Topic: Antennas and Wave Propagation
A paraboloidal-reflector antenna is designed for operation at 3 GHz. Its largest aperture dimension is 20 feet. It is desired to build a scale model of this antenna with the largest apeture dimension scaled to 18 inches. At what frequency must this model be operated in order to have the same pattern as the full-size antenna?
- A. 10 GHz
- B. 20 GHz
- C. 40 GHz
- D. 4 GHz
Answer: C. 40 GHz
Explanation: For the scale model to have the same radiation pattern, the electrical dimensions must be equal, so $D_1/\lambda_1 = D_2/\lambda_2$. Replacing $\lambda$ with $c/f$, this becomes $D_1 f_1 = D_2 f_2$. The full-size dimension $D_1 = 20 \text{ feet} = 240 \text{ inches}$, and $f_1 = 3$ GHz. The model dimension $D_2 = 18 \text{ inches}$. Thus, $f_2 = \frac{240 \times 3}{18} = 40$ GHz.