To determine the bandwidth required for frequency modulation (FM) transmission, we can use Carson's Rule. According to Carson's Rule, the bandwidth BW required for FM is given by:
BW = 2(\Delta f + f_m)
where:
This question provides the deviation ratio (which is the ratio of deviation to modulating frequency) as 10. Thus, the frequency deviation \Delta f can be calculated as:
\Delta f = \text{Deviation Ratio} \times f_m = 10 \times 20 \text{kHz} = 200 \text{kHz}
Substituting the values into Carson's Rule:
BW = 2(200 \text{kHz} + 20 \text{kHz})
= 2 \times 220 \text{kHz} = 440 \text{kHz}
Therefore, the bandwidth required for transmission is 440 kHz.
The correct answer is, therefore, 440 kHz.
Match List-I with List-II:
| List-I (Modulation Schemes) | List-II (Wave Expressions) |
|---|---|
| (A) Amplitude Modulation | (I) \( x(t) = A\cos(\omega_c t + k m(t)) \) |
| (B) Phase Modulation | (II) \( x(t) = A\cos(\omega_c t + k \int m(t)dt) \) |
| (C) Frequency Modulation | (III) \( x(t) = A + m(t)\cos(\omega_c t) \) |
| (D) DSB-SC Modulation | (IV) \( x(t) = m(t)\cos(\omega_c t) \) |
Choose the correct answer: