Why is the RF coaxial cable impedance 50 or 75 ohms？

First of all, let's understand what is a typical cable impedance?

The most typical impedance values used for RF coaxial cables are 50 ohms and 75 ohms. The 50 ohm coaxial cable is probably the most common in use, generally used in radio transmitter receivers, laboratory equipment, Ethernet and other environments. Another commonly used cable type is 75 ohm coaxial cable, which is generally used in video transmission, cable television networks, antenna feeders, long-distance telecommunications applications, etc.

Coaxial Cable Results Plot

Why 50 ohm coax?

In the United States, the impedance of standard coaxial cables used for RF power transmission is almost without exception 50 ohms. Why this value was chosen is explained in a paper presented by Bird Electronics.

It is because both "minimum loss" and "maximum breakdown power" must be considered. For the air medium, the priority should be given to "minimum loss", and the optimal ratio of the "shielding layer inner diameter" to the "core wire outer diameter" of the coaxial cable is required to be 3.6 (the derivation process is complicated, skip it), and the characteristic impedance of the cable at this time is 77Ω. Under this ratio, although the cable loss is small, the shielding layer and the core wire layer will break down when encountering high power. Similarly, when considering the maximum power capacity, the ratio of the inner diameter of the shielding layer to the outer diameter of the core wire should be 1.65. At this time, the corresponding characteristic impedance is 30Ω, and the cable loss is relatively large at this time.

Therefore, for weak signals with low transmission power (such as TV signals), 75 ohms is used as the minimum loss point lower than 77 ohms for easy calculation. And 50 ohms is an average approximation of 77 and 30, a compromise between minimum loss and maximum power handling. That is, 50 ohms can carry more power than 70 ohms.