Page 323 - Physics Coursebook 2015 (A level)

Chapter 20: Communications systems
Amplitude modulation
Figure 20.3 shows amplitude modulation (AM). The three diagrams show the carrier wave, the signal and
the modulated wave. In each case, the horizontal axis represents time, shown on the axis at the bottom. The modulated wave is the carrier wave but its amplitude rises and falls to match the value of the signal at any instant. Look at the amplitude-modulated wave on its own, and notice how the amplitude variation at top and bottom has the same pattern as the signal.
the carrier wave (no modulation)
the signal
the amplitude- modulated wave
0 20 40 60 80 100 120 140 160 180 Time/μs Figure 20.3 Amplitude modulation.
The amplitude of the signal must be less than half of the amplitude of the carrier wave; otherwise the variation in the amplitude at the top will be confused with the variation in amplitude at the bottom of the wave.
If a radio station carries music, the wave transmitted by the radio station will differ from the wave shown in Figure 20.3. There is only one signal frequency present in the signal in Figure 20.3. Music consists of many changing frequencies superposed so that it has a more complex wave pattern. The amplitude of the carrier wave will change as the music pattern changes. The carrier wave frequency does not change but the amplitude of the trace will change with time.
In amplitude modulation (AM), the frequency of the modulated wave is constant. The amplitude of the modulated wave is proportional to, and in phase with, the signal.
WORKED EXAMPLE
1 Calculate the frequencies of the carrier wave and signal shown in Figure 20.3.
Step1 Forthecarrierwave,thereare10complete waves in 100 μs. Hence:
time for one complete carrier wave, T=10μs=1×10−5s 1
carrier wave frequency fc = T = 100 000 Hz
Step2 Forthesignal,thereisonecompletewavein 100 μs. Hence: 1
frequency of the signal fs = 100 × 10−6 =10000Hz
A radio wave of 100 000 Hz is in the long-wavelength, low-frequency region of the radio electromagnetic spectrum. A sound frequency of 10 000 Hz is a very high frequency note but is audible.
QUESTIONS
1 Imagine that all the numbers on the time axis in Figure 20.3 are doubled, so that 100 becomes 200 and 200 becomes 400. Calculate the frequency of the carrier wave and the frequency of the signal.
2 Draw an amplitude-modulated wave with a carrier wave of frequency 1.0 MHz and a signal frequency of 100 kHz. The time axis on your graph should
be from 0 to 10 μs. On your graph, mark the time for one complete wave of the signal and for one complete wave of the carrier.
3 Explain how an amplitude-modulated wave changes when the input signal:
a increases in loudness
b increases in frequency.
Frequency modulation
In frequency modulation (FM) the frequency of the modulated wave varies with time. Without any signal, the frequency of the modulated wave is equal to the frequency of the carrier wave. The size of the input signal at any instant causes the frequency of the modulated wave to change. When the input signal is positive, the frequency
of the modulated wave is increased so that it is larger than the frequency of the carrier wave. The larger the signal, the greater is the increase in the frequency. When the signal
is negative, the frequency of the modulated wave is less
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