Question

A message signal $m\left(t\right)=\sin c\left(1000t\right)$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

Answer 1

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

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

Given that, m (t) = sinc (1000t) V

$k_f=1kHz/V$

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

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

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