An FM modulator has a carrier frequency of 200 MHz, is frequency modulated by a sine wave signal at a frequency of (fm= 15 kHz). The resultant FM signal has a frequency deviation of ( Af= 45 kHz). (a) Find the carrier frequency swing of the FM signal. (b) Determine the highest and lowest carrier frequencies. (c) Calculate the modulation index for the wave? (d) Sketch approximately to scale the magnitude spectrum of the modulator outnut Show

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An FM modulator has a carrier frequency of 200 MHz, is frequency modulated by a sine
wave signal at a frequency of (fm= 15 kHz). The resultant FM signal has a frequency
deviation of ( Af= 45 kHz).
(a) Find the carrier frequency swing of the FM signal.
(b) Determine the highest and lowest carrier frequencies.
(c) Calculate the modulation index for the wave?
(d) Sketch, approximately to scale, the magnitude spectrum of the modulator output. Show
all frequencies of interest.
(e) Calculate the bandwidth occupied by this FM signal?
Modulation
Sideband
index
Carrier
1
2
4
5
6
8
10
11
12
13
14
15
16
0.00
1.00
0.25
0.98
0.12
0.5
0.94
0.24 0.03
1.0
0.77
0.44
0.11
0.02
1.5
0.51
0.56 0.23
0.06
0.01
2.0
0.22 0.58 0.35 0.13
0.03
2.41
0.52 0.43
0.20
0.06
0.02
2.5
-0.05 0.50 0.45
0.22
0.07
0.02
0.01
3.0
-0.26 0.34 0.49
0.31 0.13 0.04
0.01
4.0
-0.40 -0.07
0.36
0.43
0.28
0.13
0.05 0.02
5.0
-0.18 -0.33
0.05
0.36
0.39
0.26
0.13
0.05 0.02
0. 19 0.09 0.03 0.01
0.25 0.13 0.06 0.02
5.53
-0.34 -0.13
0.25
0.40
0.32
6.0
0.15 -0.28 -0.24
0.11
0.36
0.36
7.0
0.30
0.00 -0.30 -0.17
0.16 0.35 0.34 0.23 0.130.06 0.02
8.0
0.17
0.23 -0.11 -0.29 -0.10
0.19
0.34 0.32 0.22 0.13 0.06 0.03
0.26 0.34 0.28 0.18 0.10 0.05 0.02
0.20 0.33 0.31 0.21 0.12 0.06 0.03 0.01
8.65
0.27 0.06 -0.24 -0.23
0.03
9.0
-0.09
0.25
0.14 -0.18-0.27 -0.06
10.0
-0.25
0.04
0.25
0.06 -0.22 -0.23-0.01 0.22 0.32 0.29 0.21 0.12 0.06 0.03 0.01
12.0
0.05 -0.22-0.08
0.20
0. 18 -0.07 -0.24 -0.17 0.05 0.23 0.30 0.27 0.20 0.12 0.07 0.03 0.01
Transcribed Image Text:An FM modulator has a carrier frequency of 200 MHz, is frequency modulated by a sine wave signal at a frequency of (fm= 15 kHz). The resultant FM signal has a frequency deviation of ( Af= 45 kHz). (a) Find the carrier frequency swing of the FM signal. (b) Determine the highest and lowest carrier frequencies. (c) Calculate the modulation index for the wave? (d) Sketch, approximately to scale, the magnitude spectrum of the modulator output. Show all frequencies of interest. (e) Calculate the bandwidth occupied by this FM signal? Modulation Sideband index Carrier 1 2 4 5 6 8 10 11 12 13 14 15 16 0.00 1.00 0.25 0.98 0.12 0.5 0.94 0.24 0.03 1.0 0.77 0.44 0.11 0.02 1.5 0.51 0.56 0.23 0.06 0.01 2.0 0.22 0.58 0.35 0.13 0.03 2.41 0.52 0.43 0.20 0.06 0.02 2.5 -0.05 0.50 0.45 0.22 0.07 0.02 0.01 3.0 -0.26 0.34 0.49 0.31 0.13 0.04 0.01 4.0 -0.40 -0.07 0.36 0.43 0.28 0.13 0.05 0.02 5.0 -0.18 -0.33 0.05 0.36 0.39 0.26 0.13 0.05 0.02 0. 19 0.09 0.03 0.01 0.25 0.13 0.06 0.02 5.53 -0.34 -0.13 0.25 0.40 0.32 6.0 0.15 -0.28 -0.24 0.11 0.36 0.36 7.0 0.30 0.00 -0.30 -0.17 0.16 0.35 0.34 0.23 0.130.06 0.02 8.0 0.17 0.23 -0.11 -0.29 -0.10 0.19 0.34 0.32 0.22 0.13 0.06 0.03 0.26 0.34 0.28 0.18 0.10 0.05 0.02 0.20 0.33 0.31 0.21 0.12 0.06 0.03 0.01 8.65 0.27 0.06 -0.24 -0.23 0.03 9.0 -0.09 0.25 0.14 -0.18-0.27 -0.06 10.0 -0.25 0.04 0.25 0.06 -0.22 -0.23-0.01 0.22 0.32 0.29 0.21 0.12 0.06 0.03 0.01 12.0 0.05 -0.22-0.08 0.20 0. 18 -0.07 -0.24 -0.17 0.05 0.23 0.30 0.27 0.20 0.12 0.07 0.03 0.01
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