Consider the message signal shown in the figure below:

If this message signal m(t) is applied to an FM modulator whose frequency sensitivity is $k_{f} = 0.5 H z / V$ , then the maximum phase deviation of the resultant FM signal will be _____ radians.

18.85

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Solution

The correct option is A 18.85
For an FM signal,

$Δ ϕ_{m a x} = 2 π k_{f} {∣ ∣ ∣ t \int - \infty m (t) d t ∣ ∣ ∣}_{m a x}$

${∣ ∣ ∣ t \int - \infty m (t) d t ∣ ∣ ∣}_{m a x} = Area under m(t) = (1 \times 2) + (2 \times 2) = 6$

$Δ ϕ_{m a x} = 2 π (0.5) (6) = 6 π r a d = 18.85 r a d$

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Consider the message signal shown in the figure below: If this message signal m(t) is applied to an FM modulator whose frequency sensitivity is kf=0.5Hz/V, then the maximum phase deviation of the resultant FM signal will be _____ radians. 18.85

The correct option is A 18.85For an FM signal, Δϕmax=2πkf∣∣∣t∫−∞m(t)dt∣∣∣max ∣∣∣t∫−∞m(t)dt∣∣∣max=Area under m(t) =(1×2)+(2×2)=6 Δϕmax=2π(0.5)(6)=6π rad=18.85 rad

Consider the message signal shown in the figure below:

If this message signal m(t) is applied to an FM modulator whose frequency sensitivity is $k_{f} = 0.5 H z / V$ , then the maximum phase deviation of the resultant FM signal will be _____ radians.

18.85