# Amplitude modulation

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### Amplitude modulation

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 the signal strength can be used to reflect the sounds to be reproduced by a speaker, or to specify the light intensity of television pixels. (Contrast this with frequency modulation, also commonly used for sound transmissions, in which the frequency is varied; and phase modulation, often used in remote controls, 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).

### Forms of amplitude modulation

As originally developed for the electric telephone, amplitude modulation was used to add audio information to the low-powered direct current flowing from a telephone transmitter to a receiver. As a simplified explanation, at the transmitting end, a telephone microphone was used to vary the strength of the transmitted current, according to the frequency and loudness of the sounds received. Then, at the receiving end of the telephone line, the transmitted electrical current affected an electromagnet, which strengthened and weakened in response to the strength of the current. In turn, the electromagnet produced vibrations in the receiver diaphragm, thus closely reproducing the frequency and loudness of the sounds originally heard at the transmitter.

In contrast to the telephone, in radio communication what is modulated is a continuous wave radio signal (carrier wave) produced by a radio transmitter. In its basic form, amplitude modulation produces a signal with power concentrated at the carrier frequency and in two adjacent sidebands. This process is known as heterodyning. Each sideband is equal in bandwidth to that of the modulating signal and is a mirror image of the other. Amplitude modulation that results in two sidebands and a carrier is often called double sideband amplitude modulation (DSB-AM). Amplitude modulation is inefficient in terms of power usage and much of it is wasted. 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); the remaining power is split between two identical sidebands, though only one of these is needed since they contain identical information.

To increase transmitter efficiency, the carrier can be removed (suppressed) from the AM signal. This produces a reduced-carrier transmission or double-sideband suppressed-carrier (DSBSC) signal. A suppressed-carrier amplitude modulation scheme is three times more power-efficient than traditional DSB-AM. If the carrier is only partially suppressed, a double-sideband reduced-carrier (DSBRC) signal results. DSBSC and DSBRC signals need their carrier to be regenerated (by a beat frequency oscillator, for instance) to be demodulated using conventional techniques.

Even greater 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 due to its efficient use of both power and bandwidth.

A simple form of AM often used for digital communications is on-off keying, a type of amplitude-shift keying by which binary data is represented as the presence or absence of a carrier wave. This is commonly used at radio frequencies to transmit Morse code, referred to as continuous wave (CW) operation.

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

Designation

Description

A3E

double-sideband full-carrier - the basic AM 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

### Example: double-sideband AM

A carrier wave is modeled as a simple sine wave, such as:

c(t) = C\cdot \sin(\omega_c t + \phi_c),\,

where the radio frequency (in Hz) is given by: \omega_c / (2\pi).\,

For generality, C\,and \phi_c\,are arbitrary constants that represent the carrier amplitude and initial phase. For simplicity, we set their respective values 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. For instance:

m(t) = M\cdot \cos(\omega_m t + \phi).\,

Thus, the message might be just a simple audio tone of frequency \omega_m / (2\pi).\,

It is generally assumed that \omega_m \ll \omega_c\, and that \min[ m(t) ] = -M.\,

Then amplitude modulation is created by forming the product:

y(t)\,

= [A + m(t)]\cdot c(t),\,

= [A + M\cdot \cos(\omega_m t + \phi)]\cdot \sin(\omega_c t).

A\,represents another constant we may choose. The values A=1, and M=0.5, produce a y(t) depicted by the graph labelled "50% Modulation" in 4.

For this simple example, y(t) can be trigonometrically manipulated into the following equivalent form:

y(t) = A\cdot \sin(\omega_c t) + \begin{matrix}\frac{M}{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 \omega_c.\,

Also notice that the choice A=0 eliminates the carrier component, but leaves the sidebands. That is the DSBSC transmission mode. To generate double-sideband full carrier (A3E), we must choose: A \ge M.\,

For more general forms of m(t), trigonometry is not sufficient. But if the top trace of 2 depicts the frequency spectrum, of m(t), then the bottom trace depicts the modulated carrier. It has two groups of components: one at positive frequencies (centered on + ωc) and one at negative frequencies (centered on − ωc). Each group contains the two sidebands and a narrow component in between that represents the energy at the carrier frequency. We need only be concerned with the positive frequencies. The negative ones are a mathematical artifact that contains no additional information. Therefore, we see that an AM signal's spectrum consists basically of its original (2-sided) spectrum shifted up to the carrier frequency.

