Question

1.       The maximum frequency deviation of the carrier is ± 15 kHz and the maximum modulating frequency is 3 kHz, calculate for the modulation index.

2.       Assume that the 60-dB bandwidth of a receiver is 12 kHz and the 6-dB bandwidth is 7 kHz. What is the shape factor of the circuit?

3.       What is the bandwidth of a receiver with a quality factor of 50 and a resonance frequency of 540 kHz.

4.       What is the maximum bandwidth of an FM signal with a deviation of 27 kHz and a maximum modulating signal of 4 kHz as determined by Carson’s rule?

5.       A PM signal has a maximum allowed deviation of 17 kHz and an actual deviation of 8 kHz. What is the percentage modulation?

Answer 1

Solution;

(1)

Given;

Maximum frequency deviation,$\delta_{max}=15kHz$

Maximum modulating frequency,$f_m=3kHz$

The modulations index,$m_f$ ;

$m_f=\frac{\delta_{max}}{f_m}=\frac{15}{3}=5$

(2)

Shape factor,SF, is the ratio of two bandwidth;

$SF=\frac{BW_{60-dB}}{BW_{6-dB}}=\frac{12}{7}=1.714$

(3)

$BW=\frac{f_r}{Q}=\frac{540kHz}{50}=10.8kHz$

(4)

By Carson's rule;

$BW_{max}=2(\delta_{max}+f_m)$

$BW_{max}=2(27+4)=62kHz$

(5)

Percentage modulation=$\frac{\delta_{actual}}{\delta_{max}}×100$

=$\frac{8}{17}×100$ =$47.06$ %