Radio Frequency (RF) & Wireless Design

Coax is one of the oldest and most used RF connectivity cables, but did you know that there is a reason why 50 ohms is chosen over 75 ohms or even 77 ohms ?

It turns out that the impedance of the cable is a compromise between the lowest loss (maximum power capability) at 30 ohms and the lowest dielectric loss of air (between the center conductor and the shield) at ~ 77 ohms.

The Wikipedia Coax Impedance description is here :

https://en.wikipedia.org/wiki/Coaxial_cable#Choice_of_impedance

The best coaxial cable impedances in high-power, high-voltage, and low-attenuation applications were experimentally determined at Bell Laboratories in 1929 to be 30, 60, and 77 Ω, respectively. For a coaxial cable with air dielectric and a shield of a given inner diameter, the attenuation is minimized by choosing the diameter of the inner conductor to give a characteristic impedance of 76.7 Ω.[13] When more common dielectrics are considered, the best-loss impedance drops down to a value between 52–64 Ω. Maximum power handling is achieved at 30 Ω.[14]

The approximate impedance required to match a centre-fed dipole antenna in free space (i.e., a dipole without ground reflections) is 73 Ω, so 75 Ω coax was commonly used for connecting shortwave antennas to receivers. These typically involve such low levels of RF power that power-handling and high-voltage breakdown characteristics are unimportant when compared to attenuation. Likewise with CATV, although many broadcast TV installations and CATV headends use 300 Ω folded dipole antennas to receive off-the-air signals, 75 Ω coax makes a convenient 4:1 balun transformer for these as well as possessing low attenuation.

The arithmetic mean between 30 Ω and 77 Ω is 53.5 Ω; the geometric mean is 48 Ω. The selection of 50 Ω as a compromise between power-handling capability and attenuation is in general cited as the reason for the number.[15] 50 Ω also works out tolerably well because it corresponds approximately to the drive impedance (ideally 36 ohms) of a quarter-wave monopole, mounted on a less than optimum ground plane such as a vehicle roof. The match is better at low frequencies, such as for CB Radio around 27 MHz, where the roof dimensions are much less than a quarter wavelength, and relatively poor at higher frequencies, VHF and UHF, where the roof dimensions may be several wavelengths. The match is at best poor, because the antenna drive impedance, due to the imperfect ground plane, is reactive rather than purely resistive, and so a 36 ohm coaxial cable would not match properly either. Installations which need exact matching will use some kind of matching circuit at the base of the antenna, or elsewhere, in conjunction with a carefully chosen (in terms of wavelength) length of coaxial, such that a proper match is achieved, which will be only over a fairly narrow frequency range.

There is also another explanation of the Nominal Impedance here :

https://en.wikipedia.org/wiki/Nominal_impedance#50_Ω_and_75_Ω

Belden also has a description of the history along with a graph showing the frequency and attenuation (loss), voltage and power responses for each impedance :

https://www.belden.com/blog/broadcast/50-ohms-the-forgotten-impedance

Also here's a good chart on the types of losses for common types of coax :

http://www.winsystem.org/faqs/faqs/