4.1 Chapter 4 Digital Transmission Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. - презентация

1 4.1 Chapter 4 Digital Transmission Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2 DIGITAL-TO-DIGITAL CONVERSION In this section, we see how we can represent digital data by using digital signals. The conversion involves three techniques: line coding, block coding, and scrambling. Line coding is always needed; block coding and scrambling may or may not be needed. Line Coding Line Coding Schemes Block Coding Scrambling Topics discussed in this section:

3 4.3 Figure 4.1 Line coding and decoding

4 4.4 Figure 4.2 Signal element versus data element

5 4.5 Data rate VS Signal Rate Data rate defines the number of data elements (bits ) sent in 1s. (bps) Signal rate is the number of signal elements sent in 1s (baud), pulse rate, modulation rate and etc. Aim is to increase data rate and decrease signal rate Increase speed of transmissions, decrease bandwidth requirement E.g we need to carry more people in fewer cars to prevent jams. Limited bandwidth in our transportation system.

6 4.6 A signal is carrying data in which one data element is encoded as one signal element ( r = 1). If the bit rate is 100 kbps, what is the average value of the baud rate if c is between 0 and 1? Solution We assume that the average value of c is 1/2. The baud rate is then Example 4.1

7 4.7 Although the actual bandwidth of a digital signal is infinite, the effective bandwidth is finite. Note

8 4.8 The maximum data rate of a channel (see Chapter 3) is N max = 2 × B × log 2 L (defined by the Nyquist formula). Does this agree with the previous formula for N max ? Solution A signal with L levels actually can carry log 2 L bits per level. If each level corresponds to one signal element and we assume the average case (c = 1/2), then we have Example 4.2

9 4.9 Figure 4.3 Effect of lack of synchronization Bit intervals are not matched

10 4.10 In a digital transmission, the receiver clock is 0.1 percent faster than the sender clock. How many extra bits per second does the receiver receive if the data rate is 1 kbps? How many if the data rate is 1 Mbps? Solution At 1 kbps, the receiver receives 1001 bps instead of 1000 bps. Example 4.3 At 1 Mbps, the receiver receives 1,001,000 bps instead of 1,000,000 bps.

11 4.11 Figure 4.4 Line coding schemes

12 4.12 Figure 4.5 Unipolar NRZ scheme Signal level are on one side of time axis. Positive voltage defines bit 1 and zero voltage define bit 0.

13 4.13 Figure 4.6 Polar NRZ-L and NRZ-I schemes

14 4.14 In NRZ-L the level of the voltage determines the value of the bit. In NRZ-I the inversion or the lack of inversion determines the value of the bit. Note

15 4.15 NRZ-L and NRZ-I both have an average signal rate of N/2 Bd. Note

16 4.16 NRZ-L and NRZ-I both have a DC component problem. Note

17 4.17 A system is using NRZ-I to transfer 10-Mbps data. What are the average signal rate and minimum bandwidth? Solution The average signal rate is S = N/2 = 500 kbaud. The minimum bandwidth for this average baud rate is B min = S = 500 kHz. Example 4.4

18 4.18 Figure 4.7 Polar RZ scheme

19 4.19 Figure 4.8 Polar biphase: Manchester and differential Manchester schemes

20 4.20 In Manchester and differential Manchester encoding, the transition at the middle of the bit is used for synchronization. Note

21 4.21 The minimum bandwidth of Manchester and differential Manchester is 2 times that of NRZ. Note

22 4.22 In bipolar encoding, we use three levels: positive, zero, and negative. Note

23 4.23 Figure 4.9 Bipolar schemes: AMI and pseudoternary In bipolar three voltage levels positive negative zero

24 4.24 In mBnL schemes, a pattern of m data elements is encoded as a pattern of n signal elements in which 2 m L n. Multilevel Schemes The goal is to increase the number of bits m is length of binary pattern B means binary data n is length of signal pattern L is number of levels in the signaling Instead of L a letter is often used: T (ternary), Q (quaternary)

25 4.25 Figure 4.10 Multilevel: 2B1Q scheme

26 4.26 Figure 4.11 Multilevel: 8B6T scheme

27 4.27 Block coding is normally referred to as mB/nB coding; it replaces each m-bit group with an n-bit group. Note

28 4.28 Figure 4.14 Block coding concept

29 4.29 Figure 4.15 Using block coding 4B/5B with NRZ-I line coding scheme

30 4.30 Table 4.2 4B/5B mapping codes

31 4.31 Figure 4.16 Substitution in 4B/5B block coding

32 4.32 We need to send data at a 1-Mbps rate. What is the minimum required bandwidth, using a combination of 4B/5B and NRZ-I or Manchester coding? Solution First 4B/5B block coding increases the bit rate to 1.25 Mbps. The minimum bandwidth using NRZ-I is N/2 or 625 kHz. The Manchester scheme needs a minimum bandwidth of 1 MHz. The first choice needs a lower bandwidth, but has a DC component problem; the second choice needs a higher bandwidth, but does not have a DC component problem. Example 4.5