For those interested in the mathematics of 2, it is a result of computing the Fourier transform of: [A + m(t)]\cdot \sin(\omega_c t),\,using the following transform pairs:

\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 \sin(\omega_c t) \quad \stackrel{\mathcal{F}}{\Longleftrightarrow}& \frac{1}{2\pi}\cdot \{M(\omega)\} * \{i \pi \cdot [\delta(\omega +\omega_c)-\delta(\omega-\omega_c)]\} \\ =& \frac{i}{2}\cdot [M(\omega +\omega_c) - M(\omega -\omega_c)] \end{align}

In terms of the positive frequencies, the transmission bandwidth of AM is twice the signal's original (baseband) bandwidth—since both the positive and negative sidebands are shifted up to the carrier frequency. Thus, double-sideband AM (DSB-AM) is spectrally inefficient, meaning that fewer radio stations can be accommodated in a given broadcast band. The various suppression methods in Forms of AM can be readily understood in terms of the diagram in 2. With the carrier suppressed there would be no energy at the center of a group. And with a sideband suppressed, the "group" would have the same bandwidth as the positive frequencies of M(\omega).\, The transmitter power efficiency of DSB-AM is relatively poor (about 33%). The benefit of this system is that receivers are cheaper to produce. The forms of AM with suppressed carriers are found to be 100% power efficient, since no power is wasted on the carrier signal which conveys no information.

### Modulation index

As with other modulation indices, in AM, this quantity, also called modulation depth, indicates by how much the modulated variable varies around its 'original' level. For AM, it relates to the variations in the carrier amplitude and is defined as:

h = \frac{\mathrm{peak\ value\ of\ } m(t)}{A} = \frac{M}{A}, where M\,and A\,were introduced above.

So if h = 0.5, the carrier amplitude varies by 50% above and below its unmodulated level, and for h = 1.0 it varies by 100%. To avoid distortion in the A3E transmission mode, modulation depth greater than 100% must be avoided. Practical transmitter systems will usually incorporate some kind of limiter circuit, such as a VOGAD, to ensure this.

Variations of modulated signal with percentage 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.

### Circuits

A wide range of different circuits have been used for AM, but one of the simplest circuits uses anode or collector modulation applied via a transformer. While it is perfectly possible to create good designs using solid-state electronics, valved (vacuum tube) circuits are shown here. In general, valves are able to more easily yield RF powers, in excess of what can be easily achieved using solid-state transistors. Most high-power broadcast stations still use valves.

Anode modulation using a transformer. The tetrode is supplied with an anode supply (and screen grid supply) which is modulated via the transformer. The resistor R1 sets the grid bias; both the input and outputs are tuned LC circuits which are tapped into by inductive coupling

Modulation circuit designs can be broadly divided into low and high level.

### Low level

Here a small audio stage is used to modulate a low power stage; the output of this stage is then amplified using a linear RF amplifier.

The advantage of using a linear RF amplifier is that the smaller early stages can be modulated, which only requires a small audio amplifier to drive the modulator.

The great disadvantage of this system is that the amplifier chain is less efficient, because it has to be linear to preserve the modulation. Hence Class C amplifiers cannot be employed.

An approach which marries the advantages of low-level modulation with the efficiency of a Class C power amplifier chain is to arrange a feedback system to compensate for the substantial distortion of the AM envelope. A simple detector at the transmitter output (which can be little more than a loosely coupled diode) recovers the audio signal, and this is used as negative feedback to the audio modulator stage. The overall chain then acts as a linear amplifier as far as the actual modulation is concerned, though the RF amplifier itself still retains the Class C efficiency. This approach is widely used in practical medium power transmitters, such as AM radiotelephones.

