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Iv The Telephone And Multiplex Systems

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  • 1. THE TELEPHONE SYTEM AND MULTIPLEX SYSTEMS ANALOG TELEPHONE SYSTEMS F When two computers owned by the same company or organization and located close to each other need to communicate, it is often easiest to just run a cable between them. This is how local area networks work. F However, when the distances are large, or there are many computers, or the cables would have to pass through a public road or other public right of way, the costs of running private cables are usually prohibitive. F Consequently, the network designers must rely upon the existing telecommunication facilities such as the Public Switched Telephone Network (PSTN). F The PSTN was designed many years ago with a completely different goal in mind: transmitting human voice in a more or less recognizable form. Their suitability for computer-to-computer communication is often marginal at best. The Telephone System and Multiplex Systems 1
  • 2. F The typical error of using telephone lines for computer communication is about one error per 100,000 bits sent. The error rate for a direct cable connection (LAN) is about one error per 10,000,000,000,000 bits sent. F However, the situation is changing rapidly with the introduction of fiber optics and digital technology. F Analog telephone systems provide either two or four wires that connect the telephone handset and a local telephone company central office (also called switching office or end office). TELEPHONE CENTRAL OFFICE TELEPHONE TELEPHONE TELEPHONE The Telephone System and Multiplex Systems 2
  • 3. The Telephone System and Multiplex Systems 3
  • 4. F The lines connecting the subscriber’s telephone and the central office are know as local loop lines. Local loops consist of twisted pairs nowadays, although in the early days of telephony, uninsulated wires spaced 25 cm apart on telephone poles were common. F Central offices are connected to each other via toll offices through high-bandwidth lines called trunk lines. Trunk connections are often implemented using coax cables, fiber optics, or microwave transmission. TELEPHONE TELEPHONE TOLL OFFICE CENTRAL CENTRAL OFFICE OFFICE TRUNK LINES TELEPHONE TELEPHONE TELEPHONE TELEPHONE The Telephone System and Multiplex Systems 4
  • 5. F With the advent of digital technology, long-distance trunk lines within the telephone system are rapidly being converted to digital. The old system used analog transmission over copper wires; the new one uses digital transmission over optical fibers. F Telephone lines that go through a central office switch can make two types of connections with other telephones: 1. Connecting two telephones within the same central office. In this scenario, the switching mechanism within the central office sets up a direct connection between two local loops. This connection remains intact for the duration of the call. 2. Connecting two telephones belonging to different central offices. In either case, the call requests the closure of electrical switches to make the connection (circuit-switched connection). F Telephone calls between central offices are more complex than local-loop calls. F The calls go through trunk lines and these lines aggregate several telephone calls through wire or fiber cable. The Telephone System and Multiplex Systems 5
  • 6. MULTIPLEXING F Telephone companies have developed elaborate schemes in combining several conversations over a single physical trunk line. F Multiplexing is the process of combining several signals and transmitting them through the same channel simultaneously. F Types of Multiplexing Techniques 1. Frequency Division Multiplexing (FDM) 2. Time Division Multiplexing (TDM) F Frequency division multiplexing relies on the general rule that signals with different frequencies, if transmitted simultaneously, can be easily separated at the receiver. If signals have the same frequency, FDM translates each signal to a new frequency range. The Telephone System and Multiplex Systems 6
  • 7. 0 4 KHz 60 KHz 64 KHz 0 4 KHz 65 KHz 69 KHz 0 4 KHz 70 KHz 74 KHz AFTER MULTIPLEXING: 60 KHz 64 KHz 65 KHz 69 KHz 70 KHz 74 KHz The Telephone System and Multiplex Systems 7
  • 8. The FDM technique of multiplexing requires guard bands (spaces between adjacent signals) to keep signals from contaminating each other. A radio-frequency modem (or RF modem) is just one of the several devices that can do frequency translation. FDM and adequate guard bands allow several telephone connections to take place through the same trunk. The trunk should have a high bandwidth. The multiplexed signals should be demultiplexed to bring the signals back to their original frequencies. The Telephone System and Multiplex Systems 8
