Question
Compare amplitude modulation (AM) and frequency modulation (FM) in terms of bandwidth, noise immunity, and applications. What is the bandwidth of an AM signal if the modulating frequency is 5 kHz?
(NCERT Class 12, Chapter 15)
Solution — Step by Step
In AM, the amplitude of the carrier wave varies in proportion to the message signal while the frequency remains constant. The modulated signal:
where is the modulation index ().
The AM spectrum contains three frequencies: , , and .
Bandwidth of AM =
In FM, the frequency of the carrier varies in proportion to the message signal while the amplitude stays constant:
where is the modulation index and is the maximum frequency deviation.
Bandwidth of FM (Carson’s rule). FM bandwidth is much larger than AM — typically 200 kHz for broadcast FM vs 10 kHz for AM.
| Feature | AM | FM |
|---|---|---|
| What varies | Amplitude | Frequency |
| Bandwidth | (narrow) | (wide) |
| Noise immunity | Poor (noise affects amplitude) | Excellent (noise affects amplitude, not frequency) |
| Transmission range | Long (ground wave + sky wave) | Short (line of sight) |
| Audio quality | Lower | Higher (hi-fi) |
| Power efficiency | Lower (carrier wastes power) | Higher |
| Applications | Radio broadcast (MW, SW) | FM radio, TV sound |
Why This Works
AM is susceptible to noise because most noise affects the amplitude of the signal — and amplitude is exactly what carries the information in AM. In FM, the information is in the frequency variations, so amplitude noise can be clipped off without losing the message. This is why FM radio sounds cleaner than AM.
The trade-off is bandwidth. FM needs much more bandwidth (about 200 kHz per channel vs 10 kHz for AM). This is why FM stations operate at higher frequencies (88-108 MHz) where more bandwidth is available, while AM stations use lower frequencies (535-1605 kHz).
Alternative Method
For calculating AM bandwidth with multiple modulating frequencies, use the highest modulating frequency: bandwidth = . For example, if the audio signal contains frequencies from 300 Hz to 5 kHz, the bandwidth is kHz.
For CBSE boards, the most commonly asked questions on communication systems are: (1) define modulation and why it is needed, (2) AM bandwidth = , (3) advantages of FM over AM. These are straightforward recall questions — scoring topics that require minimal calculation.
Common Mistake
Students often write “FM has longer range than AM” — it is the opposite. AM signals (especially MW and SW bands) can travel long distances via ground waves and sky wave reflection off the ionosphere. FM signals are limited to line-of-sight range because they use higher frequencies that pass through the ionosphere instead of reflecting back.