Download - Baseband Digital Modulation
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School of Electrical, Electronics and
Computer Engineering
University of Newcastle-upon-Tyne
Baseband Digital Modulation
Prof. Rolando Carrasco
Lecture Notes
University of Newcastle-upon-Tyne
2007
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Baseband digital information
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Bit-rate, Baud-rate and
Bandwidth
B
B
1denotes 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 =
E
1baud
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)
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/THz, i.e. to just allow the fundamental (1st harmonic) to pass.
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Non Return to Zero (NRZ)
(Contd)
The data sequence 1010
could then be completely
recovered
Hence the minimum channel bandwidth
RateBaudSince
RateBaud
TB EE
1
22
11min
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Return to Zero (RZ)
Considering RZ signals, the max frequency occurs when continuous 1s are transmitted.
This produces a square wave with periodic timeE
2
2min
RateBaudfB U
If the sequence was continuous 0s, the signal would be V continuously, hence
''DCfL
.
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Bi-Phase
Maximum frequency occurs when continuous
1s or 0s transmitted.
E
1
2min
RateBaudfB U
This is similar to RZ withBaud Rate = = 2 x Bit rate
The minimum frequency occurs when the sequence is 10101010.
e.g.
B E
2min
RateBaudfB L
In this case =
Baud Rate = Bit rate
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Digital Modulation and
Noise
The performance of Digital Data Systems is dependent on the bit error rate, BER, i.e.
probability of a bit being in error.
NasNbitsTotal
EErrorsofNoP
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
Noise
Amplitude Shift Keying ASK
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Digital Modulation and
Noise
Frequency Shift Keying FSK
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Digital Modulation and
Noise
Phase Shift Keying PSK
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System Block diagram for
Analysis
DEMODULATORDETECTORDECISION
For ASK and PSK
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Demodulator-Detector-Decision
FOR FSK
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Demodulator
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Demodulator Contd)
TRCdesignHence
dtVRC
V INout
1
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Detector-Decision
1V 0V- is the voltage differencebetween a 1 and 0.
)22
( 21 VVVREF
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Detector-Decision (Contd)
ND is the noise at the Detector input.
Probability of Error,
DN
erf 2212
1
Hence
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0 v1v0 v
0-
P(v0)
vn
Probability density of binary signal
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v0 v1
2
210
2
)(
02
1
2
1)(
vv
n evP
)(1 nvP
vn
n
vv
vv
e dvePn
2
20
10
2
)(
2
12
1
Using the change of variable
2
0vvx n
Probability density function of noise
(*)
DN2
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22
1
01
21
vv
dxx
e 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
vv
vv
e
e
dveP
vverfP
zerfzerfc
n
2
21
10
2
)(2
0
011
2
1
221
2
1
)(1)(
(**)
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It is clear from the symmetry of this problem that Pe0 is identical to Pe1 and the
probability of errorPe, irrespective of whether a one or zero was transmitted, can
be rewritten in terms ofv= v1v0
221
2
1
verfPe
for unipolar signalling (0 and v)
for polar signalling (symbol represented by voltage
2
v
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Detector-Decision (Contd)
PSKFSKASKOptimumFor
PRK
N
SerfPSK
NSerfFSK
OOK
N
SerfASK
IN
INe
IN
INe
IN
INe
,,
12
1
21
21
41
2
1
dB/10inSNR10
eP
eP
eP
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
ProbabilityofSymbolError
ASK
FSK
PSK
Detector-Decision (Contd)
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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
tCosVtCosVV
tVtVV
ININININ
c
x
INcINcx
ININx
2
2
1
)(.
2
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FM/ FSK Demodulation (Contd)
INININc
x
ININININININc
x
CostCosV
V
ttCosttCosV
V
22
22
2
)2(2
)1(2
22
2
2
tCosV
and
tCosV
IN
c
IN
c
i.e
Thus there are two components
Component (1) is at frequency 2 fINHz 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.
tCos
V
V INc
OUT 2
2
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FM/ FSK Demodulation (Contd)
The V/F characteristics and inputs are shown below
Analogue FM
c
cDCc
mmDCout
mmDCIN
DCIN
INout
mc
fTVf
ftCosVVfei
tCosVVV
tmVV
fVfcxmy
Vf
1,
..
)(
0
0
Modulation Index
m
m
m
c
f
V
f
f
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FM/ FSK Demodulation (Contd)
tnCosJVtVFM mcn
ncs
1
)()(
The spectrum of the analogue FM signal depends on and is given by
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Digital FSK (Contd)
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FM/ FSK Demodulation (Contd)
Consider again the output from the demodulator IN
c
OUTCos
VV
2
2
4
cT
c
cf
T1
cfThe delay is set to where and is the nominal carrier frequency
c
INcOUT
ffCosVV
42
2
2
Hence
c
INcOUT
ffCosVV
22
2
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FM/ FSK Demodulation (Contd)
The curve shows the demodulator F/V characteristics which in this case is non linear.
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Practical realization of F/V process
The comparator is LIMITERwhich is a zero crossing detector to give a digital input tothe 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 (Contd)
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Practical realization of F/V process (Contd)
INf cf
Consider now
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Practical realization of F/V process (Contd)
c
INOUT
f
fAEV
4 Plotting Vout versus
INf (Assuming A=1)