Why 50 Ω, Really

Almost every RF system you will meet is built around 50 Ω, and almost every explanation of why is a little bit wrong.

The usual answer, and its problem

You will often hear that 50 Ω is a compromise between the impedance of lowest loss and the impedance of highest power handling in coaxial cable. That is close to right, but it is worth being precise about what was being optimised and in what material.

Where it comes from

For an air-filled coaxial line, minimum attenuation occurs near 77 Ω and maximum power handling near 30 Ω. Neither of those is 50.

Fill the line with polyethylene instead of air, and the lowest-loss impedance moves. That is the number the industry settled near, and the same ratio of conductor diameters that gives it in polyethylene would give roughly 77 Ω in air.

What is actually fundamental

Nothing about 50 Ω. The only impedance in electromagnetics that is genuinely fundamental is the impedance of free space, about 377 Ω, and that one falls out of the permittivity and permeability of the vacuum rather than out of a manufacturing compromise.

Placeholder article — structure and argument are real, but this post is illustrative until the series it accompanies is published.