Answer to Question #115073 in Electric Circuits for Gaurav

Question

20 kHz audio signal is amplitude modulated over a 100 kHz carrier frequency. The
peak amplitude of carrier wave is 10 V. If the modulation index is 0.8, find out the
frequencies present in the modulated output. Also calculate the ratio of maximum and
the minimum amplitude of the envelope of modulated signal.

Answer 1

As per the given question,

Frequency of the audio signal $(f_c)=20kHz$

Frequency of the signal $(f_s)=100kHz$

Amplitude of the carrier signal $=10V$

Modulation index $=0.8$

modulating frequency $f_m=\dfrac{f_s\times 10V}{0.8}=\dfrac{100kHz\times 10}{0.8}=1250kHz$

Lower band frequency $=f_s+f_c =120kHz$

upper band frequency $=f_s-f_c=100kHz-20kHz=80kHz$

Hence the required ratio$=\dfrac{120kHz}{80kHz} =3:2$