Amplitude modulation

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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 audio 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 the early 1900s, it was also the original method used for audio radio transmissions, and remains in use by some forms of radio communication—"AM" is often used to refer to the mediumwave broadcast band (see AM radio).

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

[edit] 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 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. 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 Telecommunications Union (ITU) designated the various types of amplitude modulation as follows:

[edit] Example

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

.

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

,

with φ its phase offset relative to c(t).

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

The formula for y(t) above may be written

The broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from ω_c, known as sidebands. For the sinusoidal signals used here, these are at ω_c + ω_m and ω_c − ω_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.

[edit] A more general example

This relies on knowledge of the Fourier Transform. 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:

.

Or, in complex form:

Taking Fourier Transforms, we get:

,

where δ(x) is the Kronecker delta function — a unit impulse at x — and capital functions indicate Fourier Transforms.

This has two components: one at positive frequencies (centered on + ω_c) and one at negative frequencies (centered on − ω_c). There is nothing mathematically wrong with negative frequencies, and they need to be considered here — otherwise one of the sidebands will be missing. Shown below is a graphical representation of the above equation. It shows the modulating signal's spectrum on top, followed by the full spectrum of the modulated signal.

The (2-sided) spectrum of an AM signal.

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 frequency division multiplexing), then their carrier signals must be sufficiently separated that their spectra do not overlap. This analysis also shows that the transmission bandwidth of AM is twice the signal's original (baseband) bandwidth — since both the positive and negative sidebands are 'copied' up to the carrier frequency, but only the positive sideband is present originally. Thus, double-sideband AM (DSB-AM) is spectrally inefficient. The various suppression methods in Forms of AM, can be seen clearly in the figure — 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 — a significant improvement in spectrum usage.

An analysis of the power consumption of AM reveals that DSB-AM with its carrier has an efficiency of about 33% — 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.

[edit] 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:

.

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.

[edit] Amplitude modulator designs

[edit] 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.

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.

[edit] 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 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.

[edit] 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 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.

[edit] See also

• AM radio also referred to as Mediumwave
• Frequency modulation the replacer
• Shortwave radio almost universally uses AM modulation, narrow FM occurring above 25 MHz.
• Modulation, for a list of other modulation techniques
• AMSS Amplitude Modulation Signalling System, 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

[edit] 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.