What is the modulation index of an FM phone signal having a maximum frequency deviation of 3000 Hz either side of the carrier frequency if the highest modulating frequency is 1000 Hz?
The correct answer is A: 3. The modulation index of an FM phone signal with maximum frequency deviation of 3000 Hz and highest modulating frequency of 1000 Hz is 3. Modulation index = frequency deviation / modulating frequency.
Calculation: Modulation index = 3000 Hz / 1000 Hz = 3. The modulation index tells you how many times the carrier frequency deviates relative to the modulating frequency. A modulation index of 3 means the carrier frequency varies 3 times the modulating frequency. This modulation index will determine the bandwidth and number of significant sidebands in the FM signal.
Exam Tip
FM modulation index = Deviation / Modulating frequency. Remember: m = Δf / fm. With 3000 Hz deviation and 1000 Hz modulating frequency, m = 3000 / 1000 = 3.
Memory Aid
"**M**odulation **I**ndex = **3**000 / **1**000 = **3** (think 'MI = 3000/1000 = 3')"
Real-World Application
You're transmitting FM with 3000 Hz peak deviation and the highest audio frequency is 1000 Hz. The modulation index is 3000 / 1000 = 3. This means the carrier frequency varies 3 times the modulating frequency, which will create significant sidebands and determine your signal bandwidth.
FCC Part 97.307Key Concepts
Why Other Options Are Wrong
Option B: Incorrect. 0.3 would be 1000 / 3000, which is the inverse of the correct calculation. Modulation index = deviation / modulating frequency.
Option C: Incorrect. 6 would be 2 × 3, suggesting a calculation error. The correct value is 3000 / 1000 = 3.
Option D: Incorrect. 0.6 doesn't match any reasonable calculation with these values.
题目解析
The correct answer is A: 3. The modulation index of an FM phone signal with maximum frequency deviation of 3000 Hz and highest modulating frequency of 1000 Hz is 3. Modulation index = frequency deviation / modulating frequency. Calculation: Modulation index = 3000 Hz / 1000 Hz = 3. The modulation index tells you how many times the carrier frequency deviates relative to the modulating frequency. A modulation index of 3 means the carrier frequency varies 3 times the modulating frequency. This modulation index will determine the bandwidth and number of significant sidebands in the FM signal.
考试技巧
FM modulation index = Deviation / Modulating frequency. Remember: m = Δf / fm. With 3000 Hz deviation and 1000 Hz modulating frequency, m = 3000 / 1000 = 3.
记忆口诀
**M**odulation **I**ndex = **3**000 / **1**000 = **3** (think 'MI = 3000/1000 = 3')
实际应用示例
You're transmitting FM with 3000 Hz peak deviation and the highest audio frequency is 1000 Hz. The modulation index is 3000 / 1000 = 3. This means the carrier frequency varies 3 times the modulating frequency, which will create significant sidebands and determine your signal bandwidth.
错误选项分析
Option B: Incorrect. 0.3 would be 1000 / 3000, which is the inverse of the correct calculation. Modulation index = deviation / modulating frequency. Option C: Incorrect. 6 would be 2 × 3, suggesting a calculation error. The correct value is 3000 / 1000 = 3. Option D: Incorrect. 0.6 doesn't match any reasonable calculation with these values.
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.