### High level

With high level modulation, the modulation takes place at the final amplifier stage where the carrier signal is at its maximum

One advantage of using class C amplifiers in a broadcast AM transmitter is that only the final stage needs to be modulated, and that all the earlier stages can be driven at a constant level. These class C stages will be able to generate the drive for the final stage for a smaller DC power input. However, in many designs in order to obtain better quality AM the penultimate RF stages will need to be subject to modulation as well as the final stage.

A large audio amplifier will be needed for the modulation stage, at least equal to the power of the transmitter output itself. Traditionally the modulation is applied using an audio transformer, and this can be bulky. Direct coupling from the audio amplifier is also possible (known as a cascode arrangement), though this usually requires quite a high DC supply voltage (say 30 V or more), which is not suitable for mobile units.

* Frequency modulation

* Shortwave radio almost universally uses AM, narrow FM occurring above 25MHz.

* 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

### References

* 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.

Principle of PAM; (1) original Signal, (2) PAM-Signal, (a) Amplitude of Signal, (b) Time

### Overview

Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. Example: A two bit modulator (PAM-4) will take two bits at a time and will map the signal amplitude to one of four possible levels, for example −3 volts, −1 volt, 1 volt, and 3 volts. Demodulation is performed by detecting the amplitude level of the carrier at every symbol period. Pulse-amplitude modulation is widely used in baseband transmission of digital data, with non-baseband applications having been largely superseded by pulse-code modulation, and, more recently, by pulse-position modulation.

In particular, all telephone modems faster than 300 bit/s use quadrature amplitude modulation (QAM). (QAM uses a two-dimensional constellation).

### Usage of Pulse-amplitude modulation in Ethernet

It should be noted, however, that some versions of the widely popular Ethernet communication standard are a good example of PAM usage. In particular, the Fast Ethernet 100BASE-T2 medium, running at 100Mb/s, utilizes 5 level PAM modulation (PAM-5) running at 25 megapulses/sec over two wire pairs. A special technique is used to reduce inter-symbol interference between the unshielded pairs. Later, the gigabit Ethernet 1000BASE-T medium raised the bar to use 4 pairs of wire running each at 125 megapulses/sec to achieve 1000Mb/s data rates, still utilizing PAM-5 for each pair.

The IEEE 802.3an standard defines the wire-level modulation for 10GBASE-T as a Tomlinson-Harashima Precoded (THP) version of pulse-amplitude modulation with 16 discrete levels (PAM-16), encoded in a two-dimensional checkerboard pattern known as DSQ128. Several proposals were considered for wire-level modulation, including PAM with 12 discrete levels (PAM-12), 10 levels (PAM-10), or 8 levels (PAM-8), both with and without Tomlinson-Harashima Precoding (THP).
amplitude modulation

### DEFINITION- Also see modulation.

Amplitude modulation (AM) is a method of impressing data onto an alternating-current (AC) carrier waveform.The highest frequency of the modulating data is normally less than 10 percent of the carrier frequency.The instantanous amplitude (overall signal power) varies depending on the instantaneous amplitude of the modulating data.

In AM, the carrier itself does not fluctuate in amplitude.Instead, the modulating data appears in the form of signal components at frequencies slightly higher and lower than that of the carrier.These components are called sidebands. The lower sideband (LSB) appears at frequencies below the carrier frequency; the upper sideband (USB) appears at frequencies above the carrier frequency.The LSB and USB are essentially "mirror images" of each other in a graph of signal amplitude versus frequency, as shown in the illustration.The sideband power accounts for the variations in the overall amplitude of the signal.

When a carrier is amplitude-modulated with a pure sine wave, up to 1/3 (33 percent) of the overall signal power is contained in the sidebands.The other 2/3 of the signal power is contained in the carrier, which does not contribute to the transfer of data.With a complex modulating signal such as voice, video, or music, the sidebands generally contain 20 to 25 percent of the overall signal power; thus the carrier consumes 75 to 80 percent of the power.This makes AM an inefficient mode.If an attempt is made to increase the modulating data input amplitude beyond these limits, the signal will become distorted, and will occupy a much greater bandwidth than it should.This is called overmodulation, and can result in interference to signals on nearby frequencies.

