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Digital to analogue conversion

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Digital to analogue conversion

1 DIGITAL-TO-ANALOG CONVERSION

Digital-to-analog conversion is the process of changing one of the characteristics (A, f and θ) of an analog signal based on the information in digital data.

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Figure Types of digital-to-analog conversion

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Digital Data, Analog Signal

Encoding Techniques

Amplitude shift keying (ASK)• used to

transmit digital data over optical fiber

Frequency shift keying (FSK)• most common

form is binary FSK (BFSK)

Phase shift keying (PSK)• phase of carrier

signal is shifted to represent data

main use is public telephone system has frequency range

of 300Hz to 3400Hz uses modem (modulator-demodulator)

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Modulation Techniques

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Aspects of Digital-to-Analogue Conversion

Bit rate (data rate N) and Baud rate (signal rate S)

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rNS

1

r is the number of data elements carried in one signal element. In analogue transmission, r=log2L, where L is the type of signal element , not the level (could be same level but different phase).

An analog signal carries 4 bits per signal element. If 1000 signal elements are sent per second, find the bit rate.

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Amplitude Shift Keying

encode 0/1 by different carrier amplitudesusually have one amplitude zero

susceptible to sudden gain changes inefficient used for:

up to 1200bps on voice grade linesvery high speeds over optical fiber

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0binary 0

1binary )2cos()(

tfAts c

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Figure Binary amplitude shift keying

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0<=d<=1, a factor depends on the modulation and filtering process.The bandwidth of ASK B between S(signal rate) and 2S, centred fc. Frequency moved from low to high..

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Figure Implementation of binary ASK

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Example

In data communications, we normally use full-duplex links with communication in both directions. We need to divide the bandwidth into two with two carrier frequencies, as shown in Figure 5.5. The figure shows the positions of two carrier frequencies and the bandwidths. The available bandwidth for each direction is now 50 kHz, which leaves us with a data rate of 25 kbps in each direction (worst case, d=1, L=2).

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Binary Frequency Shift Keying

two binary values represented by two different frequencies (near carrier)

less susceptible to error than ASK used for:

up to 1200bps on voice grade lineshigh frequency radio ( 3 to 30 MHz)even higher frequency on LANs using coaxial

cable

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0binary )2cos(

1binary )2cos()(

2

1

tfA

tfAts

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Figure Binary frequency shift keying

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Carrier f1 for data “1”, f2 for data “0”Bandwidth of BFSK: B = (1+d) × S + 2 Δf0<=d<=1, a factor depends on the modulation and filtering process.

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Example 5.5

We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What should be the carrier frequency and the bit rate if we modulated our data by using BFSK with d = 1?

SolutionThe midpoint of the band is at 250 kHz. We choose 2Δf to be 50 kHz; this means

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FSK Transmission

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Multiple FSK

each signalling element represents more than one bit

more than two frequencies used more bandwidth efficient more prone to error

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e.g. 4 frequencies, f1, f2, f3 and f4 can be used to send 2 bits at a time;8 frequencies for 3 bits per signal. L frequencies for log2L bit per signal ( Bandwidth L×S )However, frequencies need to be 2Δf (minimum S) apart. If d = 0; the minimum bandwidth of MFSKB = (1+d)×S+(L-1)2Δf = L×SYa Bao

Phase Shift Keying

phase of carrier signal is shifted to represent data binary PSK

two phases represent two binary digits

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0binary )2cos(

1binary )2cos(

)2cos(

)2cos()(

tfA

tfA

tfA

tfAts

c

c

c

c

Bandwidth of BPSK is the same as that for BASK less than that for BFSK. No bandwidth wasted for separate two carrier signals.

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Quadrature PSK

more efficient use if each signal element represents more than one bit uses phase shifts separated by multiples of /2 (90o) each element represents two bits split input data stream in two and modulate onto

carrier and phase shifted carrier can use 8 phase angles and more than one

amplitude 9600bps modem uses 12 angles, four of which have

two amplitudes17

10binary )4

2cos(

00binary )4

32cos(

01binary )4

32cos(

11binary )4

2cos(

)(

tfA

tfA

tfA

tfA

ts

c

c

c

c

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Figure 5.11 QPSK and its implementation

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Performance

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TB

RefficiencyBandwidth R: data rate, bit rate

BT: Transmission Bandwidth

RM

MdB

RM

dR

L

dB

RdB

T

T

T

)log

)1(( :MFSK

)log

1()

1( :MPSK

)1( :ASK

2

2

0<=d<=1, a factor depends on the modulation and filtering process.

