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From Eq. (9.17): g 5 10 From Eq. (9.19): L 5 10
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From Table 9.1, for 24 channels Frms F g#L#
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35 kHz, and using Eq. (9.20), Frms > 281 kHz
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Assuming that the baseband spectrum is as shown in Fig. 9.4a, the top frequency is fm and Carson s rule gives BIF 2s F f md 778 kHz 108 kHz
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From Eq. (9.16):
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777.8 3.1
35 108
> 26.36
From Eq. (9.15): c S N d c C N d 10 logGP 14.21 4 [P] 2.5 [W]
45.7 dB
9.6.8 Signal-to-noise ratio for TV/FM
Television performance is measured in terms of the postdetector video signal-to-noise ratio, defined as (CCITT Recommendation 567-2, 1986) a S b N V peak-to-peak video voltage rms noise voltage (9.21)
Because peak-to-peak video voltage is used, 2 F replaces F in Eq. (9.8). Also, since power is proportional to voltage squared, a S b N v
C BN(2 F) N W3
(9.22)
where W is the highest video frequency. With the deviation ratio D F/W, and the processing gain for TV denoted as GPV, GPV sS/Nd2 V C/N 12D2sD 1d (9.23)
Some workers include an implementation margin to allow for nonideal performance of filters and demodulators (Bischof et al., 1981). With the implementation margin in decibels denoted by [IMP], Eq. (9.15) becomes ca S b d N V
C d N
[GPV]
[IMP]
(9.24) 10 log10X .
Recall that the square brackets denote decibels, that is, [X] This is illustrated in the following example.
Analog Signals
Example 9.6 A satellite TV link is designed to provide a video signal-to-noise ratio of 62 dB. The peak deviation is 9 MHz, and the highest video baseband frequency is 4.2 MHz. Calculate the carrier-to-noise ratio required at the input to the FM detector, given that the combined noise weighting, emphasis improvement, and implementation margin is 11.8 dB.
Solution
9 4.2
Equation (9.23) gives: GPV 12 2.1432 s2.143 1d 173.2
Therefore, [GPV] 10 log 173.2 22.4 dB
Since the required signal-to-noise ratio is 62 dB, Eq. (9.24) can be written as 62 c C N d 22.4 11.8
from which [C/N]
27.8 dB.
9.7 Problems and Exercises
9.1. State the frequency limits generally accepted for telephone transmission of speech and typical signal levels encountered in the telephone network. 9.2. Show that when two sinusoids of different frequencies are multiplied together, the resultant product contains sinusoids at the sum and difference frequencies only. Hence show how a multiplier circuit may be used to produce a DSBSC signal. 9.3. Explain how a DSBSC signal differs from a conventional amplitude modulated signal such as used in the medium-wave (broadcast) radio band. Describe one method by which an SSB signal may be obtained from a DSBSC signal. 9.4. Explain what is meant by FDM telephony. Sketch the frequency plans for the CCITT designations of group, supergroup, basic mastergroup, and super mastergroup. 9.5. With the aid of a block schematic, show how 12 VF channels could be frequency-division multiplexed.
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9.6. Explain how a 252-VF-channel group is formed for satellite transmission. 9.7. Describe the essential features of the video signal used in the NTSC color TV scheme. How is the system made compatible with monochrome reception 9.8. Explain how the sound information is added to the video information in a color TV transmission. 9.9. For the matrix network M shown in Fig. 9.7, derive the equations for the Y, Q, and I signals in terms of the input signals R, G, and B. 9.10. Explain what is meant by frequency modulation. A 70-MHz carrier is frequency modulated by a 1-kHz tone of 5-V peak amplitude. The frequency deviation constant is 15 kHz/V. Write down the expression for instantaneous frequency. 9.11. An angle-modulated wave may be written as sinq(t), where the argument q(t) is a function of the modulating signal. Given that the instantaneous angular frequency is wi dq(t)/dt, derive the expression for the FM carrier in Prob. 9.10. 9.12. (a) Explain what is meant by phase modulation. (b) A 70-MHz carrier is phase modulated by a 1-kHz tone of 5-V peak amplitude. The phase modulation constant is 0.1 rad/V. Write down the expression for the argument q(t) of the modulated wave. 9.13. Determine the equivalent peak frequency deviation for the phasemodulated signal of Prob. 9.12. 9.14. Show that when a carrier is phase modulated with a sinusoid, the equivalent peak frequency deviation is proportional to the modulating frequency. Explain the significance of this on the output of an FM receiver used to receive the PM wave. 9.15. In the early days of FM it was thought that the bandwidth could be limited to twice the peak deviation irrespective of the modulating frequency. Explain the fallacy behind this reasoning. 9.16. A 10-kHz tone is used to frequency modulate a carrier, the peak deviation being 75 kHz. Use Carson s rule to estimate the bandwidth required. 9.17. A 70-MHz carrier is frequency modulated by a 1-kHz tone of 5-V peak amplitude. The frequency deviation constant is 15 kHz/V. Use Carson s rule to estimate the bandwidth required. 9.18. A 70-MHz carrier is phase modulated by a 1-kHz tone of 5-V peak amplitude. The phase modulation constant is 0.1 rad/V. Find the equivalent peak deviation and, hence, use Carson s rule to estimate the bandwidth required for the PM signal.
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