Have you ever wondered why most of our Amateur Radio equipment is designed for 50 Ohm transmission lines?
The following graph was originally produced by two researchers, Lloyd Espenscheid and Herman Affel, working for Bell Labs in 1929.
The graph shows the power handling and voltage handling ability of various coax impedances.
The characteristic impedance of coax cable formed by two concentric conductors can be calculated using the following formula ZO=138.16/√ε .Log D/d. Where D is inside diameter of the outer conductor d is the outside diameter of the inner conductor and ℰ is the dielectric constant of the medium between the two conductors, for air ℰ is equal to 1.
As you can see from the graph different impedance values are optimum for different parameters.
For minimum attenuation the best Impedance is 77Ω and for best power handling 30Ω is best, but for voltage handling ability 60Ω is the impedance to use. 77Ω air line was initially selected for systems where low loss was the major consideration, however power handling ability is way less than 50% of that of a 30Ω line. 50Ω sits about halfway between giving us reasonable attenuation and good voltage handling characteristics and reasonable power handling. An interesting fact to note is that if a 77 ohm air line is filled with polypropylene with a dielectric constant of 2.3 the impedance is reduced to 51 ohms.
So as for most things in life it appears that 50 ohms is simply just another compromise. With the power levels used by amateurs and dipoles exhibiting impedance’s around 70 ohms with an SWR of somewhere near 1.5:1 on a 50 ohm system it could be wise for the frugal amateur to transfer the mismatch from the antenna end to the transceiver end of the coax and consider using 75 ohm RG6 cable that is available for vastly less than RG213 with about the same attenuation characteristics.
Very few amateur antennas naturally have a 50 ohm impedance, and it usual to employ some form of matching scheme to achieve the desired 50 ohms and resulting low SWR.