Amplitudo Modulation

Up until now we've just considered the creation, transmission and reception of electromagnetic fields. In effect, we've seen how EM power can be carried from place to place. Now we'll look at how EM fields and waves can be used to communicate information. In general, we can represent a sinewave coherent field or wave as

where A, f, and are the amplitude, frequency, and phase of the wave. We can send information by modulating one or more of these quantities. Fields or signals modulated in these ways are — for obvious reasons — called AM (Amplitude Modulated), FM (Frequency Modulated), or PM (Phase Modulated) waves. In fact, since EM fields are vector fields we can also modulate the Polarisation of a wave to communicate information. However, polarisation modulation is only normally used for special purposes as the polarisation state of a wave can easily be ‘scrambled’ during free space transmission by effects like unwanted reflections from buildings. (The polarisation state of a field moving along a guide or fibre can also be altered by bends or imperfections in the guide/fibre.)

9.2 An Amplitude Modulation Circuit.

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We can define amplitude modulation by saying that a modulating signal , , should produce an AM wave of the form

(We'll use ‘S’ instead of ‘V’ or ‘E’ to indicate that we're talking about a modulated quantity and that it can be either a field or a voltage.) represents the ‘unmodulated amplitude’ of the wave (i.e. when ). A +ve value of makes the wave's amplitude larger, a -ve value makes its amplitude smaller. Amplitude modulation can be produced in various ways. Here we'll use the example of a Square Law FET as illustrated in figure 9.1. The steady signal, is called the carrier. This gives us something to modulate and ‘carry’ the information pattern from place to place. The frequency, f , is called the carrier frequency and is the unmodulated carrier amplitude.

A square law n-channel FET (Field Effect Transistor) will pass a drain-source current

where is the FET's pinch-off voltage and is the gate voltage. This expression is correct provided that we keep in the range, . In the circuit shown in 9.1 we apply a gate voltage which is a combination of the output from a local oscillator, , and a modulation input, , which is the information pattern we want to send from place to place. As a result, the gate voltage (assuming the two gate resistors have the same value) will be

Provided we keep this in the required range it will produce a drain-source current

where k and are constants whose values depend upon the FET we've chosen. This can be expanded and re-written as

This produces a drain voltage of

where R is the resistance between the FET's drain terminal and the bias voltage,

By consulting a book on trig we can discover that . Hence the last term in expression 9.6 is a combination of a steady current and a fluctuation at the frequency, . For simplicity we can arrange that the frequencies with which fluctuate are all . This means that the first part of the expression consists of a steady current plus some fluctuations at frequencies well below f. We can now use a bandpass filter, designed to only pass frequencies to strip away low and high frequencies and obtain an output

which we can re-write in the form

where

i.e. the output is a wave whose unmodulated amplitude is and is amplitude modulated by an amount, , proportional to the input modulating signal, . The circuit therefore behaves as an amplitude modulator.

There are various ways to measure or detect the amplitude (as opposed to the power) of a waveform. Here we'll consider one of the simplest, used by most portable radios, etc, the Envelope Detector.

This is essentially just a halfwave rectifier which charges a capacitor to a voltage to the peak voltage of the incoming AM waveform, . When the input wave's amplitude increases, the capacitor voltage is increased via the rectifying diode. When the input's amplitude falls, the capacitor voltage is reduced by being discharged by a ‘bleed’ resistor, R. The main advantage of this form of AM Demodulator is that it is very simple and cheap! Just one diode, one capacitor, and one resistor. That's why it is used so often. However, it does suffer from some practical problems.

The circuit relies upon the behaviour of the diode — allowing current through when the input is +ve with respect to the capacitor voltage, hence ‘topping up’ the capacitor voltage to the peak level, but blocking any current from flowing back out through the diode when the input voltage is below the capacitor voltage. Unfortunately, all real diodes are non-linear. The current they pass varies with the applied voltage. As a result, the demodulated output is slightly distorted in a way which depends upon the diode's I/V characteristic. For example, most AM transistor radios produce output signals (music, Radio 4, etc) with about 5-10% distortion. OK for casual listening, but hardly Hi-Fi! As a result, this simple type of AM demodulator isn't any good if we want the recovered waveform to be an accurate representation of the original modulating waveform. The circuit also suffers from the problems known as Ripple and Negative Peak Clipping. These effects are illustrated in figure 9.3. The ripple effect happens because the capacitor will be discharged a small amount in between successive peaks of the input AM wave.

