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 ?

Options

A. 42.8 m
B. 42.8 mm
C. 21.4 mm
D. 21.4 m

Answer

To determine the minimum size of the antenna required to transmit the modulated signal, we need to calculate the wavelength of the carrier signal. The size of the antenna is typically a fraction of the wavelength of the carrier signal.

### Step-by-Step Solution:

1. **Identify the Frequencies**:
- Baseband signal frequency, \( f_b = 3.5 \, \text{MHz} = 3.5 \times 10^6 \, \text{Hz} \)
- Carrier signal frequency, \( f_c = 3.5 \, \text{GHz} = 3.5 \times 10^9 \, \text{Hz} \)

2. **Calculate the Wavelength**:
The wavelength \( \lambda \) of the carrier signal can be calculated using the formula:
\[ \lambda = \frac{c}{f_c} \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

3. **Substitute the Values**:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{3.5 \times 10^9 \, \text{Hz}} \]

4. **Perform the Calculation**:
\[ \lambda = \frac{3}{3.5} \times 10^{-1} \, \text{m} \]
\[ \lambda \approx 0.0857 \, \text{m} \quad (\text{or } 8.57 \, \text{cm}) \]

5. **Determine the Minimum Size of the Antenna**:
The minimum size of the antenna is typically taken to be \( \frac{\lambda}{4} \) for efficient transmission.
\[ \text{Minimum antenna size} = \frac{\lambda}{4} = \frac{0.0857}{4} \approx 0.0214 \, \text{m} \quad (\text{or } 2.14 \, \text{cm}) \]

### Final Answer:
The minimum size of the antenna required to transmit the modulated signal is approximately **2.14 cm**.