An angle modulated signal with carrier frequency fc is given by-st-Accos -2-fct - 5 sin 3000- t-10sin 2000- t-The bandwidth using Carson-s rule of the signal st will be

θ(t)= 2πf_ct + 5 sin (3000π t)+10sin (2000π t) f_t=12πdθ (t)dt=f_c+7500cos (3000π t)+10000cos (2000π t) So, nbsp; nbsp; nbsp; nbsp; nbsp;Δ f ...

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Standard XII

Physics

Frequency of a Wave

An angle modu...

Question

An angle modulated signal with carrier frequency $f_{c}$ is given by,
$s (t) = A_{c} cos [2 π f_{c} t + 5 sin (3000 π t) + 10 sin (2000 π t)]$
The bandwidth (using Carson's rule) of the signal s(t) will be

38 kHz

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42 kHz

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28 kHz

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33 kHz

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Solution

The correct option is A 38 kHz

$θ (t) = 2 π f_{c} t + 5 sin (3000 π t) + 10 sin (2000 π t)$
$f_{t} = \frac{1}{2 π} \frac{d θ (t)}{d t} = f_{c} + 7500 cos (3000 π t) + 10000 cos (2000 π t)$

So, $Δ f = 7500 + 10000 = 17.5 k H z$

$f_{m (max)}$ = 1500 Hz = 1.5 kHz

Deviation ratio, $D = \frac{Δ f}{f_{m (max)}} = \frac{17.5}{1.5} = \frac{35}{3}$

Bandwidth, $B W = (1 + D) 2 f_{m (max)} = (1 + \frac{35}{3}) (3) k H z = 38 k H z$

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An angle modulated signal with carrier frequency fc is given by, s(t)=Accos[2πfct+5sin(3000πt)+10sin(2000πt)] The bandwidth (using Carson's rule) of the signal s(t) will be

The correct option is A 38 kHz θ(t)=2πfct+5sin(3000πt)+10sin(2000πt) ft=12πdθ(t)dt=fc+7500cos(3000πt)+10000cos(2000πt) So, Δf=7500+10000=17.5 kHz fm(max) = 1500 Hz = 1.5 kHz Deviation ratio, D=Δffm(max)=17.51.5=353 Bandwidth, BW=(1+D)2fm(max)=(1+353)(3) kHz=38 kHz

An angle modulated signal with carrier frequency $f_{c}$ is given by,
$s (t) = A_{c} cos [2 π f_{c} t + 5 sin (3000 π t) + 10 sin (2000 π t)]$
The bandwidth (using Carson's rule) of the signal s(t) will be