### Analog modulation methods

A low-frequency message signal (top) may be carried by an AM or FM radio wave. Common analog modulation techniques are:

* Amplitude modulation (AM) (here the amplitude of the carrier signal is varied in accordance to the instantaneous amplitude of the modulating signal)

o Double-sideband modulation (DSB)

§ Double-sideband modulation with unsuppressed carrier (DSB-WC) (used on the AM radio broadcasting band)

§ Double-sideband suppressed-carrier transmission (DSB-SC)

§ Double-sideband reduced carrier transmission (DSB-RC)

o Single-sideband modulation (SSB, or SSB-AM),

§ SSB with carrier (SSB-WC)

§ SSB suppressed carrier modulation (SSB-SC)

o Vestigial sideband modulation (VSB, or VSB-AM)

* Angle modulation

o Frequency modulation (FM) (here the frequency of the carrier signal is varied in accordance to the instantaneous frequency of the modulating signal)

o Phase modulation (PM) (here the phase shift of the carrier signal is varied in accordance to the instantaneous phase shift of the modulating signal)

### How it works.

We know that something as simple as a crystal diode (rectifier) can be used to capture sound from the air and put it into a pair of earphones or an amplifier and speaker. How can this work? We will cover that here and now. All AM (Amplitude Modulation) detectors work basically the same way.

### What is AM?

What we can hear as audio is classically considered to be the frequency range between 20 and 20,000 cycles per second (here after referred to as "cycles" and abandoning "hertz") which I have never liked). In reality most adults can only hear up to about 13,000 cycles. Most speakers can't reproduce anything lower than 30 cycles in spite of the exaggerated claims of proud owners. So let's be generous and call audio 30 to 15,000 cycles.

Radio frequencies are between 8,000 cycles and 50,000 megacycles. That's right there is a range of frequencies that depending on how they are treated can be audio or radio. The AM radio band begins at 540 kilocycles.

For simplicity let's say that we want to transmit a 10,000 cycle tone on a radio transmitter operating on 250 kilocycles.

The 250 kc transmitting frequency is called the carrier wave because it may be thought of as carrying the audio.

The 10,000 cycle audio frequency is called the modulating frequency. We may get into side-bands later.

In the above the upper wave is the modulating wave and three cycles of it can be seen. The lower wave is the modulated carrier wave and 75 cycles are visible. (You can count them for yourself or take my word for it.)

Notice as the modulating wave goes up the total amplitude of the carrier wave (measured from negative peak to positive peak) goes up. As the modulating wave goes down the amplitude of the carrier wave goes down. When the modulating wave is at zero (the point where it begins and ends) the carrier wave is at its middle or unmodulated value. Think of the modulating wave as controlling a valve that the carrier wave is passing through. (I have direct conformation from England, that's why the British call tubes valves.)

The carrier wave can then be sent to an antenna which radiates it out for all the world to hear.

### Detecting the signal

Detection is the word applied to the process of recovering the audio frequencies from the radio frequency carrier. In the case of amplitude modulation it is very simple. All we need to do is to rectify the signal. Rectification is the process used in power supplies to change AC to DC. It's really quite similar for detecting radio signals. Compare the carrier wave in the below with the one in the above.

The wave has been run through a rectifier which removed the bottom half of every cycle. If we draw a line connecting the peaks we have the original modulating signal back again. Connecting the peaks is done by using a capacitor to charge up to the peak value and discharge through a resistor just fast enough to follow the modulating frequency but not so fast as to cause a large variation at the carrier frequency.

The frequencies chosen for this drawing are fairly close together to make it possible to see the individual cycles on your computer screen. When dealing with the AM broadcast band the carrier frequencies range from 540 kc to 1600 kc. 10,000 cycles is the absolute upper limit for audio on AM and most transmitters only make it to about 8,000 cycles.

