Bandwidth Requirement for Amplitude Modulated Waves

An Amplitude Modulated (AM) wave is created when the amplitude of a high-frequency carrier wave is varied in proportion to the instantaneous amplitude of the modulating signal. This process is fundamental in many communication systems.

AM Wave Spectrum and Sidebands

When a single tone modulating signal of frequency \(f_m\) modulates a carrier signal of frequency \(f_c\), the resulting Amplitude Modulated wave consists of three main frequency components:

• The carrier frequency: \(f_c\)
• The Upper Sideband (USB) frequency: \(f_c + f_m\)
• The Lower Sideband (LSB) frequency: \(f_c - f_m\)

These two sidebands carry all the information from the modulating signal.

Calculating Amplitude Modulation Bandwidth

The bandwidth requirement for any modulated signal is the difference between the highest and lowest frequencies present in its spectrum. For an Amplitude Modulated wave, if the modulating signal consists of a range of frequencies up to a maximum modulating frequency, say \(f_{m(max)}\), then:

• The highest frequency component in the AM spectrum will be \(f_c + f_{m(max)}\) (from the Upper Sideband).
• The lowest frequency component in the AM spectrum will be \(f_c - f_{m(max)}\) (from the Lower Sideband).

Therefore, the total bandwidth (B.W.) occupied by the Amplitude Modulated wave is calculated as:

$$ \text{B.W.} = (\text{Highest Frequency}) - (\text{Lowest Frequency}) $$ $$ \text{B.W.} = (f_c + f_{m(max)}) - (f_c - f_{m(max)}) $$ $$ \text{B.W.} = f_c + f_{m(max)} - f_c + f_{m(max)} $$ $$ \text{B.W.} = 2f_{m(max)} $$

In the context of bandwidth requirement for AM, \(f_m\) typically refers to the highest modulating frequency present in the message signal.

AM Bandwidth Summary

The bandwidth requirement for an Amplitude Modulated wave is twice the highest frequency present in the modulating signal. This ensures that both the upper and lower sidebands, which contain the complete information of the modulating signal, are transmitted.

Thus, the correct expression for the bandwidth requirement of an Amplitude Modulated wave is \(2f_m\), where \(f_m\) represents the highest modulating frequency.