# AM – Amplitude Modulation

## What is Modulation

Modulation is the process of modifying the characteristic of one signal in accordance with some characteristic of another signal.  In most cases, the information signal, voice, video, binary data or some other information, is normally used to modify a higher frequency signal known as carrier.  The information signal is usually called the modulating signal, and the higher frequency signal which is being modulated is called the carrier of modulated wave.  The carrier is usually a sine wave, while the information signal can be of any shape, permitting both analog and digital signals to be transmitted .  In most cases, the carrier frequency is considerably higher than the highest information frequency to be transmitted.

### Amplitude Modulation (AM) with Sine wave:

In AM, the information signal varies the amplitude of the carrier sine wave.  In other words, the instantaneous value of the carrier amplitude changes in accordance with the amplitude and frequency variation of the modulating signal.

(a). The modulating or information signal

(b) The modulated carrier

Figures (a , b)  shows a single frequency sine wave modulating a higher frequency carrier signal. Note that the carrier frequency remains constant during the modulation process but that its amplitude varies in accordance with the modulating signal.  An increase in the modulating signal amplitude causes the amplitude of the carrier to increase.  Both the positive and negative peaks of the carrier wave vary with the modulating signal.  An increase or decrease in the amplitude of the modulating signal causes a corresponding increase or decrease in both the positive and negative peaks of the carrier amplitude.

If you interconnect the positive and negative peaks of the carrier waveform with an imaginary line , the you re-create the exact shape of the modulating information signal.  This imaginary line on the carrier waveform is known as the envelope,and it is the same as the modulating signal.

Because complex waveforms like that are shown in (a, b) shown are difficult to draw, they are usually simplified by representing the high frequency carrier wave as simply many equally spaced vertical lines whose amplitude vary in accordance with a modulating signal. Figure “c” shows a sine wave tone modulating a higher-frequency carrier .

(c) A simplified method of representing an AM high-frequency sine wave

### Mathematical Representation of AM

Sinusoidal alternating current (ac) signals can be represented mathematically be trigonometric functions.  For example, we can express the sine wave carrier with the simple expression

vc = Vc sin 2Πƒct

In this expression, Vc represents the instantaneous value of the sine wave voltage at some specific time in the cycle.  The Vc represents the peak value of the sine wave as measured between zero and the maximum amplitude of either the positive or negative going alternation. The term ƒc is the frequency of the carrier sine wave.  Finally, t represents some particular point in time during the ac cycle.

In the some way, a sine wave modulating signal can also be expressed with a similar formula;

vm = Vm sin 2Πƒmt

where fm = the frequency of the modulating signal.

Referring back to figures (a, b), you can see that the modulating signal uses the peak value of the carrier rather than zero as its reference point.  The envelope of the modulating signal varies above and below the peak carrier amplitude.  That is, the zero reference line of the modulating signal coincides with the peak value of the un-modulated carrier.  Because of this, the relative amplitudes of the carrier.  If the amplitude of the modulating signal should be less than the modulating signal is greater than the amplitude of the carrier, distortion will occur.  Distortion causes incorrect information to be transmitted. It is important in AM that the peak value of the modulating signal be less than the peak value of the carrier.

Using the mathematical expression for the carrier and the modulating signal, we can create a new mathematical expression for the complete modulated wave.  First, keep in mind that the peak value of the carrier is the reference point for the modulating signal.  The modulating signal value adds to or subtracts from the peak value of the carrier.  This instantaneous value of either the top or bottom voltage envelope can be computed by the simple expression

v1 = Vc + Vm

Subtracting the trigonometric expression for vm we get

v1 = Vc + Vm sin 2Πƒmt

All this expression says is that the instantaneous value of the modulating signal algebraically adds to the peak value of the carrier.  As you can see , the value of v1 is really the envelope of the carrier wave. For that reason, we can write the instantaneous value of the complete modulated wave v2 as

v2 = v1 sin 2Πƒct

In this expression the peak value of carrier wave Vc from the first equation given is replaced by v1.  Now, substituting the previously derived expression for v1 and expanding . we get

v2 = (Vc + Vm sin 2Πƒmt) sin 2Πƒct

= Vc sin Πƒct    +   (Vm sin Πƒmt)(sin 2Πƒct)

Carrier            +  modulation    × carrier

This expression consists of two parts, the first part is simply the carrier waveform, and the second part is the carrier waveform multiplied by the modulating signal waveform.  It is this second part of the expression that is characteristic of Amplitude Modulation (AM).  A circuit must be able to produce mathematical multiplication of analog signals in order for AM to occur.

The circuit used for producing Amplitude modulation(AM)  is called modulator.  Its two inputs, the carrier and the modulating signal.

### Why Amplitude Modulation (AM) is Important:

Information signals such as voice, video, or binary data are sometimes transmitted directly from one point to another over some communications medium.  For example, voice signals are transmitted by way of wires in the telephone system.  Coaxial cables carry video signals between two points, and twisted pair cable is often used to carry binary data from one point to another in a computer network.  However,when transmission distance are far, cables are sometimes impractical.   In such cases , ratio communication is used.  To carry out reliable long distance radio communication, a high frequency signal must be used.  It is simply impractical to convert the information signal directly to electromagnetic radiation.  Excessively long antennas and interference between signals would result, if information signals were transmitted directly.  For this reason, it is desirable to translate the information signals to a point higher in the electromagnetic frequency spectrum.  It is the process of modulation that creates a higher frequency signal containing the original information.

### Amplitude Modulation Applications:

• TV picture (video)
• Aircraft
• Military communication
• Digital data transmission
• Computer Modems (used in combination with phase modulation QAM)
• NIST Time Signals

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