Amplitude Modulation

We have mentioned that amplitude modulation is a means used to transmit  by varying the .amplitude of a high-frequency carrier. In a typical apphea signal is a low-frequency audio waveform and the amplitude of a high-frequency (radio-frequency, or rf) carrier is made to increase and decrease as the audio Q:~al increases and decreases. Figure 16-36 shows the waveforms that are generar ”’

an amplitude modulator when the signal input is a small de value, a large de value, and a low-frequency sinusoidal wave. Notice that the carrier input to the modulator is a constant-amplitude, constant-frequency rf sine wave. It can be seen that the audio waveform is reproduced in the variations of the positive and negative peaks of the output. The audio waveform superimposed on the high-frequency peaks is called the envelope of the modulated wave.

It is important to note that amplitude modulation is achieved by multiplying two waveforms (signal x carrier), which is a nonlinear process. As such, the rnodu lated output contains frequency components that are not present in either the signal or the carrier. Amplitude modulation cannot be achieved by simply adding two wave forms. Unfortunately, the term mixing is used in the broadcast industry to mean both the summation of signals and the multiplication of signals (some modulators are called mixers), but these are two very distinct processes. N« will now demonstrate that amplitude modulation creates new frequency components. Let the input signal be a pure sine wave designated

Equation 16-80 shows that the modulated waveform contains the new frequency components We + w, and We – WI! called the slim and difference frequencies, as well as a component at the carrier frequency, We’ Note that there is no frequency component equal to w,. In practice, the input signal will consist of a complex waveform containing many different frequencies. Therefore, the AM output will
contain many different sum and difference frequencies. The band of difference frequencies is called the lower sideband because its frequencies are all less than the carrier frequency, and the band of sum frequencies is called the upper sideband, each of its frequencies being greater than the carrier frequency. The significance of this result is that it allows us to determine the bandwidth that an amplifier must have to pass an AM waveform. The bandwidth must extend from the smallest difference frequency to the largest sum frequency.

Example 16-14

An amplitude modulator is driven by a 580-kHz carrier and has an audio signal input containing frequency components between 200 Hz and 9.S kHz

1. What range of frequencies must be included in th • passband of an amplifier that” will be used to amplify the modulated signal?
2. What frequency components are in the lower sideband of the AM output? In the upper sideband

solution

1. The smallest difference frequency is 217(580 x 103) – 217(9.5 X 103) rad/s, or (580 kHz) – (9.5 kHz) = 570.5 kHz, and the largest sum frequency is (580 kHz) + (9.5 kHz) = 589.5 kHz. Therefore, the amplifier must pass frequencies in the range from 570.5 kl-Iz to 589.5 kHz. An amplifier having only this range would be considered a narrowband amplifier

2. The lowest sideband extends from the smallest difference frequency to the largest difference frequency: [(580 kHz) – (9.5 kHz)] to [(580 kHz) – (200 Hz)]. or 570.5 kHz to 579.8 kHz. The upper sideband extends from the smallest sum frequency to the largest sum frequency: [(580 kHz) + (200 Hz)] to [(580 ~Hz) + (9.5 kHz)], or 580.2 kHz to 589.5 kHz

Figure 16-37 shows how a class-C amplifier can be used to produce amplitude modulation. The circuit issimilar to Figure 16-35, except that the coil in the collector circuit has been replaced by the secondary winding of a transformer. The lowfrequency signal input is connected to the transformer primary. The voltage at the collector is then the sum of Vcc and a signal proportional to Vs. As Vs increases and . decreases, so does the collector voltage. In effect, we·are varying the supply voltage on the collector. When the carrier signal on the base drives the transistor to saturation, the peak collector current le(sal) that flows depends directly on the supply voltage: the greater the supply voltage, the greater the peak current. Since the supply voltage varies with the signal input, so does the peak collector current. As a consequence, the collector current is amplitude modulated by Us> and the tank circuit produces an AM output voltage, as shown