit-rate, Baud-rate and Bit-rate, Baud-rate and BandwidthBandwidth
BB1 denotes the duration of the 1 bit
Hence Bit rate = bits per second
All the forms of the base band signalling shown transfer data at the same bit rate.
E denotes the duration of the shortest signalling element.Baud rate is defined as the reciprocal of the duration of the shortest signalling element.
Baud Rate = E1
baud
In general Baud Rate ≠ Bit Rate
For NRZ : Baud Rate = Bit Rate
RZ : Baud Rate = 2 x Bit Rate
Bi-Phase: Baud Rate = 2 x Bit Rate
AMI: Baud Rate = Bit Rate
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Non Return to Zero (NRZ)Non Return to Zero (NRZ)
The highest frequency occurs when the data is 1010101010…….i.e.
This sequence produces a square wave with periodic time E 2
Fourier series for a square wave,
If we pass this signal through a LPF then the maximum bandwidth would be 1/T Hz, i.e. to just allow the fundamental (1st harmonic) to pass.
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Non Return to Zero (NRZ) Non Return to Zero (NRZ) (Cont’d)(Cont’d)
The data sequence 1010…… could then be completely recovered
Hence the minimum channel bandwidth
RateBaudSinceRateBaudT
BEE
1
2211
min
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Return to Zero (RZ)Return to Zero (RZ)
Considering RZ signals, the max frequency occurs when continuous 1’s are transmitted.
This produces a square wave with periodic time E 2
2minRateBaudfB U
If the sequence was continuous 0’s, the signal would be –V continuously, hence
''DCfL
.
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Bi-PhaseBi-Phase
Maximum frequency occurs when continuous 1’s or 0’s transmitted.
E1
2minRateBaud
fB U
This is similar to RZ with Baud Rate = = 2 x Bit rate
The minimum frequency occurs when the sequence is 10101010…….e.g.
B E
2minRateBaudfB L
In this case =
Baud Rate = Bit rate
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Digital Modulation and Digital Modulation and NoiseNoise
The performance of Digital Data Systems is dependent on the bit error rate, BER, i.e. probability of a bit being in error.
NasNbitsTotalEErrorsofNoP
Digital Modulation
There are four basic ways of sending digital data
The BER (P) depends on several factors• the modulation type, ASK FSK or PSK• the demodulation method• the noise in the system• the signal to noise ratio
Prob. of Error or BER,
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Digital Modulation and Digital Modulation and NoiseNoise
Amplitude Shift Keying ASK
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Digital Modulation and Digital Modulation and NoiseNoise
Frequency Shift Keying FSK
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Digital Modulation and Digital Modulation and NoiseNoise
Phase Shift Keying PSK
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System Block diagram for System Block diagram for AnalysisAnalysis
DEMODULATOR – DETECTOR – DECISION DEMODULATOR – DETECTOR – DECISION
For ASK and PSK
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Demodulator-Detector-DecisionDemodulator-Detector-Decision
FOR FSK
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DemodulatorDemodulator
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Demodulator Cont’d)Demodulator Cont’d)
TRCdesignHence
dtVRC
V INout
1
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Detector-DecisionDetector-Decision
1V 0V - is the voltage difference between a ‘1’ and ‘0’.
