Question

A message signal m(t) = sinc(1000t) V is applied to an FM modulator, whose frequency Sensitivity is $k_f=1kHz/V$. The modulation index (or deviation ratio) of the resultant FM signal will be

• A. 1
• B. 4
• C. 3
• D. 2

Answer 1

The correct option is D 2

The deviation ratio, $D=\frac{\Delta f}{f_{m\left(max\right)}}$

Maximum frequency deviation,

$\Delta f=k_f|m\left(t\right){|}_{max}$

Given that, $m\left(t\right)=sinc\left(1000t\right)V$

$k_f=1kHz/V$

$f_{m\left(max\right)}=\frac{1000}{2}=500Hz$

$|m\left(t\right){|}_{max}=1$

So, $D=\frac{1\left(1000\right)}{500}=2$