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The carrier c(t)=10 cos (27 f, t) is frequency modulated (FM) by the signal m(t)=5cos(20000nt), where fc =100MHz. The peak frequency deviation is 50 kHz. 1) Find the FM modulation index (B), and the frequency sensitivity (kf) in Hz/volt. 2) What is the type of this FM signal, and why? 3) Use Carson's rule to determine the approximate bandwidth of this FM signal.

The carrier c(t)=10 cos (27 f, t) is frequency modulated (FM) by the signal m(t)=5cos(20000nt), where fc =100MHz. The peak frequency deviation is 50 kHz. 1) Find the FM modulation index (B), and the frequency sensitivity (kf) in Hz/volt. 2) What is the type of this FM signal, and why? 3) Use Carson's rule to determine the approximate bandwidth of this FM signal.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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The carrier c(t)=10 cos (27 f, t) is frequency modulated (FM) by the signal m(t)=5cos(20000nt), where fc =100MHz. The peak frequency deviation is 50 kHz. 1) Find the FM modulation index (B), and the frequency sensitivity (kf) in Hz/volt. 2) What is the type of this FM signal, and why? 3) Use Carson's rule to determine the approximate bandwidth of this FM signal. 4) Determine the amplitude and frequency of all signal components that have a power level of at least 68% of the power of the unmodulated carrier component. 5) Draw the spectrum of these selected components. J,(4) J.(5) J(6) M 0 1 t 3 10 11 12 13 14 0.7652 0.2239 0.4401 0.3767 0.1149 0.3528 0.0196 0.1289 0.0340 J.(3) -0.2601 0.3391 0.4961 0.3091 0.1320 0.0430 0.0114 -0.3971 0.0660 0.3641 0.4302 0.2811 0.1321 0.0491 0.01:32 -0.1776 -0.3276 0.0466 0.3648 0.3912 0.2611 0.1310 0.0534 0.0184 0.1506 -0.2767 -0.2429 0,1148 0.3367 0.3621 0.2458 0.1296 0.0565 0.0212 J(7) 0.3001 -0.0047 -0.3014 -0.1676 J,(8) 0.3392 0.2336 0 1280 0.0589 0.0235 0.1717 0.2346 0.1578 -0.1054 0.3479 -0.0903 0.2453 -0.1130 0.1448 -0.2911 -0.1809 -0.2196 -0.2655 0.1858 -0.0550 -0.2341 0.3376 -0.0145 0.3206 0.2167 0.2235 0.3179 0.1263 0.2919 0.2075 0.1231 0.0634 0.0290 0.0119 (677 0.0608 0.0256 0.2043 0.3275 0.3051 0.2149 0.1247 0.0622 J(10) -0.2459 0.0435 0.2546 0.0584 0.0274 0.0108
Transcribed Image Text:The carrier c(t)=10 cos (27 f, t) is frequency modulated (FM) by the signal m(t)=5cos(20000nt), where fc =100MHz. The peak frequency deviation is 50 kHz. 1) Find the FM modulation index (B), and the frequency sensitivity (kf) in Hz/volt. 2) What is the type of this FM signal, and why? 3) Use Carson's rule to determine the approximate bandwidth of this FM signal. 4) Determine the amplitude and frequency of all signal components that have a power level of at least 68% of the power of the unmodulated carrier component. 5) Draw the spectrum of these selected components. J,(4) J.(5) J(6) M 0 1 t 3 10 11 12 13 14 0.7652 0.2239 0.4401 0.3767 0.1149 0.3528 0.0196 0.1289 0.0340 J.(3) -0.2601 0.3391 0.4961 0.3091 0.1320 0.0430 0.0114 -0.3971 0.0660 0.3641 0.4302 0.2811 0.1321 0.0491 0.01:32 -0.1776 -0.3276 0.0466 0.3648 0.3912 0.2611 0.1310 0.0534 0.0184 0.1506 -0.2767 -0.2429 0,1148 0.3367 0.3621 0.2458 0.1296 0.0565 0.0212 J(7) 0.3001 -0.0047 -0.3014 -0.1676 J,(8) 0.3392 0.2336 0 1280 0.0589 0.0235 0.1717 0.2346 0.1578 -0.1054 0.3479 -0.0903 0.2453 -0.1130 0.1448 -0.2911 -0.1809 -0.2196 -0.2655 0.1858 -0.0550 -0.2341 0.3376 -0.0145 0.3206 0.2167 0.2235 0.3179 0.1263 0.2919 0.2075 0.1231 0.0634 0.0290 0.0119 (677 0.0608 0.0256 0.2043 0.3275 0.3051 0.2149 0.1247 0.0622 J(10) -0.2459 0.0435 0.2546 0.0584 0.0274 0.0108
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