Question

The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance $49\,\mu H$ and a capacitance of $2.5 \,nF$. It is modulated by an audio signal of $12 \,kHz$. The frequency range occupied by the side bands is:

• A. 13482 kHz - 13494 kHz
• B. 442 kHz - 466 kHz
• C. 63 kHz - 75 kHz
• D. 18 kHz - 30 kHz

Answer 1

Answer: (B)

442 kHz - 466 kHz

Answer 2

The tank circuit of an inductance and a capacitance is know that $\omega=\frac{1}{\sqrt{L C}}=\frac{1}{\sqrt{49 \mu H \times 2.5\, nF }}=\frac{1}{\sqrt{49 \times 10^{-6} \times 2.5 \times 10^{-9}}}$ $\Rightarrow \omega=\frac{1}{\sqrt{49 \times 25 \times 10^{-16}}}=\frac{1}{7 \times 5 \times 10^{-8}}$ $\omega=2 \pi f \Rightarrow f=\frac{\omega}{2 \pi}=\frac{1}{7 \times 5 \times 10^{-8} \times 2 \pi} \Rightarrow f=454.5\, kHz$ Given carrier frequency is modulated by audio signal of $12 \,kHz$. Therefore, $f=454.5\, kHz \pm 12 \,kHz$ $\Rightarrow f=442 \,kHz -466\, kHz$