Question 9
A carrier wave is frequency modulated.
(a) Describe what is meant by frequency modulation. [2]
(b) The sinusoidal carrier wave has a frequency of 750 kHz and an amplitude of 5.0 V.
The carrier wave is frequency modulated by a sinusoidal signal of frequency 7.5 kHz and amplitude 1.5 V.
The frequency deviation of the carrier wave is 20 kHz V-1.
Determine, for the frequency-modulated carrier wave,
(i) the amplitude, [1]
(ii) the minimum frequency, [1]
(iii) the maximum frequency, [1]
(iv) the number of times per second that the frequency changes from its minimum value to its maximum value and then back to the minimum value. [1]
Reference: Past Exam Paper – November 2015 Paper 41 & 42 Q11
Solution:
(a)
Frequency modulation means that the frequency of the carrier wave varies in synchrony with the displacement of the signal (information) wave.
(b)
(i) 5.0 V
{In FM, the amplitude does not change but the frequency changes.}
(ii) the minimum frequency, [1]
720 kHz
{The frequency of the unmodulated carrier wave is 750 kHz.
The frequency deviation of the carrier wave is 20 kHz V-1. This means that the (above) frequency can deviate (from its value of 750 kHz) by 20 kHz per volt of the signal wave.
1 V - - - > deviation of 20 kHz
The amplitude of the signal wave is 1.5 V.
1 V - - - > deviation of 20 kHz
1.5 V - - - > 1.5 × 20 = 30 kHz
So, the frequency of the carrier wave can deviate (can increase or decrease) by up to 30 kHz.
Minimum frequency = 750 – 30 = 720 kHz}
(iii) 780 kHz
{Maximum frequency = 750 + 30 = 780 kHz}
(iv) 7500
{This is the frequency of the signal wave (= 7.5 kHz = 7500 Hz)}
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