Amplitude modulation

carrier signal

using AM or FM methods.

Passband modulation
Analog modulation
AM FM PM QAM SM SSB
Digital modulation
ASK APSK CPM FSK MFSK MSK OOK PPM PSK QAM SC-FDE TCM WDM
Hierarchical modulation
QAM WDM
Spread spectrum
CSS DSSS FHSS THSS
See also
Capacity-approaching codes Demodulation Line coding Modem AnM PoM PAM PCM PDM PWM ΔΣM OFDM FDM Multiplexing
v t e

Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.

AM was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of the 20th century beginning with Roberto Landell de Moura and Reginald Fessenden's radiotelephone experiments in 1900.^[1] This original form of AM is sometimes called double-sideband amplitude modulation (DSBAM), because the standard method produces sidebands on either side of the carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly the carrier signal, which improves the ratio of message power to total transmission power, reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium.

AM remains in use in many forms of communication in addition to

.

Foundation

In

.

In general form, a modulation process of a sinusoidal carrier wave may be described by the following equation:^[2]

${\displaystyle m(t)=A(t)\cdot \cos(\omega t+\phi (t))\,}$.

A(t) represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency ${\displaystyle \omega }$, and the instantaneous phase deviation ${\displaystyle \phi (t)}$. This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In angle modulation, the term A(t) is constant and the second term of the equation has a functional relationship to the modulating message signal. Angle modulation provides two methods of modulation, frequency modulation and phase modulation.

In amplitude modulation, the angle term is held constant and the first term, A(t), of the equation has a functional relationship to the modulating message signal.

The modulating message signal may be analog in nature, or it may be a digital signal, in which case the technique is generally called amplitude-shift keying.

For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The message signal determines the

to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" (DSBAM).

A disadvantage of all amplitude modulation techniques, not only standard AM, is that the receiver amplifies and detects

noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio, say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio

etc.).

AM is also inefficient in power usage; at least two-thirds of the power is concentrated in the carrier signal. The carrier signal contains none of the original information being transmitted (voice, video, data, etc.). However its presence provides a simple means of demodulation using

short wave

broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs the extra power cost to greatly increase potential audience.

Shift keying

A simple form of digital amplitude modulation which can be used for transmitting

quadrature amplitude modulation

is now more commonly used with digital data, while making more efficient use of the available bandwidth.

Analog telephony

A simple form of amplitude modulation is the transmission of speech signals from a traditional analog telephone set using a common battery local loop.[3] The direct current provided by the central office battery is a carrier with a frequency of 0 Hz. It is modulated by a microphone (transmitter) in the telephone set according to the acoustic signal from the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber.

Amplitude reference

An additional function provided by the carrier in standard AM, but which is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so the AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However it is absolutely undesired for music or normal broadcast programming, where a faithful reproduction of the original program, including its varying modulation levels, is expected.

ITU type designations

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

Designation	Description
A3E	double-sideband a full-carrier – the basic amplitude modulation scheme
R3E	single-sideband reduced-carrier
H3E	single-sideband full-carrier
J3E	single-sideband suppressed-carrier
B8E	independent-sideband emission
C3F	vestigial-sideband
Lincompex	linked compressor and expander (a submode of any of the above ITU Emission Modes)

History

tuned circuit

. Modulation is done by the large carbon microphone (cone shape) in the antenna lead.

Amplitude modulation was used in experiments of multiplex telegraph and telephone transmission in the late 1800s.

damped waves

, pulses of radio waves that declined to zero, and sounded like a buzz in receivers. In effect they were already amplitude modulated.

Continuous waves

The first AM transmission was made by Canadian-born American researcher Reginald Fessenden on 23 December 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter, over a distance of one mile (1.6 km) at Cobb Island, Maryland, US. His first transmitted words were, "Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?". The words were barely intelligible above the background buzz of the spark.^{[citation needed]}

Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced

sinusoidal continuous waves, was needed. This was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters – the Alexanderson alternator, with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM is based, heterodyning, and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or "liquid baretter", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector

(1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not a problem.

Early technologies

Early experiments in AM radio transmission, conducted by Fessenden,

Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation was usually accomplished by a carbon microphone

inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled.

Vacuum tubes

The 1912 discovery of the amplifying ability of the

Edwin Armstrong and Alexander Meissner, was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn't have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked a great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting

began after World War II.

At the same time as AM radio began,

Single-sideband

In 1915, John Renshaw Carson formulated the first mathematical description of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device creates a sideband on both sides of the carrier frequency. Passing the modulated signal through another nonlinear device can extract the original baseband signal.^[4] His analysis also showed that only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915.^[4] This advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW-II, it was developed for military aircraft communication.

