Download - School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne
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
Baseband digital informationBaseband digital information
Bit-rate, Baud-rate and Bit-rate, Baud-rate and BandwidthBandwidth
BB1
denotes the duration of the 1 bitHence 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
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.
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
RateBaudSinceRateBaud
TB
EE
1
22
11min
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
2min
RateBaudfB U
If the sequence was continuous 0’s, the signal would be –V continuously, hence
''DCfL
.
Bi-PhaseBi-Phase
Maximum frequency occurs when continuous 1’s or 0’s transmitted.
E1
2min
RateBaudfB 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
2min
RateBaudfB L
In this case =
Baud Rate = Bit rate
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.
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,
Digital Modulation and Digital Modulation and NoiseNoise
Amplitude Shift Keying ASK
Digital Modulation and Digital Modulation and NoiseNoise
Frequency Shift Keying FSK
Digital Modulation and Digital Modulation and NoiseNoise
Phase Shift Keying PSK
System Block diagram for System Block diagram for AnalysisAnalysis
DEMODULATOR – DETECTOR – DECISION DEMODULATOR – DETECTOR – DECISION
For ASK and PSK
Demodulator-Detector-DecisionDemodulator-Detector-Decision
FOR FSK
DemodulatorDemodulator
Demodulator Cont’d)Demodulator Cont’d)
TRCdesignHence
dtVRC
V INout
1
Detector-DecisionDetector-Decision
1V 0V - is the voltage difference between a ‘1’ and ‘0’.
)22
( 21 VVVREF
Detector-Decision (Cont’d)Detector-Decision (Cont’d)
ND is the noise at the Detector input.
Probability of Error,
DNerf
221
2
1
Hence
0 v1v0 v
0-
P(v0)
vn
Probability density of binary signalProbability density of binary signal
v0v1
2
210
2
)(
02
1
2
1)(
vv
n evP
)(1 nvP
vn
n
vv
vve dveP
n2
20
10
2
)(
2
12
1
Using the change of variable2
0vvx n
Probability density function of noiseProbability density function of noise
(*)
DN2
22
1
01
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
2
1
221
2
1
)(1)(
(**)
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
12
1
v
erfPe
for unipolar signalling (0 and v)
for polar signalling (symbol represented by voltage 2
v
Detector-Decision (Cont’d)Detector-Decision (Cont’d)
PSKFSKASKOptimumFor
PRK
N
SerfPSK
N
SerfFSK
OOK
N
SerfASK
IN
INe
IN
INe
IN
INe
,,
12
1
21
2
1
41
2
1
dB/10in SNR10
ePePeP
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
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
Pro
bab
ility
of
Sym
bo
l Err
or
ASK
FSK
PSK
Detector-Decision (Cont’d)Detector-Decision (Cont’d)
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
ININININc
x
INcINcx
ININx
2
2
1
)(.
2
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.
tCosV
V INc
OUT 2
2
FM/ FSK Demodulation (Cont’d)
The V/F characteristics and inputs are shown belowAnalogue FM
ccDCc
mmDCout
mmDCIN
DCIN
INout
mc
fTVf
ftCosVVfei
tCosVVV
tmVV
fVf
cxmy
Vf
1,
..
)(
0
0
Modulation Index m
m
m
c
f
V
f
f
FM/ FSK Demodulation (Cont’d)
tnCosJVtVFM mcn
ncs
1
)()(
The spectrum of the analogue FM signal depends on and is given by
Digital FSK
ccDCc
DC
DC
DCIN
DCIN
DCIN
INout
fTVf
sforfVVf
sforfVVf
sforVVV
sforVVV
tmVV
fVf
cxmy
1,
'0
'1
'0
'1
)(
000
011
0
1
0
Normalized frequency Deviation ratio
0101 .. ffModulusei
R
ffh
b
The spectrum of FSK depends on h
Digital FSK (Cont’d)
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
T1
cfThe delay is set to where and is the nominal carrier frequency
c
INcOUT f
fCos
VV
4
2
2
2 Hence
c
INcOUT f
fCos
VV
22
2
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.
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
Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
INf cf
Consider now
≠
Practical realization of F/V process (Cont’d)Practical realization of F/V process (Cont’d)
c
INOUT f
fAEV
4 Plotting Vout versus
INf (Assuming A=1)