Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. For example, changes in signal strength may be used to specify the sounds to be reproduced by a loudspeaker, or the light intensity of television pixels. Contrast this with frequency modulation, in which the frequency is varied, and phase modulation, in which the phase is varied.

In the mid-1870s, a form of amplitude modulation—initially called "undulatory currents"—was the first method to successfully produce quality audio over telephone lines. Beginning with Reginald Fessenden's audio demonstrations in 1906, it was also the original method used for audio radio transmissions, and remains in use today by many forms of communication—"AM" is often used to refer to the mediumwave broadcast band (see AM radio).

Fig 1: An audio signal (top) may be carried by an AM or FM radio wave.

Forms of amplitude modulation[link]

In radio communication, a continuous wave radio-frequency signal (a sinusoidal carrier wave) has its amplitude modulated by an audio waveform before transmission. The audio waveform modifies the amplitude of the carrier wave and determines the envelope of the waveform. In the frequency domain, amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Amplitude modulation resulting in two sidebands and a carrier is called "double-sideband amplitude modulation" (DSB-AM). Amplitude modulation is inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal, which carries no useful information (beyond the fact that a signal is present).

To increase transmitter efficiency, the carrier may be suppressed. This produces a reduced-carrier transmission, or DSB "double-sideband suppressed-carrier" (DSB-SC) signal. A suppressed-carrier AM signal is three times more power-efficient than AM. If the carrier is only partially suppressed, a double-sideband reduced-carrier (DSBRC) signal results. For reception, a local oscillator will typically restore the suppressed carrier so the signal can be demodulated with a product detector.

Improved bandwidth efficiency is achieved at the expense of increased transmitter and receiver complexity by completely suppressing both the carrier and one of the sidebands. This is single-sideband modulation, widely used in amateur radio and other communications applications. A simple form of AM, often used for digital communications, is on-off keying: a type of amplitude-shift keying in which binary data is represented by the presence or absence of a carrier. This is used by radio amateurs to transmit Morse code and is known as continuous wave (CW) operation.

ITU designations[link]

In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation:

Example: double-sideband AM[link]

Fig 2: Double-sided spectra of baseband and AM signals.

A carrier wave is modeled as a sine wave:

Failed to parse (Missing texvc executable; please see math/README to configure.): c(t) = A\cdot \sin(\omega_c t + \phi_c),\,

in which the frequency in Hz is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_c / (2\pi).\,

The constants Failed to parse (Missing texvc executable; please see math/README to configure.): A\,

and Failed to parse (Missing texvc executable; please see math/README to configure.): \phi_c\,
represent the carrier amplitude and initial phase, and are introduced for generality. For simplicity, their respective values can be set to 1 and 0.

Let m(t) represent an arbitrary waveform that is the message to be transmitted, and let the constant M represent its largest magnitude:

Failed to parse (Missing texvc executable; please see math/README to configure.): m(t) = M\cdot \cos(\omega_m t + \phi).\,

The message might be just a simple audio tone of frequency:

Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_m / (2\pi).\,

It is assumed that  Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_m \ll \omega_c\,   and that  Failed to parse (Missing texvc executable; please see math/README to configure.): \min[ m(t) ] = -M.\,

Amplitude modulation is formed by the product:

Failed to parse (Missing texvc executable; please see math/README to configure.): y(t)\,	Failed to parse (Missing texvc executable; please see math/README to configure.): = [1 + m(t)]\cdot c(t),\,
	Failed to parse (Missing texvc executable; please see math/README to configure.): = A\cdot[1 + M\cdot \cos(\omega_m t + \phi)]\cdot \sin(\omega_c t).

Failed to parse (Missing texvc executable; please see math/README to configure.): A\,

represents the carrier amplitude, which is a constant that demonstrates the modulation index. The values A=1 and M=0.5 produce y (t), depicted by the top graph (labelled "50% Modulation") in Figure 4.

