# Amplitude Modulation Concepts

## What Is Amplitude Modulation?

As the name suggests, in AM, the information signal varies the amplitude of the carrier sine wave. The instantaneous value of the carrier amplitude changes in accordance with the amplitude and frequency variations of the modulating signal. Fig. 3-1 shows a  single frequency sine wave intelligence signal modulating a higher-frequency carrier.

The carrier frequency remains constant during the modulation process, but its amplitude varies in accordance with the modulating signal. An increase in the amplitude of the modulating signal causes the amplitude of the carrier to increase. Both the positive and the negative peaks of the carrier wave vary with the modulating signal.

An increase or a decrease in the amplitude of the modulating signal causes a corresponding increase or decrease in both the positive and the negative peaks of the carrier amplitude. An imaginary line connecting the positive peaks and negative peaks of the carrier waveform (the dashed line in Fig. 3-1) gives the exact shape of the modulating information signal. This imaginary line on the carrier waveform is known as the envelope.

Because of complex waveforms such as that shown in Fig. 3-1 are difficult to draw, they are often simplified by representing the high-frequency carrier wave as many equally spaced vertical lines whose amplitudes vary in accordance with a modulating signal, as in Fig. 3-2. This method of representation is used throughout this book. The signals illustrated in Figs. 3-1 and 3-2 show the variation of the carrier amplitude with respect to time and are said to be in the time domain. Time-domain signals— voltage or current variations that occur over time—are displayed on the screen of an oscilloscope. Using trigonometric functions, we can express the sine wave carrier with the simple expression

In this expression, υc represents the instantaneous value of the carrier sine wave voltage at some specific time in the cycle; Vc represents the peak value of the constant unmodulated carrier sine wave as measured between zero and the maximum amplitude of either the positive-going or the negative-going alternations (Fig. 3-1); fc is the frequency of the carrier sine wave, and t is a particular point in time during the carrier cycle. A sine wave modulating signal can be expressed with a similar formula

where υm = instantaneous value of information signal
Vm = peak amplitude of information signal
fm = frequency of modulating signal

In Fig. 3-1, 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 unmodulated carrier. Because of this, the relative amplitudes of the carrier and modulating signal are important.

In general, the amplitude of the modulating signal should be less than the amplitude of the carrier. When the amplitude of the modulating signal is greater than the amplitude of the carrier, distortion will occur, causing incorrect information to be transmitted. In amplitude modulation, it is particularly important that the peak value of the modulating signal be less than the peak value of the carrier. Mathematically,

Vm < Vc

Values for the carrier signal and the modulating signal can be used in a formula to express the complete modulated wave. First, keep in mind that the peak value of the carrier is the reference point for the modulating signal; the value of the modulating signal is added to or subtracted from the peak value of the carrier. The instantaneous value of either the top or the bottom voltage envelope υ1 can be computed by using the equation

which expresses the fact that the instantaneous value of the modulating signal algebraically adds to the peak value of the carrier. Thus, we can write the instantaneous value of the complete modulated wave υ2 by substituting υ1 for the peak value of carrier voltage Vc as follows:

Now substituting the previously derived expression for v1 and expanding, we get the following:

where υ2 is the instantaneous value of the AM wave (or υAM), Vc sin 2πfct is the carrier waveform, and (Vm sin 2πfmt) (sin 2πfct) is the carrier waveform multiplied by the modulating signal waveform. It is the second part of the expression that is characteristic of AM. A circuit must be able to produce mathematical multiplication of the carrier and modulating signals in order for AM to occur. The AM wave is the product of the carrier and modulating signals.

The circuit used for producing AM is called a modulator. Its two inputs, the carrier, and the modulating signal, and the resulting outputs are shown in Fig. 3-3. Amplitude modulators compute the product of the carrier and modulating signals. Circuits that compute the product of two analog signals are also known as analog multipliers, mixers, converters, product detectors, and phase detectors. A circuit that changes a lower-frequency baseband or intelligence signal to a higher-frequency signal is usually called a modulator. A circuit used to recover the original intelligence signal from an AM wave is known as a detector or demodulator. Mixing and detection applications are discussed in detail in later Articles.

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