33 4.33 Figure B/10B block encoding

34 4.34 Figure 4.18 AMI used with scrambling

35 4.35 Figure 4.19 Two cases of B8ZS scrambling technique

36 4.36 B8ZS substitutes eight consecutive zeros with 000VB0VB. Note

37 4.37 Figure 4.20 Different situations in HDB3 scrambling technique

38 4.38 HDB3 substitutes four consecutive zeros with 000V or B00V depending on the number of nonzero pulses after the last substitution. Note

39 ANALOG-TO-DIGITAL CONVERSION We have seen in Chapter 3 that a digital signal is superior to an analog signal. The tendency today is to change an analog signal to digital data. In this section we describe two techniques, pulse code modulation and delta modulation. Pulse Code Modulation (PCM) Delta Modulation (DM) Topics discussed in this section:

40 4.40 Figure 4.21 Components of PCM encoder

41 4.41 Figure 4.22 Three different sampling methods for PCM

42 4.42 According to the Nyquist theorem, the sampling rate must be at least 2 times the highest frequency contained in the signal. Note

43 4.43 Figure 4.23 Nyquist sampling rate for low-pass and bandpass signals

44 4.44 For an intuitive example of the Nyquist theorem, let us sample a simple sine wave at three sampling rates: f s = 4f (2 times the Nyquist rate), f s = 2f (Nyquist rate), and f s = f (one-half the Nyquist rate). Figure 4.24 shows the sampling and the subsequent recovery of the signal. It can be seen that sampling at the Nyquist rate can create a good approximation of the original sine wave (part a). Oversampling in part b can also create the same approximation, but it is redundant and unnecessary. Sampling below the Nyquist rate (part c) does not produce a signal that looks like the original sine wave. Example 4.6

45 4.45 Figure 4.24 Recovery of a sampled sine wave for different sampling rates

46 4.46 Consider the revolution of a hand of a clock. The second hand of a clock has a period of 60 s. According to the Nyquist theorem, we need to sample the hand every 30 s (T s = T or f s = 2f ). In Figure 4.25a, the sample points, in order, are 12, 6, 12, 6, 12, and 6. The receiver of the samples cannot tell if the clock is moving forward or backward. In part b, we sample at double the Nyquist rate (every 15 s). The sample points are 12, 3, 6, 9, and 12. The clock is moving forward. In part c, we sample below the Nyquist rate (T s = T or f s = f ). The sample points are 12, 9, 6, 3, and 12. Although the clock is moving forward, the receiver thinks that the clock is moving backward. Example 4.7

47 4.47 Figure 4.25 Sampling of a clock with only one hand

48 4.48 Figure 4.26 Quantization and encoding of a sampled signal

49 4.49 What is the SNR dB in the example of Figure 4.26? Solution We can use the formula to find the quantization. We have eight levels and 3 bits per sample, so SNR dB = 6.02(3) = dB Increasing the number of levels increases the SNR. Example 4.12

50 4.50 A telephone subscriber line must have an SNR dB above 40. What is the minimum number of bits per sample? Solution We can calculate the number of bits as Example 4.13 Telephone companies usually assign 7 or 8 bits per sample.

51 4.51 We want to digitize the human voice. What is the bit rate, assuming 8 bits per sample? Solution The human voice normally contains frequencies from 0 to 4000 Hz. So the sampling rate and bit rate are calculated as follows: Example 4.14

52 4.52 Figure 4.27 Components of a PCM decoder

53 4.53 We have a low-pass analog signal of 4 kHz. If we send the analog signal, we need a channel with a minimum bandwidth of 4 kHz. If we digitize the signal and send 8 bits per sample, we need a channel with a minimum bandwidth of 8 × 4 kHz = 32 kHz. Example 4.15

54 4.54 Figure 4.28 The process of delta modulation

55 4.55 Figure 4.29 Delta modulation components

56 4.56 Figure 4.30 Delta demodulation components

57 TRANSMISSION MODES The transmission of binary data across a link can be accomplished in either parallel or serial mode. In parallel mode, multiple bits are sent with each clock tick. In serial mode, 1 bit is sent with each clock tick. While there is only one way to send parallel data, there are three subclasses of serial transmission: asynchronous, synchronous, and isochronous. Parallel Transmission Serial Transmission Topics discussed in this section:

58 4.58 Figure 4.31 Data transmission and modes

59 4.59 Figure 4.32 Parallel transmission

60 4.60 Figure 4.33 Serial transmission

61 4.61 In asynchronous transmission, we send 1 start bit (0) at the beginning and 1 or more stop bits (1s) at the end of each byte. There may be a gap between each byte. Note

62 4.62 Asynchronous here means asynchronous at the byte level, but the bits are still synchronized; their durations are the same. Note

63 4.63 Figure 4.34 Asynchronous transmission

64 4.64 In synchronous transmission, we send bits one after another without start or stop bits or gaps. It is the responsibility of the receiver to group the bits. Note

65 4.65 Figure 4.35 Synchronous transmission