# Amplitude modulation **Amplitude modulation** (AM) is a method of impressing a message on a [[Carrier_wave|carrier wave]] by varying the carrier's instantaneous amplitude in direct proportion to the message, while its frequency and phase stay fixed. It is the oldest of the classical modulation families and remains the method behind standard AM broadcast radio, aviation voice communication, and shortwave transmission. The *Amplitude modulation* microsim on this page draws the message, the bare carrier, and the modulated result on top of one another, and lets the reader push the modulation depth from a faint imprint on the carrier through a full, undistorted envelope and on into audible overmodulation. Amplitude modulation contrasts with angle modulation, the family that holds amplitude fixed and instead varies the carrier's frequency, as in [[Frequency_modulation|frequency modulation]], or its phase. Both families are specific cases of the general idea of [[Signal_modulation|signal modulation]]: choosing one of a sinusoidal carrier's few free parameters and driving it with a message. What distinguishes amplitude modulation in practice is how directly the message can be recovered — a receiver only has to track how strongly the carrier swells and shrinks, which is why amplitude modulation produced the simplest and cheapest receivers of the broadcast era and still does. ## Foundation The foundational idea behind amplitude modulation is older than continuous-wave radio itself: interrupting a carrier completely, fully on or fully off, in the pattern of a code is already a form of amplitude modulation, at 100 percent depth, carrying a two-level message. Continuous analog telephony asks for the same mechanism applied gently and continuously instead of switched abruptly, so that a microphone's varying voltage rides on the carrier's amplitude as a smoothly moving envelope rather than a sequence of pulses. The digital descendant of the switched case survives as [[Amplitude-shift_keying|amplitude-shift keying]], which chooses among a small set of discrete amplitude levels once per symbol instead of following a continuous waveform. Describing "how much" a carrier is modulated requires a reference amplitude to measure against, and that reference is the carrier's own unmodulated amplitude — the level it would sit at with no message applied at all. Every other definition in this article, from the modulation index to the overmodulation limit, is stated relative to that one reference level. ## ITU type designations International radio regulations classify amplitude-modulated emissions with a short alphanumeric code that states the necessary bandwidth, the basic modulation type, and the nature of the signal carried, so that a receiver's operator or an interference investigation can identify what a transmission ought to look like without hearing it first. A conventional double-sideband broadcast signal that carries a full, unsuppressed carrier is designated A3E; a signal that has had one sideband and the carrier filtered away, leaving only the other sideband to carry the same information in half the bandwidth, is designated J3E. The designation system covers many more combinations of bandwidth, modulation family, and signal type than these two examples.[^cnitu] ## History Amplitude modulation grew out of early-twentieth-century efforts to replace the damped, spark-generated pulses of wireless telegraphy with a steady carrier that a modulator could act on continuously, work that historians of radio associate with early radiotelephone experimenters of the period.[^cnhist] What turned that idea into a broadcast medium, more than any change to the modulation scheme itself, was the vacuum tube: a tube oscillator could hold a stable, continuous carrier frequency indefinitely, and a tube amplifier could raise a modulated signal to broadcast power without discarding the shape of its envelope, while tube-based receivers could amplify a faint signal enough for an inexpensive detector to recover it. Single-sideband transmission came later, developed once engineers recognized that an ordinary amplitude-modulated signal spends most of its power on a carrier that carries no information and most of its bandwidth on a second sideband that duplicates the first; removing both was a deliberate, later refinement rather than part of amplitude modulation's original design. ## Analysis A single-tone amplitude-modulated signal is written `s(t) = A_c·[1 + m·cos(2π f_m t)]·cos(2π f_c t)`, the product of a slowly varying envelope and a fast carrier [[Sine_wave|sinusoid]] running at the [[Angular_frequency|angular frequency]] 2π f_c. Multiplying the two factors out turns the product of two cosines into a sum of cosines at the sum and difference of their frequencies, the same trigonometric step that turns two nearby tones into an audible beat: adding a 10 Hz tone to a 12 Hz tone, for instance, produces a single wave whose strength swells and fades twice a second, at the 2 Hz difference between them, rather than two separate tones.[^stib033] Amplitude modulation performs the identical trick deliberately, at a carrier frequency far above the message rather than between two audio tones. The resulting envelope is the magnitude of the signal's underlying [[Analytic_signal|analytic signal]], the complex-valued representation whose real part is the physical waveform and whose magnitude strips the fast carrier oscillation away to leave only the slowly varying quantity a receiver actually wants. ## Spectrum Multiplying the carrier by the message shifts the message's own spectrum up, in the [[Frequency_domain|frequency domain]], so that it sits centered on the carrier frequency rather than at baseband. For a message tone at frequency f_m, the product-to-sum expansion of the modulation equation places three components in the spectrum: the untouched carrier at f_c, and two sidebands at f_c − f_m and f_c + f_m, each carrying an identical copy of the message spectrum, one mirrored and one upright.