Page 325 - Physics Coursebook 2015 (A level)

Chapter 20: Communications systems
0 (fc – fm) fc bandwidth 2fm
WORKED EXAMPLE
3 Radio stations, which broadcast in the long-wave (LW) region of the electromagnetic spectrum, use carrier frequencies between 140 kHz and 280 kHz. The sidebands are within 4.5 kHz on either side of the carrier frequency. State the bandwidth of each radio station in the LW region of the spectrum and calculate the maximum number of radio stations which can transmit in the LW region.
Step1 Thebandwidthofanindividualstationis twice the width of an individual sideband:
bandwidth = 2 × 4.5 = 9.0 kHz
Step2 TheLWregionisdividedintoregionsofwidth 9.0 kHz. Hence:
number of stations = allowed frequency range
bandwidth
= (280−140) 9.0
= 15.5 = 15 stations
Suppose a country decides to increase the quality of music transmitted by each radio station. What happens to the bandwidth and the maximum number of stations in the LW region? Better sound quality requires an increase in the maximum frequency of the signal that modulates the carrier wave, and so the bandwidth needed increases. This decreases the number of available stations in the LW region of the spectrum.
Comparing AM and FM transmissions
You may have noticed crackle on a radio when you switch lights in your house on and off or when there is a lightning strike nearby. The lightning strike or switching a current on or off creates a burst of radio waves. These radio waves produce unwanted electrical interference and change the amplitude of the radio wave received by a radio. Since the amplitude of the wave carries the signal, when amplitude modulation is used the output of the radio is affected. Most electrical interference does not affect the frequency of the radio wave received by a radio and thus electrical interference affects FM less than AM. FM radio was actually invented to overcome the electrical interference and noise problems of AM radio and this remains an important advantage today.
FM came later than AM and had to use higher frequencies than AM. Although there was extra cost in developing the electronics to work at these higher
(fc + fm)
Figure 20.5 The frequency spectrum of a carrier wave
Frequency modulated in amplitude by a signal of one frequency.
frequency present in the spectrum is ( fc + fm) = 1.015 MHz and the lowest frequency is ( fc − fm) = 0.985 MHz.
The actual shape of the sidebands in Figure 20.6 will vary at any instant as the signal changes. The maximum and minimum values are important, as these must not overlap the sidebands from any other radio station.
The value of fm needed depends on the quality required in the signal. High-quality music only needs frequencies up to 15 kHz, even though the ear can hear frequencies up to 20 kHz. Speech only needs frequencies up to 3.4 kHz for people to understand one another.
carrier lower sideband
0 0.985 1.000
upper sideband
1.015 Frequency / MHz
Figure 20.6 The frequency spectrum for an amplitude- modulated wave.
You can see that the modulated carrier wave occupies a region of the spectrum from 0.985 MHz to 1.015 MHz. The bandwidth of a signal is the range of frequencies that the signal occupies. In other words, it is the difference between the highest-frequency signal component and the lowest- frequency signal component.
In Figure 20.6 the bandwidth is
1.015 − 0.985 = 0.030 MHz
In Figure 20.5 the bandwidth is (fc + fm) − (fc − fm) = 2fm. The frequency spectrum of a frequency-modulated
(FM) carrier wave is more complex. In particular, there are often more than two sideband frequencies for each signal frequency. This means that frequency modulation requires a greater bandwidth for each radio station.
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Signal power
Signal power