Power Distribution in Amplitude Modulation (AM)

Power Distribution

In practice, the AM wave s(t) is a voltage or current signal. In either case, the average power delivered to a 1-ohm load resistor by s(t) is comprised of three components:

Carrier power = (1/2)A_c²
Upper side-frequency power = (1/8)μ²A_c²
Lower side-frequency power = (1/8)μ²A_c²

The ratio of the total sideband power to the total power in the modulated wave is therefore equal to μ² / (2 + μ²), which depends only on the modulation factor μ. If μ = 1, that is, 100% modulation is used, the total power in the two side-frequencies of the resulting AM wave is only one-third of the total power in the modulated wave.

A major topic in Amplitude Modulation (AM) is the analysis of how power is distributed within the transmitted signal. In the standard AM, a significant portion of the total transmitted power is concentrated in the carrier signal. Critically, this carrier wave itself conveys no information. The useful information—the original message signal—is contained entirely within the sidebands. The power efficiency (η) is a crucial metric that quantifies what fraction of the total power resides in these information-carrying sidebands.

• The efficiency is calculated using the formula:
  η = μ² / (2 + μ²)
  where μ represents the modulation index.
• Even under optimal conditions, such as 100% modulation (when μ=1), the maximum theoretical efficiency is only 33.3%. This means that a full two-thirds of the transmitter's power is expended just to send the carrier wave. This pronounced inefficiency is the primary motivation behind the development of more advanced, carrier-suppressed modulation techniques like Double-Sideband Suppressed-Carrier (DSB-SC) and Single-Sideband (SSB) modulation.  

Further Reading

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