Question

A message signal of frequency 14 kHz is used to modulate a carrier of frequency 900 kHz. Then, the frequencies of the sidebands are:

• A. 907 kHz, 893 kHz
• B. 920 kHz, 880 kHz
• C. 914 kHz, 886 kHz
• D. 900 kHz, 914 kHz

Hint:

For frequency modulation, the sidebands are located at the carrier frequency plus or minus the message signal frequency. For AM, this same formula applies. However, in FM, the modulation may also introduce further higher-order sidebands depending on the modulation index, but for simplicity, we focus on the first-order sidebands here.

Answer 1

The Correct Option is C

Understanding the concept of modulation.
In frequency modulation (FM), the carrier signal is varied in frequency according to the message signal. The frequencies of the sidebands are directly related to the message signal frequency. Specifically, in standard amplitude modulation (AM), the sidebands occur at \( f_c + f_m \) and \( f_c - f_m \), where \( f_c \) is the carrier frequency and \( f_m \) is the message signal frequency.
In this case, we are using frequency modulation (FM), where the modulation creates sidebands at frequencies slightly offset from the carrier frequency. Given:
Carrier frequency \( f_c = 900 \) kHz
Message signal frequency \( f_m = 14 \) kHz
The frequencies of the sidebands will occur at: \[ f_c + f_m = 900 \, \text{kHz} + 14 \, \text{kHz} = 914 \, \text{kHz} \] \[ f_c - f_m = 900 \, \text{kHz} - 14 \, \text{kHz} = 886 \, \text{kHz} \] Thus, the sideband frequencies are 914 kHz and 886 kHz.
Verifying the modulation process.
In FM, the carrier signal is altered by the amplitude or frequency variations corresponding to the message signal. This creates upper and lower sidebands that are spaced symmetrically around the carrier frequency. The sideband frequencies are exactly the sum and difference of the carrier frequency and the message frequency, hence giving us 914 kHz and 886 kHz.
Thus, we conclude that the frequencies of the sidebands are 914 kHz and 886 kHz. Recap of sideband formula.
For any modulation scheme, the formula for the sideband frequencies is: \[ f_{\text{upper}} = f_c + f_m \] \[ f_{\text{lower}} = f_c - f_m \] In this case, the sidebands are symmetrically placed around the carrier at 914 kHz and 886 kHz.