  • 9. DIGITAL TELEPHONE SYSTEMS F While long-distance trunk lines are now largely digital in the more advanced countries, the local loops are still analog and are likely to remain so for at least a decade or two, due to the enormous cost of converting them. F To switch from analog-based equipment to digital- based communications networks requires an analog-to- digital conversion. Central Office Telephone Analog Local Loop Digital Trunk F A codec (coder/decoder) is a device that translates analog voice signals into digital signals. The Telephone System and Multiplex Systems 9
  • 10. F Steps in analog-to-digital conversion: 1. Pulse-Amplitude Modulation (PAM). The first step in analog-to-digital conversion is to convert the analog signal into discrete signals that have amplitudes that simulate the original signal (pulses). This technique is commonly called as signal sampling. 2. Pulse Code Modulation (PCM). PCM converts the stream of continuously varying PAM signals into a stream of binary digital signals PCM requires two steps: A. Quantization. This reduces the PAM signal to a limited number of discrete amplitudes. B. Coding. This converts each PAM pulse into a binary word. The Telephone System and Multiplex Systems 10
  • 11. F Pulse-Amplitude Modulation A PAM signal consists of a sequence of pulses in which the amplitude of each pulse is proportional to the amplitude of the analog information signal at the corresponding point where the sample was taken. analog information signal x(t) fs P sampling pulse 0 train p(t) sampled-data signal xs(t) Ts The Telephone System and Multiplex Systems 11
  • 12. F A sampling pulse train, p(t), guides the sampling process. F In order for the sampling to take place, x(t) should be observed during short intervals of time of width τs seconds (which is the aperture time), which corresponds to a pulse. So at the presence of a pulse, the system takes a sample. F The system takes a sample after every Ts seconds, where Ts is the sampling period (the time between the beginning of one sample to the beginning of the next sample). From this, the sampling rate f s = 1 / Ts samples per second. F Therefore, the amplitudes of the pulses in the pulse train are modulated by the information signal. In other words, this train of pulses acts as the carrier instead of the usual analog sine wave. F The amplitude of the pulses of the sampled-data signal xs(t) corresponds to the amplitude of the modulating signal x(t) at the point where it was sampled F The frequency of the sampling pulse train (the number of samples per second) should be at least 2 x the highest frequency of the analog signal. This is known as Shannon’s Sampling Theorem. The Telephone System and Multiplex Systems 12
  • 13. F Pulse-Code Modulation For the discussions, assume that the number of bits to be used is n = 4 bits. This choice results in m = 24 = 16 digital or PCM words. Natural Binary Decimal Unipolar Bipolar Number Value Normalized Normalized Decimal Value Decimal Value 0000 0 0/16 = 0.0000 -8/8 = -1.000 0001 1 1/16 = 0.0625 -7/8 = -0.875 0010 2 2/16 = 0.1250 -6/8 = -0.750 0011 3 3/16 = 0.1875 -5/8 = -0.625 0100 4 4/16 = 0.2500 -4/8 = -0.500 0101 5 5/16 = 0.3125 -3/8 = -0.375 0110 6 6/16 = 0.3750 -2/8 = -0.250 0111 7 7/16 = 0.4375 -1/8 = -0.125 1000 8 8/16 = 0.5000 0/8 = 0.000 1001 9 9/16 = 0.5625 1/8 = 0.125 1010 10 10/16 = 0.6250 2/8 = 0.250 1011 11 11/16 = 0.6875 3/8 = 0.375 1100 12 12/16 = 0.7500 4/8 = 0.500 1101 13 13/16 = 0.8125 5/8 = 0.625 1110 14 14/16 = 0.8750 6/8 = 0.750 1111 15 15/16 = 0.9375 7/8 = 0.875 The Telephone System and Multiplex Systems 13
  • 14. Because of the different possible voltage levels and the widely different decimal values of the binary number system as the number of bits is changed, it is frequently desirable to normalize the levels of both the analog signal and the digital words so that the maximum magnitudes of both forms have (or at least) approached unity. Normalized Input = Actual Input Analog Voltage Analog Voltage FSV of A/D Converter where FSV = Full-Scale Voltage Actual Output = Normalized Value of x FSV of Analog Voltage Digital Word DAC Two Most Common Forms Employed in A/D Conversion 1. Unipolar 2. Bipolar The Telephone System and Multiplex Systems 14