The illustration shows what happens in the worst possible situation where the modulating signal is a squarewave whose frequency isn't much lower than the carrier frequency. Similar, but less severe, problems can arise with other modulating signals.

Consider what happens when we have a carrier frequency, , and use an envelope detector whose time constant, . The time between successive peaks of the carrier will be

Each peak will charge the capacitor to some voltage, , which is proportional to the modulated amplitude of the AM wave. Between each peak and the next the capacitor voltage will therefore be discharged to

which, provided that , is approximately the same as

The peak-to-peak size of the ripple, , will therefore be

A sudden, large reduction in the amplitude of the input AM wave means that capacitor charge isn't being ‘topped up’ by each cycle peak. The capacitor voltage therefore falls exponentially until it reaches the new, smaller, peak value. To assess this effect, consider what happens when the AM wave's amplitude suddenly reduces from to a much smaller value. The capacitor voltage then declines according to

This produces the negative peak clipping effect where any swift reductions in the AM wave's amplitude are ‘rounded off’ and the output is distorted. Here we've chosen the worst possible case of squarewave modulation. In practice the modulating signal is normally restricted to a specific frequency range. This limits the maximum rate of fall of the AM wave's amplitude. We can therefore hope to avoid negative peak clipping by arranging that the detector's time constant where

and is the highest modulation frequency used in a given situation.

The above implies that we can avoid negative peak clipping by choosing a small value of . However, to minimise ripple we want to make as large as possible. In practice we should therefore choose a value

to minimise the signal distortions caused by these effects. This is clearly only possible if the modulation frequency . Envelope detectors only work satisfactorily when we ensure this inequality is true.  

In general, we can imagine amplitude modulating a carrier with a modulation input

where all the modulation's frequency components, , are all within some Information bandwidth (or Modulation bandwidth), , which extends from about zero Hertz up to a maximum frequency, .

This produces an AM wave

which, after a bit of maths manipulation, can be shown to be the same as

The modulated wave is said to consist of three parts:-

• The carrier, , which is unaffected by the modulation.
• The Upper Sideband Components, , which are an ‘up converted’ copy of the original modulation spectrum.
• The Lower Sideband Components, , which are a ‘mirror image’ of the upper sideband spectrum.

This process is illustrated in figure 9.4 shown above.






The AM wave essentially carries two copies of the modulation pattern — one in each transmission sideband. As a result, it occupies a Transmission Bandwidth, . i.e. it takes up twice as much bandwidth as the original information. This represents one of the main disadvantages of AM modulation. The number of independent transmissions we can make will be limited by the range of frequencies available and how much bandwidth each transmission requires. The double sideband nature of AM halves the number of independent signals we can send using a given range of transmission frequencies.

Some transmission systems adopt a modified form of AM called Single Sideband Modulation (SSB). This is essentially an AM wave with one sideband suppressed or filtered before transmission. SSB modulated transmissions are called either Upper Sideband (USB) or Lower Sideband (LSB) depending on which sideband is used to carry the modulation information pattern. By using SSB we can double the number of transmissions which will ‘fit’ into a given transmission band. However, SSB transmitters and receivers are more complicated (and expensive!) than the simple AM circuits described earlier. Hence they tend only to be used for specialised purposes like aircraft or ship communications.

From the above arguments we can see that normal AM is prone to signal distortion and is wasteful of transmission bandspace. Another feature of AM is that it is also wasteful of power. To see why, consider what happens when the carrier is modulated by a single sinewave

where . This means that, at times, and the carrier becomes phase inverted. This process is illustrated in figure 9.5.

An envelope detector can't know that the carrier phase has been altered, hence it just responds to the +ve peaks of the inverted modulated carrier. This means it produces a distorted output whenever . A number of more complex/expensive techniques can be used to avoid this problem. In effect, better AM demodulators sense the carrier phase and take this into account. However most AM receiver systems just use the ‘cheap and cheerful’ envelope detection technique. For this reason it is usually necessary to ensure that the modulation is always limited so that — i.e., that — to avoid this problem.

