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PowerPedia:Amplitude modulation

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Amplitude modulation (AM) is a technique used in electronics, most commonly for transmission via a There was an error working with the wiki: Code[23] wirelessly.

Introduction

Amplitude modulation 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 sounds being reproduced for a speaker or light intensity for a television pixel. (Contrast this with There was an error working with the wiki: Code[4] is varied.)

In the mid-1870s, a form of amplitude modulation&mdashinitially called "undulatory currents"&mdashwas the first method to successfully produce quality over lines. Beginning in the early 1900s, it was also the original method used for radio transmissions, and remains in use by some forms of radio communication&mdash"AM" is often used to refer to the There was an error working with the wiki: Code[5] (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 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 There was an error working with the wiki: Code[24] radio signal (There was an error working with the wiki: Code[25]) 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 There was an error working with the wiki: Code[26]s. Each sideband is equal in There was an error working with the wiki: Code[27] to that of the modulating signal and is a mirror image of the other. Thus, most of the power output by an AM transmitter is effectively wasted: half the power is concentrated at the carrier frequency, which carries no useful information (beyond the fact that a signal is present) the remaining power is split between two identical sidebands, only one of which is needed.

To increase transmitter efficiency, the carrier can be removed (suppressed) from the AM signal. This produces a There was an error working with the wiki: Code[28] or double-sideband suppressed carrier (DSBSC) signal. 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 There was an error working with the wiki: Code[29], for instance) to be demodulated using conventional techniques.

Even greater efficiency is achieved&mdashat the expense of increased transmitter and receiver complexity&mdashby completely suppressing both the carrier and one of the sidebands. This is There was an error working with the wiki: Code[30], widely used in Amateur radio due to its efficient use of both power and bandwidth.

A simple form of AM often used for There was an error working with the wiki: Code[6] data is represented as the presence or absence of a carrier wave. This is commonly used at radio frequencies to transmit There was an error working with the wiki: Code[31], referred to as There was an error working with the wiki: Code[32] (CW) operation.

In 1982, the There was an error working with the wiki: Code[33] (ITU) designated the various types of amplitude modulation as follows:

{|class="wikitable"

|-

!Designation!!Description

|-

|A3E||There was an error working with the wiki: Code[34] full carrier - the basic AM modulation scheme

|-

|R3E||There was an error working with the wiki: Code[7] There was an error working with the wiki: Code[8]

|-

|H3E||There was an error working with the wiki: Code[9] full carrier

|-

|J3E||There was an error working with the wiki: Code[10]

|-

|B8E||There was an error working with the wiki: Code[35] emission

|-

|C3F||There was an error working with the wiki: Code[36]

|-

|Lincompex||linked There was an error working with the wiki: Code[11]

|}

Example

Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency \omega_c, taking its phase to be a reference phase of zero, is

:c(t) = C \sin(\omega_c t).

The equation for the simple sine wave of frequency \omega_m (the signal we wish to broadcast) is

:m(t) = M \sin(\omega_m t + \phi),

with \phi its phase offset relative to c(t).

Amplitude modulation is performed simply by adding m(t) to C. The amplitude-modulated signal is then

:y(t) = (C + M \sin(\omega_m t + \phi)) \sin(\omega_c t)

The formula for y(t) above may be written

:y(t) = C \sin(\omega_c t) + M \frac{\cos(\phi + (\omega_m - \omega_c) t)}{2} - M \frac{\cos(\phi + (\omega_m + \omega_c) t)}{2}

The broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from \omega_c, known as sidebands. For the sinusoidal signals used here, these are at \omega_c + \omega_m and \omega_c - \omega_m. As long as the broadcast (carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap, stations will not interfere with one another.

A more general example

:This relies on knowledge of the There was an error working with the wiki: Code[37]. The discussion of the figure may prove more useful for a quicker understanding.

Consider a general modulating signal m(t), which can now be anything at all. The same basic rules apply:

:\,y(t) = [C + m(t)]\cos(\omega_c t).