[^stib032] A message with many frequency components, such as speech, produces two full mirrored copies of its spectrum, an upper sideband from f_c up to f_c plus the highest message frequency and a lower sideband from f_c down to f_c minus that same highest frequency, so the total occupied bandwidth is twice the message's own bandwidth. ## Power and spectrum efficiency The double-sideband, full-carrier signal that this taxonomy calls A3E pays for its simple receivers with wasted power and wasted bandwidth. At full, 100 percent single-tone modulation, the carrier alone still holds two-thirds of the transmitted power, and the two sidebands together, which are the only part of the signal carrying the message, hold the remaining third split evenly between them; every additional [[Decibel|decibel]] of message power the sidebands are given raises the total transmitted power far more than it raises the recovered message strength, because the wasted carrier scales along with everything else. The bandwidth cost is separate from the power cost: since the two sidebands duplicate each other's information, an ordinary amplitude-modulated signal occupies twice the bandwidth that the message alone requires, which single-sideband transmission exists specifically to recover. ## Modulation index The modulation index m compares the message's swing to the reference carrier amplitude: at m = 0 the carrier is untouched and carries no message at all, and at m = 1 the envelope swings from zero all the way up to twice the carrier's unmodulated amplitude without ever crossing zero into negative territory. In the sketch, the modulation-depth control runs from 0 to 2, well past this limit, and a meter marks exactly where m = 1 falls. Pushing m past 1 overmodulates the carrier: the mathematical envelope `1 + m·cos(2π f_m t)` now dips below zero for part of each message cycle, which a real transmitter cannot produce and a real detector cannot follow, so the recovered message comes back with its troughs flattened and folded — audible [[Distortion|distortion]] that is the direct, visible signature of exceeding this one index. ## Modulation methods A transmitter can introduce the modulation at low power or at high power, and the choice shapes the rest of its design. Low-level generation modulates a small-signal stage early in the transmitter and then raises the already-modulated waveform to full power with a linear amplifier chain, one built to reproduce the envelope's peaks and troughs faithfully rather than to run at its own most efficient operating point. High-level generation instead amplifies the bare, constant-amplitude carrier up to full power first and performs the modulation at that final, highest-power stage, commonly by varying the power amplifier's own supply voltage in step with the message; because the amplifier itself can then run in a more efficient switching or near-switching mode rather than a linear one, high-level generation has been the traditional choice for high-power broadcast transmitters, at the cost of having to modulate a stage that is handling the full transmitted power. ## Demodulation methods The simplest receiver recovers the message with an envelope detector: a [[Diode|diode]] conducts on the peaks of the incoming wave and charges a capacitor, which a parallel resistor slowly discharges between peaks, so the voltage across the pair traces the envelope while smoothing away the carrier ripple riding underneath it. The circuit needs no oscillator of its own and no knowledge of the carrier's exact frequency or phase, which is why it has served in receivers from the earliest crystal sets to today's inexpensive integrated circuits, and why it fails as soon as the modulation index passes 1: the diode can only follow an envelope that stays positive. Synchronous detection instead multiplies the incoming signal by a locally generated copy of the carrier and low-pass filters the product, a method that works even on a suppressed-carrier signal an envelope detector cannot touch at all, provided the receiver's local oscillator is held to the transmitter's frequency and phase, typically by a [[Phase-locked_loop|phase-locked loop]]; done this way, demodulation generally holds a better [[Signal-to-noise_ratio|signal-to-noise ratio]] than an envelope detector reaches at the same received carrier power. In both cases the incoming radio-frequency signal is normally shifted down to one fixed intermediate frequency by a [[Superheterodyne_receiver|superheterodyne receiver]] before either detector ever sees it, which lets one detector design work across an entire tuning range instead of one built for each station. ## Microsims The *Amplitude modulation* sketch stacks four panels: the message m(t), the bare carrier c(t), the modulated output s(t) with its envelope traced on top, and a live spectrum showing the carrier line flanked by its two sidebands. Carrier frequency f_c (2–20 Hz) and message frequency f_m (0.2–4 Hz) set the two tones; the modulation-depth slider m (0–2) carries the reader straight through the healthy range and on into overmodulation, flagged on screen once m exceeds 1; the space bar pauses the animation and "r" resets it. A readout below the plots gives the carrier frequency, the two sideband frequencies at f_c − f_m and f_c + f_m, and the occupied bandwidth 2 f_m, updating live as the sliders move. *Try:* Raise the modulation-depth slider slowly through m = 1 and watch the envelope in the third panel stop tracking the message cleanly and start folding through zero, exactly where the on-screen "OVERMODULATED" warning appears. A three.js companion renders the same signal at m = 0.5 and then carries it past overmodulation at m = 1, as a single continuous sweep. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Amplitude_modulation) : [Wikitube](https://en.wikitube.io/wiki/Amplitude_modulation) Skeleton mirrored at revision 1371986437. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Signal_modulation]] - [[Frequency_modulation]] - [[Carrier_wave]] - [[Superheterodyne_receiver]] - [[Analytic_signal]] - [[Amplitude-shift_keying]] ## References [^cnitu]: Citation needed: the ITU Radio Regulations Appendix (emission designators) has not been checked directly here for the complete table of amplitude-modulation type codes beyond A3E and J3E. [^cnhist]: Citation needed: a primary-source date, venue, and account for the specific early-twentieth-century continuous-wave radiotelephone demonstrations that first carried a continuously varying amplitude-modulated voice signal. [^stib033]: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2016 ed., p. 33 (PDF page), Fig. 1.7: a 10 Hz tone and a 12 Hz tone summing to a beat envelope repeating at 2 Hz. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. [^stib032]: Stiber, M.; Stiber, B.; Larson, E. *Signal Computing: Digital Signals in the Software Domain*. 2016 ed., pp. 32–33 (PDF pages), Eq. 1-16: `a1·exp(jωt) + a2·exp(j(ω+δ)t) = (a1 + a2·exp(jδt))·exp(jωt)`, a slow envelope factor multiplying a fast carrier. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain . CC BY-SA. ## Bibliography - Steven Ellingson. *Radio Systems Engineering*, Revised 1st Edition (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain* (2020). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain - Don Johnson. *Fundamentals of Electrical Engineering I* (2014). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 ## External links - Live sketch: https://editor.p5js.org/sciencenibber/full/mSUZLEd6C - Editor source: https://editor.p5js.org/sciencenibber/sketches/mSUZLEd6C <!-- Hubs: Signal_processing. Portals: PORTAL_Signal_Processing. Signal Processing portal wave 1 · 2026-09-17 · drafted. -->