Question
How much does the gain of an ideal parabolic reflector antenna increase when the operating frequency is doubled?
Answer Options
- A) 2 dB
- B) 3 dB
- C) 4 dB
- D) 6 dB
Correct Answer: D
Explanation
The gain (G) of a parabolic dish antenna is proportional to the square of the ratio of the antenna diameter (D) to the wavelength (\lambda), expressed as G \propto (D / \lambda)^2. Since frequency (f) and wavelength (\lambda) are inversely related (\lambda \propto 1/f), the gain of the dish is proportional to the square of the operating frequency, G \propto f^2.
If the operating frequency (f) is doubled (2f), the gain increases by a factor of 2^2 = 4. Converting a power ratio of 4 to decibels: 10 \times \log_{10}(4) \approx 6.02 dB. Therefore, the gain of an ideal parabolic reflector antenna increases by approximately 6 dB when the operating frequency is doubled.
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