Page 324 - Physics Coursebook 2015 (A level)

312
Cambridge International A Level Physics
WORKED EXAMPLE
than the frequency of the carrier wave. Figure 20.4 shows frequency modulation.
In frequency modulation (FM), the modulated wave has a constant amplitude. It is the frequency of the modulated wave that changes as the signal changes.
The frequency deviation of the carrier wave may be given a value, for example, 25 kHz V−1. This means that for every 1.0 V change in the voltage of the signal, the frequency of the carrier wave changes by 25 kHz. In some countries, the maximum allowed change in frequency during FM is set as 75 kHz, in order that the frequency
of one station does not overlap the frequency of the next station. If the frequency deviation is 25 kHz V−1 and the maximum change is 75 kHz, then the maximum signal producing the FM is 3.0V.
2 A carrier wave of frequency 300 kHz and amplitude
5.0 V is frequency modulated by a sinusoidal signal of frequency 6 kHz and amplitude 2.0 V. The frequency deviation of the carrier wave is 30 kHz V−1. Describe the modulated carrier wave produced.
Step1 Considertheamplitudeofthemodulatedsignal. The amplitude of the carrier wave is unchanged at 5.0 V during frequency modulation. The signal alters the frequency of the carrier wave, not its amplitude.
QUESTIONS
4 Explain how a frequency-modulated wave changes, when the input signal:
a increases in loudness
b increases in frequency.
5 A signal of frequency 16 kHz and amplitude 3.0 V is used for frequency modulation of a carrier wave of frequency 500 kHz. The frequency deviation of the carrier wave is 8.0 kHz V−1.
a What is the maximum frequency shift produced?
b What is the maximum frequency of the
modulated carrier wave?
c How many times per second does the modulated carrier wave increase and decrease in frequency?
signal +ve
frequency higher
Figure 20.4
signal −ve
frequency lower
the carrier wave (no modulation)
the signal
the frequency- modulated wave
Time
Frequency modulation.
Step2 Nowconsiderhowthesignalwillmodifythe carrier frequency. The frequency shift produced by the signal is ± 2 × 30 = ± 60 kHz, so the carrier wave varies in frequency between 240 and 360 kHz. This variation in frequency occurs 6000 times every second as the signal varies at this frequency.
Sidebands and bandwidth
A carrier wave contains only one frequency, the carrier wave frequency fc . When the carrier wave is modulated in amplitude by a single frequency fm, then the carrier wave is found to contain two more frequencies, known as sideband frequencies, one at a frequency ( fc − fm) and the other at ( fc + fm ). Figure 20.5 shows these frequencies.
When music or speech is transmitted, the carrier is modulated by a range of frequencies which change with time. Each frequency fm present in the signal gives rise to
an extra pair of frequencies in the modulated wave. The result is a band of frequencies, called the upper and lower sidebands, stretching above and below the carrier frequency by the value of the highest modulating frequency.
Figure 20.6 shows the frequency spectrum for a carrier wave of frequency 1 MHz modulated with frequencies between 0 and fm = 15 kHz = 0.015 MHz. The highest