• # question_answer An audio signal given by $m(t)=30\,sin\,(2\pi \times 2500t)$ volts is used to amplitude modulate a carrier wave given by $c(t)=60\sin (2\pi \times 200000t)$ volts find (i) percentage modulation (ii) components of modulated wave (iii) the amplitude of each sideband.

Here, $m(t)={{A}_{m}}\sin 2\pi {{f}_{m}}t=30\sin (2\pi \times 2500t)\,volts$ and $c(t)={{A}_{c}}\sin 2\pi {{f}_{c}}t=60\sin (2\pi \times 200000t)\,volts$ Clearly, ${{A}_{m}}=30V,$ ${{f}_{m}}=2500\,Hz$             ${{A}_{c}}=60V,$ ${{f}_{c}}=200000\,Hz$
 (i) $m=\frac{{{A}_{m}}}{{{A}_{c}}}\times 100=\frac{30}{60}\times 100=50%$ (ii) The three components of the modulated carrier wave are ${{f}_{c}},$ USB, LSB. (iii) USB = 200000 + 2500 = 202500 Hz = 202.5 kHz $LSB=200000-2500=197500\,Hz=197.5\,kHz$