EMC Question of the Week: April 30, 2018
The input impedance of a lossless 50-Ω transmission line terminated with a 50-Ω load resistance is,
- 50 Ω
- 100 Ω
- 50 Ω + j50 Ω
- dependent on the length of the transmission line
Answer
The correct answer is "a." The input impedance of a matched transmission line is equal to the characteristic impedance of the line. This is true independent of the length of the line, even if the line is very long and slightly lossy.
Unmatched transmission lines have an input impedance that is a function of the length of the line and may have a reactive (imaginary) component even if the load is real. The input impedance of a lossless transmission line with a reactive load (i.e. capacitance or inductance) is always purely imaginary. The input impedance of an electrically short transmission line is approximately equal to the load impedance.
In circuits and systems operating over a broad range of frequencies, there are generally only two types of transmission lines that are allowed: Electrically-short lines and matched lines. The input impedance of both these transmission lines is easy to determine without performing complex math.
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