Using trigonometric identities, y(t) can be written in the form

Failed to parse (Missing texvc executable; please see math/README to configure.): y(t) = A\cdot \sin(\omega_c t) + \begin{matrix}\frac{AM}{2} \end{matrix} \left[\sin((\omega_c + \omega_m) t + \phi) + \sin((\omega_c - \omega_m) t - \phi)\right].\,

Therefore, the modulated signal has three components: a carrier wave and two sinusoidal waves (known as sidebands), whose frequencies are slightly above and below  Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_c.\,

Spectrum[link]

For more general forms of m(t), trigonometry is not sufficient; however, if the top trace of Figure 2 depicts the frequency of m(t) the bottom trace depicts the modulated carrier. It has two components: one at a positive frequency (centered on Failed to parse (Missing texvc executable; please see math/README to configure.): +\omega_c ) and one at a negative frequency (centered on Failed to parse (Missing texvc executable; please see math/README to configure.): -\omega_c ). Each component contains the two sidebands and a narrow segment in between, representing energy at the carrier frequency. Since the negative frequency is a mathematical artifact, examining the positive frequency demonstrates that an AM signal's spectrum consists of its original (two-sided) spectrum, shifted to the carrier frequency. Figure 2 is a result of computing the Fourier transform of:   Failed to parse (Missing texvc executable; please see math/README to configure.): [A + m(t)]\cdot \sin(\omega_c t),\,

using the following transform pairs:

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} m(t) \quad \stackrel{\mathcal{F}}{\Longleftrightarrow}&\quad M(\omega) \\ \sin(\omega_c t) \quad \stackrel{\mathcal{F}}{\Longleftrightarrow}&\quad i \pi \cdot [\delta(\omega +\omega_c)-\delta(\omega-\omega_c)] \\ A\cdot \sin(\omega_c t) \quad \stackrel{\mathcal{F}}{\Longleftrightarrow}&\quad i \pi A \cdot [\delta(\omega +\omega_c)-\delta(\omega-\omega_c)] \\ m(t)\cdot A\sin(\omega_c t) \quad \stackrel{\mathcal{F}}{\Longleftrightarrow}& \frac{A}{2\pi}\cdot \{M(\omega)\} * \{i \pi \cdot [\delta(\omega +\omega_c)-\delta(\omega-\omega_c)]\} \\ =& \frac{iA}{2}\cdot [M(\omega +\omega_c) - M(\omega -\omega_c)] \end{align}

Fig 3: The spectrogram of an AM broadcast shows its two sidebands (green), separated by the carrier signal (red).

Power and spectrum efficiency[link]

In terms of positive frequencies, the transmission bandwidth of AM is twice the signal's original (baseband) bandwidth; both the positive and negative sidebands are shifted up to the carrier frequency. Thus, double-sideband AM (DSB-AM) is spectrally inefficient since fewer radio stations can be accommodated in a given broadcast band. The suppression methods described above may be understood in terms of Figure 2. With the carrier suppressed, there would be no energy at the center of a group; with a sideband suppressed, the "group" would have the same bandwidth as the positive frequencies of Failed to parse (Missing texvc executable; please see math/README to configure.): M(\omega).\,   The transmitter-power efficiency of DSB-AM is relatively poor (about 33 percent). The benefit of this system is that receivers are cheaper to produce. Suppressed-carrier AM is 100 percent power-efficient, since no power is wasted on the carrier signal (which conveys no information).

Modulation index[link]

The AM modulation index is the measure of the amplitude variation surrounding an unmodulated carrier. As with other modulation indices, in AM this quantity (also called "modulation depth") indicates how much the modulation varies around its "original" level. For AM, it relates to variations in carrier amplitude and is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): h = \frac{\mathrm{peak\ value\ of\ } m(t)}{A} = \frac{M}{A},

  where Failed to parse (Missing texvc executable; please see math/README to configure.): M\,
and Failed to parse (Missing texvc executable; please see math/README to configure.): A\,
are the message amplitude and carrier amplitude, respectively.

So if Failed to parse (Missing texvc executable; please see math/README to configure.): h=0.5 , carrier amplitude varies by 50% above (and below) its unmodulated level; for Failed to parse (Missing texvc executable; please see math/README to configure.): h=1.0 , it varies by 100%. To avoid distortion, modulation depth must not exceed 100 percent. Transmitter systems will usually incorporate a limiter circuit (such as a VOGAD) to ensure this. However, AM demodulators can be designed to detect the inversion (or 180-degree phase reversal) that occurs when modulation exceeds 100 percent; they automatically correct for this defect.^{[citation needed]} Variations of a modulated signal with percentages of modulation are shown below. In each image, the maximum amplitude is higher than in the previous image (note that the scale changes from one image to the next).

