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. 2 Ya Bao

Figure Types of digital-to-analog conversion 3 Ya Bao

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) 4 Ya Bao

Modulation Techniques 5 Ya Bao

Aspects of Digital-to-Analogue Conversion Bit rate (data rate N) and Baud rate (signal rate S) 6 r is the number of data elements carried in one signal element. In analogue transmission, r=log 2 L, 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. Ya Bao

Amplitude Shift Keying  encode 0/1 by different carrier amplitudes usually have one amplitude zero  susceptible to sudden gain changes  inefficient  used for: up to 1200bps on voice grade lines very high speeds over optical fiber 7 Ya Bao

Figure Binary amplitude shift keying 8 0<=d<=1, a factor depends on the modulation and filtering process. The bandwidth of ASK B between S(signal rate) and 2S, centred f c. Frequency moved from low to high.. Ya Bao

Figure Implementation of binary ASK 9 Ya Bao

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). 10 Ya Bao

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 lines high frequency radio ( 3 to 30 MHz) even higher frequency on LANs using coaxial cable 11 Ya Bao

Figure Binary frequency shift keying 12 Carrier f 1 for data “1”, f 2 for data “0” Bandwidth of BFSK: B = (1+d) × S + 2 Δf 0<=d<=1, a factor depends on the modulation and filtering process. Ya Bao

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? Solution The midpoint of the band is at 250 kHz. We choose 2Δf to be 50 kHz; this means 13 Ya Bao

FSK Transmission 14 Ya Bao

Multiple FSK  each signalling element represents more than one bit  more than two frequencies used  more bandwidth efficient  more prone to error 15 e.g. 4 frequencies, f 1, f 2, f 3 and f 4 can be used to send 2 bits at a time; 8 frequencies for 3 bits per signal. L frequencies for log 2 L bit per signal ( Bandwidth L×S ) However, frequencies need to be 2Δf (minimum S) apart. If d = 0; the minimum bandwidth of MFSK B = (1+d)×S+(L-1)2Δf = L×S Ya Bao

Phase Shift Keying  phase of carrier signal is shifted to represent data  binary PSK two phases represent two binary digits 16 Bandwidth of BPSK is the same as that for BASK less than that for BFSK. No bandwidth wasted for separate two carrier signals. Ya Bao

Quadrature PSK  more efficient use if each signal element represents more than one bit uses phase shifts separated by multiples of  /2 (90 o ) 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 amplitudes 17 Ya Bao

Figure 5.11 QPSK and its implementation 18 Ya Bao

Performance 19 R: data rate, bit rate B T : Transmission Bandwidth 0<=d<=1, a factor depends on the modulation and filtering process. Ya Bao This parameter measures the efficiency with which bandwidth can be used to transmit data

Bandwidth Efficiency for Digital-to- Analog Encoding Schemes 20 Ya Bao 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: 21 Ya Bao

Theoretical Bit Error Rate for Various Encoding Schemes 22 Ya Bao  The ratio E b /N 0 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 23 Ya Bao For MFSK, the error probability for a given value E b /N 0 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. 24 Ya Bao

Example Show the constellation diagrams for an ASK, BPSK, and QPSK signals. 25 Ya Bao

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 frequency use two copies of carrier, one shifted 90 ° each carrier is ASK modulated two independent signals over same medium demodulate and combine for original binary output 26 Ya Bao

QAM Modulator 27 Ya Bao

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 28 Ya Bao

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 Asymmetric Greater capacity downstream than upstream Frequency division multiplexing Lowest 25kHz for voice Plain old telephone service (POTS) Use echo cancellation or FDM to give two bands Use FDM within bands Range 8km 30 Ya Bao

Figure Bands for ADSL 31 Ya Bao

Digital Subscriber Lines (2) 32 Ya Bao

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 33 Ya Bao

DMT Transmitter

Typical ADSL configuration 35 Ya Bao

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