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.

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 (**F**ield **E**ffect **T**ransistor) 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.

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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.