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.

 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)}