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.

Answer:

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

\[LSB=200000-2500=197500\,Hz=197.5\,kHz\]