Look back at the diagram of the crystal set. Use your back button to return here. If you are familiar with power supply circuits you will recognize it as a half wave rectifier with a capacitor to filter out ripple. The resistor makes the capacitor discharge just fast enough but not too fast.

A much more rigorous discussion of AM, including side bands, is available by clicking here. This includes not only AM but SSB and FM.

### AMPLITUDE MODULATION

Amplitude modulation or AM as it is often called, is a form of modulation used for radio transmissions for broadcasting and two way radio communication applications. Although one of the earliest used forms of modulation it is still in widespread use today.

The first amplitude modulated signal was transmitted in 1901 by a Canadian engineer named Reginald Fessenden. He took a continuous spark transmission and placed a carbon microphone in the antenna lead. The sound waves impacting on the microphone varied its resistance and in turn this varied the intensity of the transmission. Although very crude, signals were audible over a distance of a few hundred metres, although there was a rasping sound caused by the spark.

With the introduction of continuous sine wave signals, transmissions improved significantly, and AM soon became the standard for voice transmissions. Nowadays, amplitude modulation, AM is used for audio broadcasting on the long medium and short wave bands, and for two way radio communication at VHF for aircraft. However as there now are more efficient and convenient methods of modulating a signal, its use is declining, although it will still be very many years before it is no longer used.

### What is amplitude modulation?

In order that a radio signal can carry audio or other information for broadcasting or for two way radio communication, it must be modulated or changed in some way. Although there are a number of ways in which a radio signal may be modulated, one of the easiest, and one of the first methods to be used was to change its amplitude in line with variations of the sound.

The basic concept surrounding what is amplitude modulation, AM, is quite straightforward. The amplitude of the signal is changed in line with the instantaneous intensity of the sound. In this way the radio frequency signal has a representation of the sound wave superimposed in it. In view of the way the basic signal "carries" the sound or modulation, the radio frequency signal is often termed the "carrier".

### Amplitude Modulation, AM

When a carrier is modulated in any way, further signals are created that carry the actual modulation information. It is found that when a carrier is amplitude modulated, further signals are generated above and below the main carrier. To see how this happens, take the example of a carrier on a frequency of 1 MHz which is modulated by a steady tone of 1 kHz.

The process of modulating a carrier is exactly the same as mixing two signals together, and as a result both sum and difference frequencies are produced. Therefore when a tone of 1 kHz is mixed with a carrier of 1 MHz, a "sum" frequency is produced at 1 MHz + 1 kHz, and a difference frequency is produced at 1 MHz - 1 kHz, i.e. 1 kHz above and below the carrier.

If the steady state tones are replaced with audio like that encountered with speech of music, these comprise many different frequencies and an audio spectrum with frequencies over a band of frequencies is seen. When modulated onto the carrier, these spectra are seen above and below the carrier.

It can be seen that if the top frequency that is modulated onto the carrier is 6 kHz, then the top spectra will extend to 6 kHz above and below the signal. In other words the bandwidth occupied by the AM signal is twice the maximum frequency of the signal that is used to modulated the carrier, i.e. it is twice the bandwidth of the audio signal to be carried.

### Amplitude demodulation

Amplitude modulation, AM, is one of the most straightforward ways of modulating a radio signal or carrier. The process of demodulation, where the audio signal is removed from the radio carrier in the receiver is also quite simple as well. The easiest method of achieving amplitude demodulation is to use a simple diode detector. This consists of just a handful of components:- a diode, resistor and a capacitor.

### AM Diode Detector

In this circuit, the diode rectifies the signal, allowing only half of the alternating waveform through. The capacitor is used to store the charge and provide a smoothed output from the detector, and also to remove any unwanted radio frequency components. The resistor is used to enable the capacitor to discharge. If it were not there and no other load was present, then the charge on the capacitor would not leak away, and the circuit would reach a peak and remain there.

### Advantages of Amplitude Modulation, AM

There are several advantages of amplitude modulation, and some of these reasons have meant that it is still in widespread use today:

* It is simple to implement

* it can be demodulated using a circuit consisting of very few components

* AM receivers are very cheap as no specialised components are needed.