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This parameter measures the efficiency with which bandwidth can be used to transmit data

Bandwidth Efficiency for Digital-to-Analog Encoding Schemes

d = 0 d = 0.5 d = 1

ASK 1.0 0.67 0.5

Multilevel FSK

M = 4, L = 2 0.5 0.33 0.25

M = 8, L = 3 0.375 0.25 0.1875

M = 16, L = 4 0.25 0.167 0.125

M = 32, L = 5 0.156 0.104 0.078

PSK 1.0 0.67 0.5

Multilevel PSK

M = 4, L = 2 2.00 1.33 1.00

M = 8, L = 3 3.00 2.00 1.50

M = 16, L = 4 4.00 2.67 2.00

M = 32, L = 5 5.00 3.33 2.50

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The advantage of multilevel signaling methods now becomes clear.

Performance of Digital to Analog Modulation Schemes

ASK/PSK bandwidth directly relates to bit rate

multilevel PSK gives significant improvements

bandwidth

bit error rate of PSK and QPSK are about 3dB superior to ASK and FSK

for MFSK and MPSK have tradeoff between bandwidth efficiency and error performance

in presence of noise:

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Theoretical Bit Error Rate for Various Encoding Schemes

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The ratio Eb/N0 increases, the bit error rate drops.

QPSK and BPSK are about 3 dB superior to ASK and BFSK

Bit Error Rates for Multilevel FSK and PSK

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For MFSK, the error probability for a given value Eb/N0 of decreases as M increases, while the opposite is true for MPSK. The bandwidth efficiency of MFSK decrease as M increases, while the opposite is true of MPSK. An increase in bandwidth efficiency results in an increase in error probability.

constellation diagram: can help us define the amplitude and phase of a signal element.

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Example

Show the constellation diagrams for an ASK, BPSK, and QPSK signals.

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Quadrature Amplitude Modulation

QAM used on asymmetric digital subscriber line (ADSL) and some wireless

combination of ASK and PSK logical extension of QPSK send two different signals

simultaneously on same carrier frequencyuse two copies of carrier, one shifted 90°

each carrier is ASK modulatedtwo independent signals over same

mediumdemodulate and combine for original

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QAM Modulator

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tftdtftdts cc 2sin)(2cos)()(QAM 21

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QAM Variants two level ASK

each of two streams in one of two states four state system essentially QPSK

four level ASK combined stream in one of 16 states

have 64 and 256 state systems improved data rate for given bandwidth

increased potential error rate

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Asymmetrical Digital Subscriber Line (ADSL)

link between subscriber and network uses currently installed twisted pair cable is Asymmetric - bigger downstream than

up uses Frequency Division Multiplexing

reserve lowest 25kHz for voice (POTS)uses echo cancellation or FDM to give two

bands has a range of up to 5.5km

ADSL Design

AsymmetricGreater capacity downstream than

upstream Frequency division multiplexing

Lowest 25kHz for voicePlain old telephone service (POTS)

Use echo cancellation or FDM to give two bands

Use FDM within bands Range 8km

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Figure Bands for ADSL

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Digital Subscriber Lines (2)

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Discrete Multitone

DMT: Discrete Multitone Multiple carrier signals at different

frequencies Some bits on each channel 4kHz subchannels Send test signal and use subchannels

with better signal to noise ratio

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DMT Transmitter

Typical ADSL configuration

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Broadband – Provider Side

a splitter separates telephone from Internet voice traffic is connected to public switched

telephone network (PSTN) data traffic connects to a DSL multiplexer (DSLAM)

which multiplexes multiple customer DSL connections to a single high-speed ATM line.

ATM line connects ATM switches to a router which provides entry to the Internet

xDSL

high data rate DSL (HDSL) 2B1Q coding on dual twisted pairs up to 2Mbps over 3.7km

single line DSL 2B1Q coding on single twisted pair (residential) with

echo cancelling up to 2Mbps over 3.7km

very high data rate DSL DMT/QAM for very high data rates separate bands for separate services

Comparison of xDSL Alternatives