To find the bandwidth of the Frequency Modulated (FM) signal, we use Carson's Rule, which states that the bandwidth \( BW \) for a wideband FM signal can be estimated using the following formula:
\(BW = 2(\Delta f + f_m)\)
where \( \Delta f \) is the frequency deviation, and \( f_m \) is the maximum modulating signal frequency.
First, let's determine the required values:
- The frequency of the message signal, \( m(t) = \sin(2000\pi t) \), is given by \( f_m = \frac{2000\pi}{2\pi} = 1000 \, \text{Hz} = 1 \, \text{kHz} \).
- The frequency sensitivity constant \( K_f \) is 100 kHz/V. This implies that the maximum frequency deviation \( \Delta f \) is calculated as:
\(\Delta f = K_f \times A_m = 100 \, \text{kHz/V} \times 1\, \text{V} = 100 \, \text{kHz}\)
where \( A_m \) is the amplitude of the message signal, which is 1 V for \( \sin(t) \).
Using Carson's Rule, compute the bandwidth \( BW \):
\(BW = 2(\Delta f + f_m) = 2(100 \, \text{kHz} + 1 \, \text{kHz}) = 2 \times 101 \, \text{kHz} = 202 \, \text{kHz}\)
Thus, the bandwidth of the FM signal is 202 kHz. This matches the correct answer and justifies why the other options are incorrect.
Important Questions from Frequency Modulation
The range of frequency generated by VHF oscillator is -
If f mis modulating frequency and m fis modulation index, then by the Carson's rule, the bandwidth of an FM signal at the input of a conventional discriminator will be:
The appropriate value of modulation index β for transition between narrow band and wide band FM is considered as:
Which of the following is NOT the advantage of frequency modulation ?
The modulation technique in which frequency of the carrier wave is changed with respect to the modulating wave is called:
