====== Amplitude modulation ======

**Amplitude modulation (AM)** conveys information by varying a carrier's amplitude. Conventional double-sideband AM retains the carrier and creates an upper and a lower sideband. It is used in broadcasting, aviation and some [[citizens_band_radio|CB]] systems.

===== Single-tone model =====

For a sinusoidal modulating signal:

<code>
s(t) = A_c [1 + m cos(2 π f_m t)] cos(2 π f_c t)
</code>

A_c is the unmodulated carrier's peak amplitude, f_c is carrier frequency, f_m is modulation frequency and m is the modulation index. m = 0.5 represents 50% modulation; m = 1 represents 100% in this model.

The spectrum contains the carrier at f_c and sidebands at f_c - f_m and f_c + f_m. Each sideband has peak amplitude m A_c / 2.

For example, a 1 kHz tone modulating a 27.205 MHz carrier produces sidebands at 27.204 and 27.206 MHz. If a baseband signal extends to a highest frequency B, ideal double-sideband transmission spans approximately 2B.

===== Envelope and power =====

An envelope detector can recover ordinary AM when the envelope retains the correct shape. Exceeding 100% modulation in the simple model causes envelope inversion and distortion in such a detector. Clipping in the transmitter can also create unwanted emissions.

For a resistive load and one sinusoidal modulating tone:

<code>
P_average = P_carrier (1 + m² / 2)
PEP = P_carrier (1 + m)²
</code>

At m = 1, total average power is 1.5 times carrier power, while PEP is four times carrier power. These quantities are distinct; a power limit must be read using its specified measurement definition.

===== Related forms =====

Double-sideband suppressed-carrier modulation removes the transmitted carrier. [[single_sideband|Single-sideband modulation]] also removes one sideband, concentrating transmission into a smaller frequency range. These signals require an appropriate receiver rather than a simple conventional AM envelope detector.

===== References =====

  * [[https://www.keysight.com/us/en/assets/7018-06742/application-notes/5954-9130.pdf|Keysight: amplitude and frequency modulation measurements]].
  * [[https://www.keysight.com/used/kr/en/knowledge/glossary/oscilloscopes/what-is-amplitude-modulation|Keysight: AM and its variants]].