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In an amplitude modulator circuit, the carrier wave is given by, C(t)=4sin(20000\pi t) while modulating signal is given by m(t)=2sin(2000\pi t). The values of the modulation index and lower sideband frequency are:


Option 1)  0.5 and  10  kHz

Option 2)  0.4 and  10 kHz

Option 3)  0.3 and 9 kHz

Option 4)  0.5 and  9 kHz

Answers (1)

\\\text{Modulation index is given by } \mathrm{m}=\frac{\mathrm{A}_{\mathrm{m}}}{\mathrm{A}_{\mathrm{c}}}=\frac{2}{4}=0.5\\ \text{(a) carrier wave frequency is given by } =2 \pi f_{c} \\=2 \times 10^{4} \pi\\ \mathrm{f}_{\mathrm{c}}=10 \mathrm{kHz}

\\\text{(b) modulation wave frequency }$\left(\mathrm{f}_{\mathrm{m}}\right)$ \\ $2 \pi f_{m}=2000 \pi$ \\ $\Rightarrow f_{m}=1 \mathrm{kHz}$ \\ $lower side band frequency $\Rightarrow f_{c}-f_{m}$ $\Rightarrow 10 \mathrm{kHz}-1 \mathrm{kHz}=9 \mathrm{kHz}$

 

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