Amplitude modulation
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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).
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Applications in radio
Image:Amplitude-modulation.png
A basic AM radio transmitter works by first DC-shifting the modulating signal, then multiplying it with the carrier wave using a frequency mixer. The output of this process is a signal with the same frequency as the carrier but with peaks and troughs that vary in proportion to the strength of the modulating signal. This is amplified and fed to an antenna.
AM vs. FM
AM radio's main limitation is its susceptibility to atmospheric interference, which is heard as static from the receiver. The narrow bandwidth traditionally used for AM broadcasts further limits the quality of sound that can be received. Since the 1970s, wideband FM has been preferred for musical broadcasts, due to its higher audio fidelity and noise-suppression characteristics.
The fact that signals can be decoded using very simple equipment is one of the primary advantages of amplitude modulation. This was especially important in the early days of commercial radio, when electronic components were still quite expensive. This simplicity and affordability helped make AM one of the most popular methods for sending voice and music over radio during the 20th century.
An AM receiver consists primarily of a tunable filter and an envelope detector, which in simpler sets is a single diode. Its output is a signal at the carrier frequency, with peaks that trace the amplitude of the unmodulated signal. Unlike other modulation techniques, this is all that is needed to recover the original audio. In practice, a capacitor is used to undo the DC shift introduced by the transmitter and to eliminate the carrier frequency by connecting the signal peaks. The output is then fed to an audio amplifier.
To make a good AM receiver an automatic gain control loop is essential; this requires good design. To make a good FM receiver a large number of RF amps which are driven into limiting are required to create a receiver which can take advantage of the capture effect, one of the biggest advantages of FM. With valved (tube) systems it is more expensive to make active stages than it is to make the same number of stages with solid state parts, so for a valved superhet it is simpler to make an AM receiver with the automatic gain control loop while for a solid state receiver it is simpler to make an FM unit. Hence even while the idea of FM was known before WWII its use was rare because of the cost of valves - in the UK the government had a valve holder tax Template:Fact which encouraged radio receiver designers to use as few active stages as possible, - but when solid state parts became available FM started to gain favour.
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.
Example
Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency <math>\omega_c</math>, taking its phase to be a reference phase of zero, is
- <math>c(t) = C \sin(\omega_c t)</math>.
The equation for the simple sine wave of frequency <math>\omega_m</math> (the signal we wish to broadcast) is
- <math>m(t) = M \sin(\omega_m t + \phi)</math>,
with <math>\phi</math> its phase offset relative to <math>c(t)</math>.
Amplitude modulation is performed simply by adding <math>m(t)</math> to <math>C</math>. The amplitude-modulated signal is then
- <math>y(t) = (C + M \sin(\omega_m t + \phi)) \sin(\omega_c t)</math>
The formula for <math>y(t)</math> above may be written
- <math>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}</math>
The broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from <math>\omega_c</math>, known as sidebands. For the sinusoidal signals used here, these are at <math>\omega_c + \omega_m</math> and <math>\omega_c - \omega_m</math>. 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 Fourier Transform. The discussion of the figure may prove more useful for a quicker understanding.
Consider a general modulating signal <math>m(t)</math>, which can now be anything at all. The same basic rules apply:
- <math>\,y(t) = [C + m(t)]\cos(\omega_c t)</math>.
Or, in complex form:
- <math>y(t) = [C + m(t)]\frac{e^{j\omega_c t} + e^{-j\omega_c t}}{2}</math>
Taking Fourier Transforms, we get:
- <math>|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)</math>,
where <math>\delta(x)</math> is the Dirac delta function — a unit impulse at <math>x</math> — and capital functions indicate Fourier Transforms.
This has two components: one at positive frequencies (centered on <math>+\omega_c</math>) and one at negative frequencies (centered on <math>-\omega_c</math>). 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.
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 (DS-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 DS-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.
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:
- <math>h = \frac{\mathrm{peak\ value\ of\ } m(t)}{C}</math>.
So if <math>h=0.5</math>, the carrier amplitude varies by 50% above and below its unmodulated level, and for <math>h=1.0</math> 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.
See also
- AM radio also referred to as Mediumwave
- 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.
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.de:Amplitudenmodulation
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