What is the modulation index of an FM phone signal having a maximum carrier deviation of plus or minus 6 kHz if the highest modulating frequency is 2 kHz?
The correct answer is B: 3. The modulation index of an FM phone signal with maximum carrier deviation of plus or minus 6 kHz and highest modulating frequency of 2 kHz is 3. Modulation index = frequency deviation / modulating frequency.
Calculation: Peak deviation = 6 kHz, modulating frequency = 2 kHz. Modulation index = 6 kHz / 2 kHz = 3. The 'plus or minus 6 kHz' means the peak deviation is 6 kHz in either direction from the carrier. The modulation index of 3 means the carrier frequency varies 3 times the modulating frequency, which determines the bandwidth and sideband structure of the FM signal.
Exam Tip
FM modulation index = Deviation / Modulating frequency. Remember: m = Δf / fm. With ±6 kHz deviation and 2 kHz modulating frequency, m = 6 / 2 = 3.
Memory Aid
"**M**odulation **I**ndex = **6** kHz / **2** kHz = **3** (think 'MI = 6/2 = 3')"
Real-World Application
You're transmitting FM with ±6 kHz peak deviation and the highest audio frequency is 2 kHz. The modulation index is 6 kHz / 2 kHz = 3. This modulation index determines how many significant sidebands your FM signal will have and what bandwidth it occupies.
FCC Part 97.307Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. 0.3 would be 2 / 6, which is the inverse of the correct calculation. Modulation index = deviation / modulating frequency.
Option C: Incorrect. 0.6 would be 2 / 3.33 or some other incorrect calculation. The correct value is 6 / 2 = 3.
Option D: Incorrect. 6 would be the deviation value itself, not the modulation index. The index is deviation divided by modulating frequency.
题目解析
The correct answer is B: 3. The modulation index of an FM phone signal with maximum carrier deviation of plus or minus 6 kHz and highest modulating frequency of 2 kHz is 3. Modulation index = frequency deviation / modulating frequency. Calculation: Peak deviation = 6 kHz, modulating frequency = 2 kHz. Modulation index = 6 kHz / 2 kHz = 3. The 'plus or minus 6 kHz' means the peak deviation is 6 kHz in either direction from the carrier. The modulation index of 3 means the carrier frequency varies 3 times the modulating frequency, which determines the bandwidth and sideband structure of the FM signal.
考试技巧
FM modulation index = Deviation / Modulating frequency. Remember: m = Δf / fm. With ±6 kHz deviation and 2 kHz modulating frequency, m = 6 / 2 = 3.
记忆口诀
**M**odulation **I**ndex = **6** kHz / **2** kHz = **3** (think 'MI = 6/2 = 3')
实际应用示例
You're transmitting FM with ±6 kHz peak deviation and the highest audio frequency is 2 kHz. The modulation index is 6 kHz / 2 kHz = 3. This modulation index determines how many significant sidebands your FM signal will have and what bandwidth it occupies.
错误选项分析
Option A: Incorrect. 0.3 would be 2 / 6, which is the inverse of the correct calculation. Modulation index = deviation / modulating frequency. Option C: Incorrect. 0.6 would be 2 / 3.33 or some other incorrect calculation. The correct value is 6 / 2 = 3. Option D: Incorrect. 6 would be the deviation value itself, not the modulation index. The index is deviation divided by modulating frequency.
知识点
Modulation index, FM calculation, Frequency deviation, Modulating frequency
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.