What impedance does a 1/2-wavelength transmission line present to an RF generator when the line is shorted at the far end?
The correct answer is B: Very low impedance. A 1/2-wavelength transmission line shorted at the far end presents very low impedance to an RF generator. A half-wavelength line transforms the short (0 ohms) back to a short (0 ohms) at the input.
Transmission lines transform impedances based on their length. A shorted 1/4-wavelength line transforms a short to an open (high impedance). A shorted 1/2-wavelength line transforms a short back to a short (low impedance) because 1/2 wavelength is 2 × 1/4 wavelength - the transformation repeats. So a shorted 1/2-wavelength line presents very low impedance (essentially a short circuit) at the input. This is useful for certain matching applications or as a shorting stub.
Exam Tip
1/2λ shorted line = Very low impedance. Remember: A 1/2-wavelength transmission line shorted at the far end presents very low impedance (essentially a short circuit) at the input because 1/2λ transforms a short back to a short.
Memory Aid
"**1**/**2**λ **S**horted = **V**ery **L**ow **I**mpedance (think '1/2λS = VLI')"
Real-World Application
You have a 1/2-wavelength piece of transmission line shorted at the far end. At the input, you measure very low impedance (essentially a short circuit). The 1/2-wavelength length transforms the short at the far end back to a short at the input. This is different from a 1/4-wavelength shorted line, which would present very high impedance.
FCC Part 97.3Key Concepts
Why Other Options Are Wrong
Option A: Incorrect. A shorted 1/4-wavelength line presents very high impedance, but 1/2-wavelength transforms it back to low impedance.
Option C: Incorrect. The impedance isn't the same as the characteristic impedance. A shorted 1/2-wavelength line presents very low impedance, not the line's characteristic impedance.
Option D: Incorrect. The impedance isn't the same as the generator output impedance. It's very low (essentially a short) due to the 1/2-wavelength transformation.
题目解析
The correct answer is B: Very low impedance. A 1/2-wavelength transmission line shorted at the far end presents very low impedance to an RF generator. A half-wavelength line transforms the short (0 ohms) back to a short (0 ohms) at the input. Transmission lines transform impedances based on their length. A shorted 1/4-wavelength line transforms a short to an open (high impedance). A shorted 1/2-wavelength line transforms a short back to a short (low impedance) because 1/2 wavelength is 2 × 1/4 wavelength - the transformation repeats. So a shorted 1/2-wavelength line presents very low impedance (essentially a short circuit) at the input. This is useful for certain matching applications or as a shorting stub.
考试技巧
1/2λ shorted line = Very low impedance. Remember: A 1/2-wavelength transmission line shorted at the far end presents very low impedance (essentially a short circuit) at the input because 1/2λ transforms a short back to a short.
记忆口诀
**1**/**2**λ **S**horted = **V**ery **L**ow **I**mpedance (think '1/2λS = VLI')
实际应用示例
You have a 1/2-wavelength piece of transmission line shorted at the far end. At the input, you measure very low impedance (essentially a short circuit). The 1/2-wavelength length transforms the short at the far end back to a short at the input. This is different from a 1/4-wavelength shorted line, which would present very high impedance.
错误选项分析
Option A: Incorrect. A shorted 1/4-wavelength line presents very high impedance, but 1/2-wavelength transforms it back to low impedance. Option C: Incorrect. The impedance isn't the same as the characteristic impedance. A shorted 1/2-wavelength line presents very low impedance, not the line's characteristic impedance. Option D: Incorrect. The impedance isn't the same as the generator output impedance. It's very low (essentially a short) due to the 1/2-wavelength transformation.
知识点
Transmission line, Half-wavelength, Shorted line, Impedance transformation
Verified Content
Question from official FCC Extra Class question pool. Explanation reviewed by licensed amateur radio operators.