A carrier A cos ωct is modulated by a signal f(t) = 2 cos

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A carrier A cos ωct is modulated by a signal f(t) = 2 cos 10⁴. 2πt + 5 cos 10³. 2πt + 3 cos 10⁴. 4πt, then the bandwidth of the FM signal will be—
(Given that, kf = 15 × 10³ Hz per volt)

1. 170 kHz
2. 190 kHz
3. 210 kHz
4. 150 kHz

Correct Option: B

We know that bandwidth of FM modulated signal is given by

BW = 2(β + 1)f_m =2Δf		1 +	1
			β

Here, the maximum frequency component in f (t) is 20 kHz, and the maximum amplitude present in f (t) is 5 volt.
Therefore the frequency deviation Δf is given by
Δf = K_f ·A_m = 15 × 10³ × 5 = 75 kHz
and the modulation index β is given by

β =	Δf	=	75 kHz	=	7.5	= 3.75
	f_m		20kHz		2

Now, BW = 2 (β + 1) f_m = 2(3·75 + 1) 20 kHz
= 9·5 × 20 kHz = 190 kHz
Hence alternative (B) is the correct choice.