E9F04: Transmission line: What impedance does a 1/2-wavelength

Q: 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. 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.

Updated: Dec 9, 2025 | Source: 2024-2028 Question Pool | Topic: E9F

E9F04E9F

What impedance does a 1/2-wavelength transmission line present to an RF generator when the line is shorted at the far end?

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Deep Dive: E9F04

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.

Why Other Answers 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.

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 Example

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.

Source & Coverage

Question Pool: 2024-2028 Question Pool

Subelement: E9F

Reference: FCC Part 97.3

Key Concepts

Transmission line Half-wavelength Shorted line Impedance transformation

Verified Content

Question from the official FCC Extra Class pool. Explanation reviewed by licensed amateur radio operators and mapped to the E9F topic.