Or, in There was an error working with the wiki: Code[38] form:

:y(t) = [C + m(t)]\frac{e^{j\omega_c t} + e^{-j\omega_c t}}{2}

Taking Fourier Transforms, we get:

:|Y(\omega)| = \pi{}C\delta(\omega - \omega_c) + \frac{1}{2}M(\omega - \omega_c) + \pi{}C\delta(\omega + \omega_c) + \frac{1}{2}M(\omega + \omega_c),

where \delta(x) is the There was an error working with the wiki: Code[12] There was an error working with the wiki: Code[39] &mdash a unit impulse at x &mdash and capital functions indicate Fourier Transforms.

This has two components: one at positive Frequency (centered on +\omega_c) and one at There was an error working with the wiki: Code[13] (centered on -\omega_c). There is nothing mathematically wrong with negative frequencies, and they need to be considered here &mdash otherwise one of the sidebands will be missing. Shown below is a graphical representation of the above equation. It shows the modulating signal's There was an error working with the wiki: Code[14] on top, followed by the full spectrum of the modulated signal.

There was an error working with the wiki: Code[2]

This makes clear the two sidebands that this modulation method yields, as well as the carrier signals that go with them. The carrier signals are the impulses. Clearly, an AM signal's spectrum consists of its original (2-sided) spectrum shifted up to the carrier frequency. The negative frequencies are a mathematical nicety, but are essential since otherwise we would be missing the lower sideband in the original spectrum!

As already mentioned, if multiple signals are to be transmitted in this way (by There was an error working with the wiki: Code[15], can be seen clearly in the figure &mdash with the carrier suppressed there will be no impulses and with a sideband suppressed, the transmission bandwidth is reduced back to the original, baseband, bandwidth &mdash a significant improvement in spectrum usage.

An analysis of the power consumption of AM reveals that DS-AM with its carrier has an efficiency of about 33% &mdash very poor. 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 There was an error working with the wiki: Code[16], 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)}{C}.

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%. Modulation depth greater than 100% is generally to be avoided - practical transmitter systems will usually incorporate some kind of limiter circuit, such as a There was an error working with the wiki: Code[40], 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.

There was an error working with the wiki: Code[3]

Amplitude modulator designs

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 There was an error working with the wiki: Code[17] (tube) circuits are shown here. In general, valves are able to easily yield RF powers far in excess of what can be achieved using solid state. Most high-power broadcast stations still use valves. Modulation circuit designs can be broadly divided into low and high level.

Low level

Here a small There was an error working with the wiki: Code[18] stage is used to There was an error working with the wiki: Code[19] a low power stage, the output of this stage is then amplified using a There was an error working with the wiki: Code[20] RF amplifier.

Advantages

The advantage of using a linear RF amplifier is that the smaller early stages can be modulated, which only requires a small There was an error working with the wiki: Code[41] to drive the modulator.

Disadvantages

The great disadvantage of this system is that the amplifer chain is less There was an error working with the wiki: Code[21], because it has to be linear to preserve the modulation. Hence There was an error working with the wiki: Code[22] 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 There was an error working with the wiki: Code[42]) recovers the audio signal, and this is used as There was an error working with the wiki: Code[43] 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 There was an error working with the wiki: Code[44]s.

High level

Advantages

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 Direct current 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.

Disadvantages

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. There was an error working with the wiki: Code[45] from the audio amplifier is also possible (known as a There was an error working with the wiki: Code[46] arrangement), though this usually requires quite a high DC supply voltage (say 30V or more), which is not suitable for mobile units.

Related

AM radio also referred to as There was an error working with the wiki: Code[47]

There was an error working with the wiki: Code[48] almost universally uses AM modulation, narrow FM occurring above 25 MHz.

There was an error working with the wiki: Code[49], for a list of other modulation techniques

There was an error working with the wiki: Code[50] Amplitude Modulation Signalling System, a digital system for adding low bitrate information to an AM signal.

There was an error working with the wiki: Code[51], for some explanation of what this is.

There was an error working with the wiki: Code[52], for the emission types designated by the There was an error working with the wiki: Code[53]

References

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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&ndash15.36. Newington: ARRL. ISBN 0-87259-196-4.

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

See also

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