What transformer turns ratio matches an antenna’s 600-ohm feed point impedance to a 50-ohm coaxial cable?
The correct answer is A: 3.5 to 1. The transformer turns ratio that matches an antenna's 600-ohm feed point impedance to a 50-ohm coaxial cable is 3.5 to 1. Impedance ratio = 600/50 = 12:1. Turns ratio = √(impedance ratio) = √12 = 3.46 ≈ 3.5:1. For amateur radio operators, this is how impedance matching transformers work. Understanding this helps when matching antennas.
Exam Tip
Impedance matching transformer: Impedance ratio = 600/50 = 12:1, Turns ratio = √12 = 3.5:1. Think 'I'mpedance 'M'atching = 'I'mpedance ratio, 'M'ultiply by √. Turns ratio = √(impedance ratio). Not 12:1 (impedance ratio), not 24:1, not 144:1 - just 3.5:1.
Memory Aid
"Impedance matching transformer: Turns ratio = √(impedance ratio) = √12 = 3.5:1. Think 'I'mpedance 'M'atching = 'I'mpedance ratio, 'M'ultiply by √. Turns ratio = √(impedance ratio). Standard impedance matching calculation."
Real-World Application
You need to match a 600-ohm antenna to 50-ohm coax. Impedance ratio = 600/50 = 12:1. Turns ratio = √12 = 3.46 ≈ 3.5:1. A transformer with 3.5:1 turns ratio will match 600Ω to 50Ω. The square root relationship comes from impedance being proportional to turns squared.
Key Concepts
Why Other Options Are Wrong
Option B (12 to 1): Incorrect. 12:1 is the impedance ratio, not the turns ratio. Turns ratio = √(impedance ratio) = √12 = 3.5:1.
Option C (24 to 1): Incorrect. 24:1 is too high - that would be √576, not √12. Calculation error.
Option D (144 to 1): Incorrect. 144:1 is way too high - that would be √20,736, not √12. Calculation error.
题目解析
The correct answer is A: 3.5 to 1. The transformer turns ratio that matches an antenna's 600-ohm feed point impedance to a 50-ohm coaxial cable is 3.5 to 1. Impedance ratio = 600/50 = 12:1. Turns ratio = √(impedance ratio) = √12 = 3.46 ≈ 3.5:1. For amateur radio operators, this is how impedance matching transformers work. Understanding this helps when matching antennas.
考试技巧
Impedance matching transformer: Impedance ratio = 600/50 = 12:1, Turns ratio = √12 = 3.5:1. Think 'I'mpedance 'M'atching = 'I'mpedance ratio, 'M'ultiply by √. Turns ratio = √(impedance ratio). Not 12:1 (impedance ratio), not 24:1, not 144:1 - just 3.5:1.
记忆口诀
Impedance matching transformer: Turns ratio = √(impedance ratio) = √12 = 3.5:1. Think 'I'mpedance 'M'atching = 'I'mpedance ratio, 'M'ultiply by √. Turns ratio = √(impedance ratio). Standard impedance matching calculation.
实际应用示例
You need to match a 600-ohm antenna to 50-ohm coax. Impedance ratio = 600/50 = 12:1. Turns ratio = √12 = 3.46 ≈ 3.5:1. A transformer with 3.5:1 turns ratio will match 600Ω to 50Ω. The square root relationship comes from impedance being proportional to turns squared.
错误选项分析
Option B (12 to 1): Incorrect. 12:1 is the impedance ratio, not the turns ratio. Turns ratio = √(impedance ratio) = √12 = 3.5:1. Option C (24 to 1): Incorrect. 24:1 is too high - that would be √576, not √12. Calculation error. Option D (144 to 1): Incorrect. 144:1 is way too high - that would be √20,736, not √12. Calculation error.
知识点
Transformer turns ratio, Impedance matching, 600 ohm to 50 ohm, Impedance ratio
Verified Content
Question from official FCC General Class question pool. Explanation reviewed by licensed amateur radio operators.