Analysis

The carrier wave (sine wave) of frequency f_c and amplitude A is expressed by

${\displaystyle c(t)=A\sin(2\pi f_{c}t)\,}$.

The message signal, such as an audio signal that is used for modulating the carrier, is m(t), and has a frequency f_m, much lower than f_c:

${\displaystyle m(t)=M\cos \left(2\pi f_{m}t+\phi \right)=Am\cos \left(2\pi f_{m}t+\phi \right)\,}$,

where m is the amplitude sensitivity, M is the amplitude of modulation. If m < 1, (1 + m(t)/A) is always positive for undermodulation. If m > 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier c(t) is multiplied by the positive quantity (1 + m(t)/A):

${\displaystyle {\begin{aligned}y(t)&=\left[1+{\frac {m(t)}{A}}\right]c(t)\\&=\left[1+m\cos \left(2\pi f_{m}t+\phi \right)\right]A\sin \left(2\pi f_{c}t\right)\end{aligned}}}$

In this simple case m is identical to the modulation index, discussed below. With m = 0.5 the amplitude modulated signal y(t) thus corresponds to the top graph (labelled "50% Modulation") in figure 4.

Using prosthaphaeresis identities, y(t) can be shown to be the sum of three sine waves:

${\displaystyle y(t)=A\sin(2\pi f_{c}t)+{\frac {1}{2}}Am\left[\sin \left(2\pi \left[f_{c}+f_{m}\right]t+\phi \right)+\sin \left(2\pi \left[f_{c}-f_{m}\right]t-\phi \right)\right].\,}$

Therefore, the modulated signal has three components: the carrier wave c(t) which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency f_c.

Spectrum

A useful modulation signal m(t) is usually more complex than a single sine wave, as treated above. However, by the principle of

, m(t) can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of 1 + m(t) with c(t) as above, the result consists of a sum of sine waves. Again, the carrier c(t) is present unchanged, but each frequency component of m at f_i has two sidebands at frequencies f_c + f_i and f_c – f_i. The collection of the former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation m(t) may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation m(t) having simply been shifted in frequency by f_c as depicted at the bottom right of figure 2.

The short-term spectrum of modulation, changing as it would for a human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted above the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times, the carrier itself remains constant, and of greater power than the total sideband power.

Power and spectrum efficiency

The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or "

, somewhat of a compromise in terms of bandwidth) in order to reduce the required channel spacing.

Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband (

. Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and the carrier represent a net advantage and are frequently employed.

A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing the overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80's onwards.

Modulation index

The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as:

${\displaystyle m={\frac {\mathrm {peak\ value\ of\ } m(t)}{A}}={\frac {M}{A}}}$

where ${\displaystyle M\,}$ and ${\displaystyle A\,}$ are the modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter.

So if ${\displaystyle m=0.5}$, carrier amplitude varies by 50% above (and below) its unmodulated level, as is shown in the first waveform, below. For ${\displaystyle m=1.0}$, it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible

.

However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of

where the carrier is (ideally) reduced to zero. In all such cases the term "modulation index" loses its value as it refers to the ratio of the modulation amplitude to a rather small (or zero) remaining carrier amplitude.

Modulation methods

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).^[5]

Low-level generation

In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM 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).^[6] This low-level method for AM is used in many Amateur Radio transceivers.^[7]

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

High-level generation

High-power AM

Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter's final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors):[9]^[10]

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.

Doherty modulation

One tube provides the power under carrier conditions and another operates only for positive modulation peaks. Overall efficiency is good, and distortion is low.

Outphasing modulation

Two tubes are operated in parallel, but partially out of phase with each other. As they are differentially phase modulated their combined amplitude is greater or smaller. Efficiency is good and distortion low when properly adjusted.

Pulse-width modulation (PWM) or pulse-duration modulation (PDM)

A highly efficient high voltage power supply is applied to the tube plate. The output voltage of this supply is varied at an audio rate to follow the program. This system was pioneered by Hilmer Swanson and has a number of variations, all of which achieve high efficiency and sound quality.

Digital methods

The Harris Corporation obtained a patent for synthesizing a modulated high-power carrier wave from a set of digitally selected low-power amplifiers, running in phase at the same carrier frequency.^{[11][citation needed]} The input signal is sampled by a conventional audio analog-to-digital converter (ADC), and fed to a digital exciter, which modulates overall transmitter output power by switching a series of low-power solid-state RF amplifiers on and off. The combined output drives the antenna system.

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

• AM stereo
• Shortwave radio
• Amplitude modulation signalling system (AMSS)
• Modulation sphere
• Types of radio emissions
• Airband
• DSB-SC

References

Bibliography

• 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

• 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 including related topics of modulators, demodulators, etc...
• Analog Modulation online interactive demonstration using Python in Google Colab Platform, by C Foh.