Communication Systems By Carlson- pages 266 to 268 -...

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Unformatted text preview: CHAPTER 7 0 Analog Communication Systems the display represents the amplitude line spectrum or the power spectral density. {A square~law envelope detector would be used for the latter.) Some of the operational subtleties of this system are best understood by assum- ing that of!) consists of two or more sinusoids. To resolve one spectral line from the others, the IF bandwidth must be smaller than the line spacing. Hence. we call 8 the frequency resolution. and the maximum number of resolvable lines equals (1} - ‘f‘lli‘B. The IF output produced by a single line takes the form of a bandpass pulse with time duration r : BT/(s —r.) = B/fi. where fl] = {f} ~ fiJi‘Trepresenls the frequencv sweep rate in hertz per second. But a rapid sweep rate may exceed the IF. pulse response. Recall that our guide- line for bandpass pulses requires 3 2 Hr = [018, or f02f3;f1 s 83 [7] This important relation shows that accurate resolution (small [3} calls for a slow rate and correspondingly long observation time. Also note that Eq. (7) involves four parameters adjustable by the user. Some scanning spectrum analyzers have built~in hardware that prevents you from violating Eq. {7): others simply have a warning light. 7.2 MULTIPLEXING SYSTEMS When several communication channels are needed between the same two points, significant economies may be realized by sending all the messages on one transmis- sion facility—a process called multiplexing. Applications of multiplexing range from the vital. if prosaic. telephone network. to the glamour of FM stereo and space- probe telemetry systems. There are three basic multiplexing techniques: frequency- division multiplexing (FDM). time-division multiplexing (TDM), and code—division multiplexing. treated in Chapter IS. The goal of these techniques is to enable multi- ple users to share a channel. and hence they are referred to as frequency-division multiple access {FDMA}. time-division multiple access (TDMA). and code-division multiple access (CDMAJ. Frequency-Division Multiplexing The principle of FDM is illustrated by Fig. 12—10. where several input messages (three are shown) individually modulate the .ruhcarrt'ers f“. f 3. and so forth. after passing through LPFs to limit the message bandwidths. We show the subcarrier modulation as $53 as it often is. but any of the CW modulation techniques could be employed. or a mixture of them. The modulated signals are then summed to produce the baseband signal, with spectrum X,,(fl as shown in Fig. ”LE—lb. (The designation “basebantl” indicates that final carrier modulation has not yet taken place.) The basebund time function xhtr) is left to your imagination. 7.2 Multiplexing Systems i-— Guard band f‘lJfll-i-WI flagzttwlfli 121+ w; lb} Figure 7.2—] Typical FDM transmitter. [9} Input spectra and block diagram; {19] busebond FDM spectrum. Assuming that the subcarricr frequencies are properly chosen. the multiplexing operation has assigned a slot in the frequency domain for each of the individual messages in modulated form. hence the name frequency-division multiplexing. The baseband signal may then be transmitted directly or used to modulate a trans- mitted carrier of frequency fr. We are not particularly concerned here with the nature of the final carrier modulation. since the baseband spectrum tells the story. Message recovery or demodulation of FDM is accomplished in three steps por- trayed by Fig. 12-2. First. the carrier demodulator reproduces the baseband signal xbft). Then the modulated subcan‘iers are separated by a bank of bandpass filters in parallel, following which the messages are individually detected. The major practical problem of FDM is cross talk, the unwanted coupling of one message into another. Intelligible cross talk (cross«modulation) arises primarily because of nonlinear-ides in the system which cause one message signal to appear as CHAPTER ? 0 Analog Communication Systems A's-ll” xfim r‘tlllj train as: n . Figure 7.2-2 Typical FDM receiver. modulation on another subcarrier. Consequently. standard practice calls for negative feedback to minimize amplifier nonlinear-ity in FDM systems. (As a matter of his- torical fact. the FDM cross talk problem was a primary motivator for the develop- ment of negative-feedback amplifiers.) Unintelligible cross talk may come from nonlinear effects or from imperfect spectra] separation by the filter bank. To reduce the latter. the modulated message spectra are spaced out in frequency by guard hands into which the filter transition regions can be fitted. For example. the guard band marked in Fig. 7.2—1!) is of width fr; — (Li. + W J. The net basehand bandwidth is therefore the sum of the modulated message bandwidths plus the guard bands. But the scheme in Fig. 7.24 is not the only example of FDM. The commercial AM or FM broadcast bands are everyday examples of FDMA, where several broadcasters can transmit simultaneously in the same band. but at slightly different frequencies. EXAMPLE 7.2-l FDMA Satellite Systems The Intelsat global network adds a third dimension to long-distance communication. Since a particular satellite links several ground stations in different countries. various access methods have been devised for international telephony. One scheme. known as frequency—division multiple access- (FDMA). assigns a fixed number of voice channels between pairs of ground stations. These channels are grouped with standard FDM hardware, and relayed through the satellite using FM carrier modulation. For the sake of example. suppose a satellite over the Atlantic Ocean serves ground stations in the United States. Brazil. and France. Further suppose that 36 channels {three groups) are assigned to the US—France route and 24 channels (mo groups) to the US—Brazil route. Figure 7.2~3 shows the arrangement of the US transmitter and the receivers in Brazil and France. Not shown are the French and Brazilian transmitters and the US receiver needed for two~way conversations. Addi- 7.2 Multiplexing Systems Groups 1 to France {2 3 to Braztl {5 United States Groups E France 4 RCvr 5 Brazil Figure 7.2-3 Simplified FDMA satellite system. tional transmitters and receivers at slightly different cam'er frequencies would pro— 'vide a Brazil—France route. The FDMA scheme creates at the satellite a composite FDM signal? assembled with the FM signais from all ground stations. The satellite equipment consists of a bank of transponders. Each transponder has 36-MH2 bandwidth accommodating '336 to 900 voice channels, depending on the ground—pair assignments. More details and other access schemes can be found in the literature. 269 WM..— Suppose an FDM baseband amplifier has cube-law nonlinearity which produces a baseband component proportional to (02 cos trilogy, cos ails, where f] and f; are two subcarrier frequencies. Show that AM subcarrier modulation with v. = l + x10) and v2 = l + x20) results in both intelligible and unintelligible cross talk on subcar- rierfl. Compare with the D33 case cl = x10) and a2 = x20). EXERCISE 7.2-1 _.__————m——fl-——— FM Stereo Multiplexing Figure 7.2-4a diagrams the FDM system that generates the baseband signal for FM stereophonic broadcasting. The left-speaker and right—speaker signals are first matrixed and preemphasized to produce xii!) + x30) and xii!) — x30). The sum sig- nal is heard with a monophonic receiver; matrixing is required so the monaural iisv tener will not be subjected to sound gaps in program material having stereophonic Ping-Pong effects. The Mr) + x3“) signal is then inserted directly into the base— band, while xLO‘) _ xRU) DSB modulates a 38-kHz subcarrier. Double-sideband modulation is employed to preserve fidelity at iow frequencies, and a 19-kHz pilot tone is added for receiver synchronization. EXAMPLE 7.2—2 ...
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