Fig 4: Modulation depth

[edit] Modulation methods

Anode (plate) modulation. A tetrode's plate and screen grid voltage is modulated via an audio transformer. The resistor R1 sets the grid bias; both the input and output are tuned circuits with inductive coupling.

Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain—followed by amplification for transmission—or in the high-power domain of the transmitted signal).^[1]

Low-level generation[link]

In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM modulation are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with a digital to analog converter, typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency, and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion).^[2] This low-level method for AM is used in many Amateur Radio transceivers.^[3]

AM may also be generated at a low level, using analog methods described in the next section.

High-level generation[link]

High-power AM transmitters (such as those used for AM broadcasting) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage.^[4]

Older designs (for broadcast and amateur radio) also generate AM by controlling the transmitter’s final amplifier (generally a class-C, for efficiency) gain. The following types are for vacuum tube transmitters (but similar options are available with transistors):^[5]

• Plate modulation: In plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is 50 percent of the RF-carrier power.
• Heising (constant-current) modulation: RF amplifier plate voltage is fed through a “choke” (high-value inductor). The AM modulation tube plate is fed through the same inductor, so the modulator tube diverts current from the RF amplifier. The choke acts as a constant current source in the audio range. This system has a low power efficiency.
• Control grid modulation: The operating bias and gain of the final RF amplifier can be controlled by varying the voltage of the control grid. This method requires little audio power, but care must be taken to reduce distortion.
• Clamp tube (screen grid) modulation: The screen-grid bias may be controlled through a “clamp tube”, which reduces voltage according to the modulation signal. It is difficult to approach 100-percent modulation while maintaining low distortion with this system.

[edit] Demodulation methods

The simplest form of AM demodulator consists of a diode which is configured to act as envelope detector. Another type of demodulator, the product detector, can provide better-quality demodulation with additional circuit complexity.

See also[link]

• AM radio
• AM stereo
• Mediumwave band used for AM broadcast radio
• Longwave band used for AM broadcast radio
• Frequency modulation
• Shortwave radio almost universally uses AM, narrow FM occurring above 25 MHz.
• Modulation, for a list of other modulation techniques
• Amplitude modulation signalling system (AMSS), a digital system for adding low bitrate information to an AM signal.
• Sideband, for some explanation of what this is.
• Types of radio emissions, for the emission types designated by the ITU
• Airband
• Quadrature amplitude modulation

References[link]

• Newkirk, David and Karlquist, Rick (2004). Mixers, modulators and demodulators. In D. G. Reed (ed.), The ARRL Handbook for Radio Communications (81st ed.), pp. 15.1–15.36. Newington: ARRL. ISBN 0-87259-196-4.

External links[link]

• Amplitude Modulation by Jakub Serych, Wolfram Demonstrations Project.
• Amplitude Modulation, by S Sastry.
• Amplitude Modulation, an introduction by Federation of American Scientists.
• Amplitude Modulation tutorial video with example transmitter circuit.

