Which decibel value represents a power increase from 20 watts to 200 watts?
The correct answer is A: 10 dB. A power increase from 20 watts to 200 watts represents 10 dB. This is because 200 watts is 10 times (10×) the power of 20 watts, and a 10:1 power ratio equals 10 dB.
Using the formula: dB = 10 × log(200/20) = 10 × log(10) = 10 × 1 = 10 dB. This is another fundamental dB relationship: 10× power = +10 dB, 1/10 power = -10 dB. These are key relationships to memorize: 2× = +3 dB, 4× = +6 dB, 10× = +10 dB.
Exam Tip
10× power = +10 dB. Remember: Multiplying power by 10 equals +10 dB. Going from 20W to 200W is 10×, so it's +10 dB.
Memory Aid
"**1**0× **P**ower = **1**0 **d**B (think '10P = 10dB' = 10× Power = 10 dB)"
Real-World Application
You increase your transmitter power from 20 watts to 200 watts. This multiplies your power by 10, which is a 10 dB increase. This is a significant increase that will make your signal much stronger on the receiving end. Understanding that 10× power = +10 dB helps you understand the impact of major power changes.
FCC Part 97.313Key Concepts
Why Other Options Are Wrong
Option B: Incorrect. 12 dB represents a power ratio of about 15.85:1, not 10:1. 200 watts is exactly 10 times 20 watts, which is 10 dB.
Option C: Incorrect. 18 dB represents a power ratio of about 63:1, not 10:1. The correct value for 10× power is 10 dB.
Option D: Incorrect. 28 dB represents a power ratio of about 631:1, way too large. 10× power is 10 dB.
题目解析
The correct answer is A: 10 dB. A power increase from 20 watts to 200 watts represents 10 dB. This is because 200 watts is 10 times (10×) the power of 20 watts, and a 10:1 power ratio equals 10 dB. Using the formula: dB = 10 × log(200/20) = 10 × log(10) = 10 × 1 = 10 dB. This is another fundamental dB relationship: 10× power = +10 dB, 1/10 power = -10 dB. These are key relationships to memorize: 2× = +3 dB, 4× = +6 dB, 10× = +10 dB.
考试技巧
10× power = +10 dB. Remember: Multiplying power by 10 equals +10 dB. Going from 20W to 200W is 10×, so it's +10 dB.
记忆口诀
**1**0× **P**ower = **1**0 **d**B (think '10P = 10dB' = 10× Power = 10 dB)
实际应用示例
You increase your transmitter power from 20 watts to 200 watts. This multiplies your power by 10, which is a 10 dB increase. This is a significant increase that will make your signal much stronger on the receiving end. Understanding that 10× power = +10 dB helps you understand the impact of major power changes.
错误选项分析
Option B: Incorrect. 12 dB represents a power ratio of about 15.85:1, not 10:1. 200 watts is exactly 10 times 20 watts, which is 10 dB. Option C: Incorrect. 18 dB represents a power ratio of about 63:1, not 10:1. The correct value for 10× power is 10 dB. Option D: Incorrect. 28 dB represents a power ratio of about 631:1, way too large. 10× power is 10 dB.
知识点
Decibels, Power ratio, 10 dB, Ten times power
Verified Content
Question from official FCC Technician Class question pool. Explanation reviewed by licensed amateur radio operators.