Baseband Digital Modulation

7/30/2019 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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Noise

Amplitude Shift Keying ASK


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Noise

Frequency Shift Keying FSK


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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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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



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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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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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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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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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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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INf cf

Consider now


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c

INOUT

f

fAEV

4 Plotting Vout versus

INf (Assuming A=1)

Baseband Digital Modulation

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