v t e Telecommunications (general) History Beacons Broadcasting Communications satellites Computer networks Drums Electrical telegraphs Fax Heliographs Hydraulic telegraphs Internet Mass media Mobile phones Optical telegraphy Photophones Radio Radiotelephones Telegraphy Telephones The Telephone Cases Television Undersea telegraph lines Videophones Pioneers Edwin Howard Armstrong John Logie Baird Alexander Graham Bell Tim Berners-Lee Jagadish Chandra Bose Vint Cerf Claude Chappe Lee De Forest Philo Farnsworth Reginald Fessenden Elisha Gray Guglielmo Marconi Alexander Stepanovich Popov Johann Philipp Reis Nikola Tesla Alfred Vail Charles Wheatstone Vladimir K. Zworykin Media Coaxial cable Free-space optical Optical fiber Radio waves Telephone lines Terrestrial microwave Networks ARPANET BITNET Ethernet FidoNet ISDN Internet Local area Mobile NGN Packet switched Public Switched Telephone Radio Television Telex Wide area World Wide Web Wireless Geographic v t e Telecommunications in Africa Sovereign states Algeria Angola Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Central African Republic Chad Comoros Democratic Republic of the Congo Republic of the Congo Côte d'Ivoire (Ivory Coast) Djibouti Egypt Equatorial Guinea Eritrea Ethiopia Gabon The Gambia Ghana Guinea Guinea-Bissau Kenya Lesotho Liberia Libya Madagascar Malawi Mali Mauritania Mauritius Morocco Mozambique Namibia Niger Nigeria Rwanda São Tomé and Príncipe Senegal Seychelles Sierra Leone Somalia South Africa South Sudan Sudan Swaziland Tanzania Togo Tunisia Uganda Zambia Zimbabwe States with limited recognition Azawad Sahrawi Arab Democratic Republic Somaliland Dependencies and other territories Canary Islands / Ceuta / Melilla / Plazas de soberanía (Spain) Madeira (Portugal) Mayotte / Réunion (France) Saint Helena / Ascension Island / Tristan da Cunha (United Kingdom) Western Sahara v t e Telecommunications in Asia Sovereign states Afghanistan Armenia Azerbaijan Bahrain Bangladesh Bhutan Brunei Burma (Myanmar) Cambodia People's Republic of China Cyprus East Timor (Timor-Leste) Egypt Georgia India Indonesia Iran Iraq Israel Japan Jordan Kazakhstan North Korea South Korea Kuwait Kyrgyzstan Laos Lebanon Malaysia Maldives Mongolia Nepal Oman Pakistan Philippines Qatar Russia Saudi Arabia Singapore Sri Lanka Syria Tajikistan Thailand Turkey Turkmenistan United Arab Emirates Uzbekistan Vietnam Yemen States with limited recognition Abkhazia Nagorno-Karabakh Northern Cyprus Palestine Republic of China (Taiwan) South Ossetia Dependencies and other territories British Indian Ocean Territory Christmas Island Cocos (Keeling) Islands Hong Kong Macau v t e Telecommunications in Europe Sovereign states Albania Andorra Armenia Austria Azerbaijan Belarus Belgium Bosnia and Herzegovina Bulgaria Croatia Cyprus Czech Republic Denmark Estonia Finland France Georgia Germany Greece Hungary Iceland Ireland Italy Kazakhstan Latvia Liechtenstein Lithuania Luxembourg Macedonia Malta Moldova Monaco Montenegro Netherlands Norway Poland Portugal Romania Russia San Marino Serbia Slovakia Slovenia Spain Sweden Switzerland Turkey Ukraine United Kingdom England Northern Ireland Scotland Wales States with limited recognition Abkhazia Kosovo Nagorno-Karabakh Northern Cyprus South Ossetia Transnistria Dependencies and other territories Åland Faroe Islands Gibraltar Guernsey Jersey Isle of Man Svalbard Other entities European Union v t e Telecommunications in North America Sovereign states Antigua and Barbuda Bahamas Barbados Belize Canada Costa Rica Cuba Dominica Dominican Republic El Salvador Grenada Guatemala Haiti Honduras Jamaica Mexico Nicaragua Panama Saint Kitts and Nevis Saint Lucia Saint Vincent and the Grenadines Trinidad and Tobago United States Dependencies and other territories Anguilla Aruba Bermuda Bonaire British Virgin Islands Cayman Islands Curaçao Greenland Guadeloupe Martinique Montserrat Navassa Island Puerto Rico Saint Barthélemy Saint Martin Saint Pierre and Miquelon Saba Sint Eustatius Sint Maarten Turks and Caicos Islands United States Virgin Islands v t e Telecommunications in Oceania Sovereign states Australia East Timor (Timor-Leste) Fiji Indonesia Kiribati Marshall Islands Federated States of Micronesia Nauru New Zealand Palau Papua New Guinea Samoa Solomon Islands Tonga Tuvalu Vanuatu Dependencies and other territories American Samoa Christmas Island Cocos (Keeling) Islands Cook Islands Easter Island French Polynesia Guam Hawaii New Caledonia Niue Norfolk Island Northern Mariana Islands Pitcairn Islands Tokelau Wallis and Futuna v t e Telecommunications in South America Sovereign states Argentina Bolivia Brazil Chile Colombia Ecuador Guyana Paraguay Peru Suriname Uruguay Venezuela Dependencies and other territories Aruba Bonaire Curaçao Falkland Islands French Guiana South Georgia and the South Sandwich Islands