  • 15. Unipolar Encoding The unipolar representation is most appropriate when the analog signal x(t) is always of one polarity (including zero). If the signal is negative, it can be inverted before sampling. The normalized range, x, is therefore: 0≤x<1 Let xu be the unipolar quantized decimal representation of x following the A/D conversion. The maximum value of xu is therefore: xu(max) = 1 - 2-n Let ∆xu be the normalized step size, which represents in a decimal value the difference between successive levels. ∆xu = 2-n The Telephone System and Multiplex Systems 15
  • 16. Bipolar Encoding The bipolar representation is most appropriate when the analog signal x(t) has both polarities. The normalized range, x, is therefore: -1 ≤ x < 1 Let xb be the bipolar quantized decimal representation of x following the A/D conversion. The maximum value of xb is therefore: xb(max) = 1 - 2-n + 1 Let ∆xb be the normalized step size, which represents in a decimal value the difference between successive levels. ∆xb = 2-n + 1 The Telephone System and Multiplex Systems 16
  • 17. Quantization may be done in two ways: 1. Rounding. The sampled value of the analog signal is assigned to the nearest quantized level. 2. Truncation. The sampled value is adjusted to the next lowest quantized level. Example: A certain 5-bit A/D converter with a FSV of 8V is to be employed in a binary PCM system. The input analog signal is adjusted to cover the range from zero to slightly under 8V, and the converter is connected for unipolar encoding. 1. What is the normalized step size? 2. What is the actual step size in volts? 3. What is the normalized maximum quantized analog level? 4. What digital word would the value 0.51 V correspond to? 5. What voltage would the digital word 00101 correspond to? The Telephone System and Multiplex Systems 17
  • 18. Solution: 1. Normalized Step Size ∆xu = 2-n = 2-5 = 0.03125 2. Actual Step Size Actual Step Size = ∆xu x FSV = 0.03125 x 8 = 0.25 v 3. Normalized Maximum Quantized Analog Level xu(max) = 1 - 2-n = 1 - 2-5 = 0.96875 The Telephone System and Multiplex Systems 18
  • 19. Natural Binary Decimal Unipolar Normalized Actual Value Number Value Decimal Value in volts 00000 0 0/32 = 0.0000 0v 00001 1 1/32 = 0.03125 0.25 v 00010 2 2/32 = 0.0625 0.5 v 00011 3 3/32 = 0.09375 0.75 v 00100 4 4/32 = 0.125 1.0 v 00101 5 5/32 = 0.15625 1.25 v 00110 6 6/32 = 0.1875 1.5 v 00111 7 7/32 = 0.21875 1.75 v . . . . . . . . . . . . 11011 27 27/32 = 0.84375 6.75 v 11100 28 28/32 = 0.875 7.0 v 11101 29 29/32 = 0.90625 7.25 v 11110 30 30/32 = 0.9375 7.50 v 11111 31 31/32 = 0.96875 7.75 v 4. What digital word would the value 0.51 V correspond to? 00010 5. What voltage would the digital word 00110 correspond to? 1.5 v The Telephone System and Multiplex Systems 19
  • 20. Rounding or truncation always results in quantization error since the rounded or truncated value can never be recovered at the receiver side. For unipolar representation: Normalized Resolution = ± ½ ∆xu = ± 2-(n+1) Actual Resolution = ± 2-(n+1) x FSV % Resolution = ± 2-(n+1) x 100% For bipolar representation: Normalized Resolution = ± ½ ∆xb = ± 2-n Actual Resolution = ± 2-n x FSV % Resolution = ± 2-n x 100% To minimize quantization errors, the system should use more bits. The Telephone System and Multiplex Systems 20
  • 21. Example: A certain 5-bit A/D converter with a FSV of 8V is to be employed in a binary PCM system. The input analog signal is adjusted to cover the range from zero to slightly under 8V, and the converter is connected for unipolar encoding. 1. What is the normalized resolution? 2. What is the actual resolution in volts? Solution: Normalized Resolution = ± ½ ∆xu = ± 2-(n+1) = ± 2-(5+1) = ± 0.015625 Actual Resolution = ± 2-(n+1) x FSV = ± 0.015625 x 8 = ± 0.125 v The Telephone System and Multiplex Systems 21
  • 22. F Time division multiplexing is used to combine several digital voice signals into one channel. This technique interleaves more than one individual digital signal into another channel by giving each original signal time slots in the multiplexed channel. 1 ADC DAC 1 Telephone Telephone TIME DIVISION MULTIPLEXER TIME DIVISION MULTIPLEXER 2 ADC DAC 2 Telephone Telephone n ADC DAC n Telephone Telephone MULTIPLEXED DATA: byte 2 byte 2 byte 2 byte 1 byte 1 byte 1 from from from from from from ... channel ... channel channel channel ... channel channel n 2 1 n 2 1 The Telephone System and Multiplex Systems 22
  • 23. F Case Study: T1 Channel Banks AT&T combines 24 digitized voice signals into one high-capacity channel called the T1 Carrier. TIME DIVISION MULTIPLEXER 1 Telephone CODEC T1 Channel 2 Telephone 1.544 Mbps 24 Telephone Central Office data rate per phone = 8000 samples/sec x 8 bits/sample (output of each codec) = 64,000 bps total data rate of T1 = 64,000 bps x 24 = 1.536 Mbps The Telephone System and Multiplex Systems 23
  • 24. channel The Telephone System and Multiplex Systems 24