How much does the gain of an ideal parabolic reflector antenna increase when the operating frequency is doubled?
The correct answer is D: 6 dB. When the operating frequency of an ideal parabolic reflector antenna is doubled, the gain increases by 6 dB. This is because gain is proportional to (diameter/λ)², so doubling frequency (halving wavelength) quadruples the gain ratio, which is 6 dB.
For parabolic reflectors, gain = (πD/λ)² × efficiency, where D is diameter and λ is wavelength. If frequency doubles, wavelength halves. So gain becomes (πD/(λ/2))² = (2πD/λ)² = 4 × (πD/λ)². This is 4× the original gain, which is 6 dB (10 log₁₀(4) = 6 dB). This relationship is important for understanding how parabolic antennas scale with frequency. Higher frequencies allow smaller dishes to achieve the same gain, or the same dish to achieve higher gain.
Exam Tip
Parabolic: Double frequency = +6 dB gain. Remember: When operating frequency doubles, ideal parabolic reflector gain increases by 6 dB (gain is proportional to frequency squared, so 2² = 4× = 6 dB).
Memory Aid
"**P**arabolic **D**ouble **F**requency = **+6** **d**B (think 'PDF = +6dB')"
Real-World Application
You have a 2-meter (144 MHz) parabolic dish with 20 dBi gain. You use the same dish at 70 cm (432 MHz, 3× frequency). The gain increases by about 9.5 dB (3² = 9× = 9.5 dB), so you'd have about 29.5 dBi. If you doubled frequency (288 MHz), gain would increase by 6 dB to 26 dBi.
FCC Part 97.3Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. 2 dB would be too small. Doubling frequency quadruples the gain ratio, which is 6 dB.
Option B: Incorrect. 3 dB would be half the correct value. The gain increases by 6 dB when frequency doubles.
Option C: Incorrect. 4 dB is close but not the exact value. The correct increase is 6 dB (4× gain ratio).
题目解析
The correct answer is D: 6 dB. When the operating frequency of an ideal parabolic reflector antenna is doubled, the gain increases by 6 dB. This is because gain is proportional to (diameter/λ)², so doubling frequency (halving wavelength) quadruples the gain ratio, which is 6 dB. For parabolic reflectors, gain = (πD/λ)² × efficiency, where D is diameter and λ is wavelength. If frequency doubles, wavelength halves. So gain becomes (πD/(λ/2))² = (2πD/λ)² = 4 × (πD/λ)². This is 4× the original gain, which is 6 dB (10 log₁₀(4) = 6 dB). This relationship is important for understanding how parabolic antennas scale with frequency. Higher frequencies allow smaller dishes to achieve the same gain, or the same dish to achieve higher gain.
考试技巧
Parabolic: Double frequency = +6 dB gain. Remember: When operating frequency doubles, ideal parabolic reflector gain increases by 6 dB (gain is proportional to frequency squared, so 2² = 4× = 6 dB).
记忆口诀
**P**arabolic **D**ouble **F**requency = **+6** **d**B (think 'PDF = +6dB')
实际应用示例
You have a 2-meter (144 MHz) parabolic dish with 20 dBi gain. You use the same dish at 70 cm (432 MHz, 3× frequency). The gain increases by about 9.5 dB (3² = 9× = 9.5 dB), so you'd have about 29.5 dBi. If you doubled frequency (288 MHz), gain would increase by 6 dB to 26 dBi.
错误选项分析
Option A: Incorrect. 2 dB would be too small. Doubling frequency quadruples the gain ratio, which is 6 dB. Option B: Incorrect. 3 dB would be half the correct value. The gain increases by 6 dB when frequency doubles. Option C: Incorrect. 4 dB is close but not the exact value. The correct increase is 6 dB (4× gain ratio).
知识点
Parabolic reflector, Gain vs frequency, 6 dB per frequency doubling, Antenna gain
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.