A baseband signal of $$3.5$$ MHz frequency is modulated with a carrier signal of $$3.5$$ GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal?

We need to find the minimum antenna size required to transmit an amplitude-modulated signal with a carrier frequency of $$3.5$$ GHz.

Key Concept: In amplitude modulation (AM), the signal is transmitted at the carrier frequency. The minimum antenna size required for efficient transmission is $$\frac{\lambda}{4}$$, where $$\lambda$$ is the wavelength of the carrier signal.

Calculate the wavelength of the carrier signal: $$\lambda = \frac{c}{f} = \frac{3 \times 10^8 \text{ m/s}}{3.5 \times 10^9 \text{ Hz}}$$

$$\lambda = \frac{3}{3.5} \times 10^{-1} \text{ m} = \frac{30}{35} \text{ m} = \frac{6}{7} \text{ m} \approx 0.0857 \text{ m}$$

$$\lambda = 85.7 \text{ mm}$$

Calculate the minimum antenna size:: $$\text{Antenna size} = \frac{\lambda}{4} = \frac{85.7}{4} \text{ mm} \approx 21.4 \text{ mm}$$

The correct answer is Option C: 21.4 mm.