The modulation index of a single tone FM signal is 2 $π$ rad. If the frequency and the amplitude of the message signal are increased by a factor of 2, then the modulation index of the modified FM signal will be equal to

$π r a d$

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4 π r a d

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2 π r a d

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8 π r a d

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Solution

The correct option is C $2 π r a d$

The modulation index of a single tone FM signal can be given as,
$β = k_{f} \frac{A_{m}}{f m}$

$β_{1} = k_{f} \frac{{A_{m}}_{1}}{f m_{1}}$

$β_{2} = k_{f} \frac{{A_{m}}_{2}}{f m_{2}} = k_{f} \frac{(2 {A_{m}}_{1})}{(2 f m_{1})} = k_{f} \frac{{A_{m}}_{1}}{f m_{1}} = β_{1} = 2 π r a d$

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The modulation index of a single tone FM signal is 2π rad. If the frequency and the amplitude of the message signal are increased by a factor of 2, then the modulation index of the modified FM signal will be equal to

The correct option is C 2π rad The modulation index of a single tone FM signal can be given as, β=kfAmfm β1=kfAm1fm1 β2=kfAm2fm2=kf(2Am1)(2fm1)=kfAm1fm1=β1=2π rad

The modulation index of a single tone FM signal is 2 $π$ rad. If the frequency and the amplitude of the message signal are increased by a factor of 2, then the modulation index of the modified FM signal will be equal to