Amplitude Modulation (AM)

The Principle of Amplitude Modulation

Amplitude Modulation (AM) varies the amplitude of a high-frequency signal, called the carrier wave, according to the information signal (the modulating signal). In standard AM, the carrier frequency and phase remain fixed while its amplitude follows the message.

The carrier translates a low-frequency message to a radio-frequency band that can be radiated, filtered, and transmitted over the intended distance. The message changes the carrier envelope, while the selected carrier frequency determines the centre of that band.

The Mathematics and Waveforms of AM

The following equations use a sinusoidal message and a cosine carrier phase convention:

• Modulating Signal (Information): This is the low-frequency signal we want to transmit, for example, a single audio tone.

  $u_{we}(t) = U_m \sin(\omega_m t)$

• Carrier Signal (Carrier Wave): This is the high-frequency reference signal that carries the message spectrum.

  $u_n(t) = U_n \cos(\omega_n t)$

With the carrier phase convention above, the modulated signal is:

$u_{wy}(t) = U_n (1 + m \cdot \sin(\omega_m t)) \cos(\omega_n t)$

Modulation Depth

The parameter $m$ is the modulation depth. It is the ratio of the message amplitude to the carrier amplitude, defined as $m = U_m / U_n$ for a single-tone message.

• If $m = 0$, there is no modulation.
• If $m = 1$ (or 100%), the envelope reaches zero at its minimum. This is the largest index that avoids envelope crossings for standard envelope detection.
• If $m > 1$, the envelope crosses zero. An envelope detector then produces distortion. A synchronized coherent detector can still recover the unclipped mathematical waveform.

The AM Spectrum: Carrier and Sidebands

In the frequency domain, AM translates the message spectrum into two sidebands around the carrier.

For a single-tone message, a standard AM spectrum contains three components:

• Carrier Frequency ($f_n$): The original, powerful high-frequency carrier wave.
• Upper Sideband (USB): A copy of the information signal's spectrum, shifted up in frequency, located at $f_n + f_m$.
• Lower Sideband (LSB): Another copy of the information signal's spectrum, shifted down in frequency, located at $f_n - f_m$.

The upper and lower sidebands contain the same message information. For a single-tone message at $f_m$, the required bandwidth is $B = 2f_m$. For a message whose highest baseband frequency is $B_m$, the general relation is $B = 2B_m$.

Power Efficiency and AM Variants

For a single-tone message and an ideal load, the total power of the AM signal ($P_{\text{TOT}}$) is the carrier power ($P_n$) plus the power in both sidebands ($P_{\text{wb}}$):

$P_{\text{TOT}} = P_n + \frac{m^2}{2} P_n$

The sidebands carry the message spectrum. The carrier term provides a reference and consumes the largest share of power. Message variation is carried by the sidebands. The efficiency ($\eta$) is the ratio of sideband power to total power, $\eta = \frac{m^2}{2 + m^2}$.

For full modulation ($m=1$), the total power is $P_n + 0.5 P_n = 1.5 P_n$, while the sidebands carry $0.5 P_n$. Thus the efficiency is 33.3% in this single-tone case. Suppressed-carrier and single-sideband variants reduce this overhead.

AM Variants

• DSB-SC (Double-Sideband Suppressed-Carrier): Both sidebands are transmitted and the carrier is suppressed. This improves power efficiency but requires a receiver to regenerate the carrier frequency. A ring modulator is one circuit used to generate this signal.
• SSB-SC (Single-Sideband Suppressed-Carrier): It transmits one sideband, upper or lower, and suppresses the carrier.
  • Power Efficiency: 100% of the transmitted power is useful information.
  • Bandwidth Efficiency: For a single-tone message, it requires half the bandwidth of a standard AM signal ($B = f_m$).
  • Disadvantage: It requires a complex receiver to precisely re-insert the carrier and filter the single sideband.

AM Broadcasting and Other Applications

Amplitude Modulation, especially the standard DSB-WC form, became widely used because its receivers can use simple demodulators.

Advantages of AM

• Simple Receiver Design: Standard AM radios can use inexpensive components such as an envelope detector, which supported their mass adoption.
• High Efficiency (for SSB): The SSB variant uses power and bandwidth efficiently, so it is suitable for amateur radio and long-distance voice communication.

Disadvantages of AM

• Poor Power Efficiency (for DSB): Standard AM wastes at least two-thirds of its power on the carrier.
• Susceptibility to Noise: Because the information is encoded in the amplitude, any noise that affects the amplitude (e.g., from lightning, electrical equipment) directly degrades the received signal.