Amplitude modulation

Amplitude modulation (AM) is a form of modulation in which the amplitude of a carrier wave is varied in direct proportion to that of a modulating signal. (Contrast this with frequency modulation, in which the frequency of the carrier is varied; and phase modulation, in which the phase is varied.)

AM is commonly used at radio frequencies and was the first method used to broadcast commercial radio. The term "AM" is sometimes used generically to refer to the AM broadcast (mediumwave) band (see AM radio).

Forms of AM

In its basic form, amplitude modulation produces a signal with power concentrated at the carrier frequency and in two adjacent sidebands. Each sideband is equal in bandwidth 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 reduced-carrier transmission 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 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 Telecommunications 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	linked compressor and expander

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.

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)}{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 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.

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 transformer. While it is perfectly possible to create good designs using solid-state electronics, valved (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 audio stage is used to modulate a low power stage, the output of this stage is then amplified using a linear 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 audio amplifier to drive the modulator.

Disadvantages

The great disadvantage of this system is that the amplifer 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

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 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.

Disadvantages

A large audio amplifer 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 30V or more), which is not suitable for mobile units.

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.

Radio modulation modes

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