A parabolic reflector used for reception with the direct broadcast system is 18 inches in diameter and operates at 12.4 GHz. The far-field distance for this antenna is:

Question

Quizplus · Accepted Answer

The far-field distance (R) of a parabolic reflector can be calculated using the formula $R = \frac{2D^2}{\lambda}$, where $D$ is the diameter of the reflector and $\lambda$ is the wavelength. Given the frequency (f) is 12.4 GHz, the wavelength ($\lambda$) can be calculated using $\lambda = \frac{c}{f}$, where $c$ is the speed of light ($3 \times 10^8$ m/s). First, convert 12.4 GHz to Hz (12.4 GHz = $12.4 \times 10^9$ Hz), then calculate $\lambda = \frac{3 \times 10^8}{12.4 \times 10^9}$ m. After finding $\lambda$, plug it into the far-field distance formula along with the diameter in meters (18 inches = 0.4572 meters). This calculation yields a value close to 17.3 meters, making option D the correct answer.

A Parabolic Reflector Used for Reception with the Direct Broadcast