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A message signal with bandwidth 10 kHz is lower sideband SSB modulated with carrier frequency fc1 = 106 Hz. The resulting signal is then passed though a narrow band frequency modulator with carrier frequency fc2 = 109 Hz. The bandwidth of the output would be
  • a)
    4 x 104 Hz
  • b)
    2 x 106 Hz
  • c)
    2 x 109 Hz
  • d)
    2 x 1010 Hz
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A message signal with bandwidth 10 kHz is lower sideband SSB modulated...
Bandwidth = 2Δf + 2B
But for NBFM, B < 1
BW ≈ 2fm 2fc1 2 x 106 Hz.
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Most Upvoted Answer
A message signal with bandwidth 10 kHz is lower sideband SSB modulated...
Given Information:

Bandwidth of message signal = 10 kHz
Carrier frequency for SSB modulation = fc1 = 106 Hz
Carrier frequency for narrowband FM modulation = fc2 = 109 Hz

To Find: Bandwidth of the output signal

Solution:

SSB Modulation

- Single Sideband (SSB) modulation is a type of amplitude modulation where one of the sidebands and the carrier frequency are suppressed.
- In Lower Sideband (LSB) modulation, the lower sideband and the carrier frequency are transmitted while the upper sideband is suppressed.
- The bandwidth of an SSB signal is equal to the bandwidth of the message signal.
- In this case, the message signal's bandwidth is 10 kHz. Therefore, the bandwidth of the SSB modulated signal is also 10 kHz.

Narrowband FM Modulation

- In Narrowband FM modulation, the frequency deviation of the carrier signal is much smaller than the carrier frequency.
- The bandwidth of a narrowband FM signal can be calculated using the Carson's rule, which states that the bandwidth is equal to twice the sum of the maximum deviation and the highest modulating frequency.
- In this case, the maximum deviation can be assumed to be equal to the message signal's amplitude. Therefore, the maximum deviation is 1.
- The highest modulating frequency is equal to the message signal's bandwidth. Therefore, the highest modulating frequency is 10 kHz.
- Using Carson's rule, the bandwidth of the narrowband FM signal is given by,

Bandwidth = 2 x (1 + 10 kHz) = 2 x 10,001 Hz = 20,002 Hz ≈ 2 x 106 Hz

Therefore, the bandwidth of the output signal is 2 x 106 Hz, which is option (B).
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A message signal with bandwidth 10 kHz is lower sideband SSB modulated with carrier frequency fc1 = 106 Hz. The resulting signal is then passed though a narrow band frequency modulator with carrier frequency fc2 = 109 Hz. The bandwidth of the output would bea)4 x 104 Hzb)2 x 106 Hzc)2 x 109 Hzd)2 x 1010 HzCorrect answer is option 'B'. Can you explain this answer?
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