)22
( 21 VVVREF
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Detector-Decision (Cont’d)Detector-Decision (Cont’d)
ND is the noise at the Detector input.Probability of Error,
DNerf
221
21
Hence
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0 v1v0 v
0-
P(v0)
vn
Probability density of binary signalProbability density of binary signal
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v0 v1
2
210
2)(
0 21
21)(
vv
n evP
)(1 nvP
vn
n
vv
vve dveP
n2
20
10
2)(
2
1 21
Using the change of variable2
0vvx n
Probability density function of noiseProbability density function of noise
(*)
DN2
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22
101
21
vv
dxxe eP
dxezerfcz
x
22)(
222
1 011
vverfcPe
This becomes
The incomplete integral cannot be evaluated analytically but can be recast as a complimentary error function, erfc(x), defined by
Equations (*) and (**) become
n
vvvv
e
e
dveP
vverfP
zerfzerfc
n2
21
10
2)(2
0
011
21
221
21
)(1)(
(**)
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It is clear from the symmetry of this problem that Pe0 is identical to Pe1 and the probability of error Pe, irrespective of whether a ‘one’ or ‘zero’ was transmitted, can be rewritten in terms of v = v1 – v0
22
121
verfPe
for unipolar signalling (0 and v)
for polar signalling (symbol represented by voltage 2v
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Detector-Decision (Cont’d)Detector-Decision (Cont’d)
PSKFSKASKOptimumFor
PRK
NSerfPSK
NSerfFSK
OOK
NSerfASK
IN
INe
IN
INe
IN
INe
,,
121
21
21
41
21
dB/10in SNR10ePePeP
SNR in wattASK FSK PSK
000.002415.848912
00.00080.012710.0010
0.00020.0060.03796.30968
0.00240.0230.07913.98116
0.01250.05650.13122.51194
0.03750.1040.18671.58492
0.07860.15870.23981.000
Linear gainSNR in dB
000.002415.848912
00.00080.012710.0010
0.00020.0060.03796.30968
0.00240.0230.07913.98116
0.01250.05650.13122.51194
0.03750.1040.18671.58492
0.07860.15870.23981.000
Linear gainSNR in dB
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Probability of Symbol Error
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
0 2 4 6 8 10 12 14
SNR in dB
Prob
abili
ty o
f Sym
bol E
rror
ASKFSKPSK
Detector-Decision (Cont’d)Detector-Decision (Cont’d)
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FM/ FSK Demodulation
One form of FM/FSK demodulator is shown below
In general VIN (t) will be
tCosVtV INcIN )(
IN ININ f 2Where is the input frequency (rad/sec)
ttCosttCosV
V
BACosBACosCosBCosASince
tCosVtCosVVtVtVV
ININININc
x
INcINcx
ININx
2
21
)(.
2
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FM/ FSK Demodulation (Cont’d)
INININc
x
ININININININc
x
CostCosV
V
ttCosttCosV
V
22
22
2
)2(
2
)1(222
2
2
tCosV
and
tCosV
INc
INc
i.e
Thus there are two components
Component (1) is at frequency 2 fIN Hz and component (2) is effectively a ‘DC’ voltage if
IN is constant.
The cut-off frequency for the LPF is designed so that component (1) is removed and component (2) is passed to the output.
tCosVV INc
OUT 2
2
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FM/ FSK Demodulation (Cont’d)
The V/F characteristics and inputs are shown belowAnalogue FM
ccDCc
mmDCout
mmDCIN
DCIN
INout
mc
fTVf
ftCosVVfeitCosVVV
tmVVfVf
cxmyVf
1,
..
)(
0
0
Modulation Index m
m
m
c
fV
ff
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FM/ FSK Demodulation (Cont’d)
tnCosJVtVFM mcn
ncs
1
)()(
The spectrum of the analogue FM signal depends on and is given by
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Digital FSK
ccDCc
DC
DC
DCIN
DCIN
DCIN
INout
fTVf
sforfVVfsforfVVf
sforVVVsforVVV
tmVVfVf
cxmy
1,
'0'1
'0'1
)(
000
011
0
1
0
Normalized frequency Deviation ratio
0101 .. ffModulusei
Rff
hb
The spectrum of FSK depends on h
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Digital FSK (Cont’d)
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FM/ FSK Demodulation (Cont’d)FM/ FSK Demodulation (Cont’d)
Consider again the output from the demodulator INc
OUT CosV
V2
2
4cT
cc f
T 1 cfThe delay is set to where and is the nominal carrier frequency
c
INcOUT f
fCos
VV
42
2
2 Hence
c
INcOUT f
fCos
VV
22
2
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FM/ FSK Demodulation (Cont’d)FM/ FSK Demodulation (Cont’d)
The curve shows the demodulator F/V characteristics which in this case is non linear.
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Practical realization of F/V processPractical realization of F/V process
The comparator is LIMITER – which is a zero crossing detector to give a ‘digital’ input to the first gate.
This is form of ‘delay and multiply’ circuit where the delay is set by C and R with
= CR
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Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
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Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
INf cfConsider now
≠
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Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
c
INOUT f
fAEV4
Plotting Vout versus INf (Assuming A=1)