For simple sinewave modulation this means that we require . This means that a sinewave modulated AM wave will have the form

Now the mean carrier power transmitted will be

where R is the impedance of the medium or system which the wave is being propagated along/through. Similarly, the combined mean power of the two sideband components will be

Since we can expect we can say that the ratio of the sideband power to the total power transmitted, , will be

i.e., the largest acceptable amount of modulation means that only one third of the total transmitted power appears in the modulation sideband components of the AM wave. Put another way, this means that at least 2/3rds of the transmitted power is devoted to sending a steady carrier wave. This power is virtually wasted. It only serves two purposes: 1) to let envelope detectors work correctly; 2) to provide a steady signal which is maintained when there is no actual modulation, confirming the existence of the transmitter!

In situations like domestic broadcasting one transmitter may serve ten million receivers. Under these circumstances the cheapness of the ten million envelope detectors can justify the waste of transmitter power. For specialised applications it may however be more sensible to use a more power efficient modulation system and a more expensive receiver. Some transmission systems therefore use a suppressed carrier method. This is similar to conventional AM or SSB, but with the carrier filtered away. The resulting transmissions are very power efficient, but require complex receivers which can be relatively difficult to tune. A particular problem of suppressed carrier systems arises when no modulation is being sent. Then there will be no sideband components. Nor will there be any carrier wave since it has been suppressed. Hence the suppressed carrier wave consists of nothing at all when there is no modulation! This certainly saves energy, but it can make it difficult to tune in a receiver correctly...

AM also suffers from being prone to interference effects. The AM demodulator essentially measures the power or amplitude of the signals presented to it. Any other power — e.g. pulses radiated by electric drills, Tornado radars, etc — can also be detected. This is why AM radio tends to suffer from buzzes, crackles, whistles, etc. Other forms of modulation can avoid this sensitivity and are less prone to unwanted interference.

Summary

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You should now know that it is possible to communicate information by Modulating a Carrier wave. That Amplitude Modulation uses variations in the carrier size to convey information. That one way of AM modulating a wave is to use a Square Law device such as an FET. That these amplitude modulations can be demodulated using an Envelope detector. You should also see why this form of detector suffers from Ripple and Negative peak clipping distortions. That the magnitude of the modulation must be limited to avoid distortions arising due to carrier phase inversion. That AM is wasteful of transmission bandwidth and transmitter power. That it is inherently sensitive to interference. That single sideband and suppressed carrier methods exist and are less wasteful of transmission bandwidth and power. That the drawback of these ‘improved’ forms of AM is that the receiver/demodulator becomes more complicated (expensive) and difficult to use. 

Amplitude-Modulation

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High Level (Plate) Amplitude Modulation

In the design of an AM transmitter there are two ways to go:   (1) The low level generation of AM (DSB + Carrier) and the progressive amplification of that RF signal with  the final stage being a Linear RF amplifier--Class AB. In the case of the low level modulation approach, one could use either a 2 quadrant or 4 quadrant multiplier as the modulator.  TOP The difference being: with the 2 quadrant multiplier, negative modulation of greater than 100% causes severe distortion as well as interference on adjacent bands. This is due to the carrier being cut off when the 2 quadrant multiplier cannot furnish any output for negative values of the modulating signals, hence the RF output becomes a pulsed spectrum. If, however, a 4 quadrant multiplier is used, negative modulation starts to appear as a double sideband suppressed carrier--or in this case, reduced carrier. (2) The second method is the progressive amplification of only the Carrier Wave with the output stage being, a more efficient, Class C (non-linear) RF amplifier; the modulation is introduced as a very high level audio signal at the final stage --more precisely, the positive plate supply of the RF "Final" Amplifier is made to vary as the modulation audio input signal.  The High Level modulation cannot handle negative modulation of greater than 100%. As with the 2 quadrant multiplier in the first approach, the carrier is cut off during negative peaks that exceed 100% negative modulation.  Most commercial AM and FM transmitter output stages--called "Finals"--use Class "C" amplifiers.  Other transmitters, like Television (visual), SSB, etc., use "Linear Amplifiers," Class AB1 or AB2, which are a combination of Class A and Class B (both being much less efficient than the Class C amplifier).

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Overmodulation as seen at the Receiver