Updated: Dec 9, 2025 | Source: 2024-2028 Question Pool | Topic: E9F
E9F12E9F

What impedance does a 1/4-wavelength transmission line present to an RF generator when the line is open at the far end?

Deep Dive: E9F12

The correct answer is D: Very low impedance. A 1/4-wavelength transmission line open at the far end presents very low impedance to an RF generator. A quarter-wavelength line transforms an open (infinite ohms) to a short (very low impedance) at the input. Transmission lines transform impedances based on length. An open 1/4-wavelength line inverts the impedance - an open at the far end becomes a short (very low impedance) at the input. This is the opposite of a shorted 1/4-wavelength line, which transforms a short to an open. This property is useful for creating low-impedance points, shorting circuits at specific frequencies, or creating RF shorts. The 1/4-wavelength transformation is fundamental to many matching and filtering applications.

Why Other Answers Are Wrong

Option A: Incorrect. The impedance isn't the same as the characteristic impedance. An open 1/4-wavelength line presents very low impedance (essentially a short circuit). Option B: Incorrect. The impedance isn't the same as the generator input impedance. It's very low due to the 1/4-wavelength transformation. Option C: Incorrect. An open 1/4-wavelength line presents very low impedance, not very high. A shorted 1/4-wavelength line presents very high impedance.

Exam Tip

1/4λ open line = Very low impedance. Remember: A 1/4-wavelength transmission line open at the far end presents very low impedance (essentially a short circuit) at the input because 1/4λ transforms an open to a short.

Memory Aid

**1**/**4**λ **O**pen = **V**ery **L**ow **I**mpedance (think '1/4λO = VLI')

Real-World Example

You have a 1/4-wavelength piece of transmission line open at the far end. At the input, you measure very low impedance (essentially a short circuit). The 1/4-wavelength length transforms the open at the far end to a short at the input. This is useful for creating RF shorts or blocking certain frequencies.

Source & Coverage

Question Pool: 2024-2028 Question Pool

Subelement: E9F

Reference: FCC Part 97.3

Key Concepts

Transmission line Quarter-wavelength Open 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.