[AMRadio] Why 50 instead of 75 ohms

John Lyles jtml at losalamos.com
Thu Apr 5 20:41:59 EDT 2007

Coaxial transmission line equations for high frequency attenuation determine that the optimal ratio of outer conductor to inner conductor diameters is 3.592. This is determined to include skin effect, but not dielectric loss. With air dielectric this corresponds to 76.6 Ohms characteristic Z. There is a broad minimum on the graphs however, with 1/2% variation from 3.2 to 4.1 ratio of diameters. For maximum power, however, breakdown due to spacing, and heating due to center conductor area are the determining factors. In this case, for breakdown, the optimal Z is 30 Ohms with air dielectric, and for heating is 60 Ohms. Remember that the radius of the center conductor is larger for low Z, which helps on arcing. 

According to R. Chipman, Theory and Problems of Transmission Lines, Schaums Outline(!) Series, 50 Ohms was chose as a compromise of these factors. The attenuation is 10% higher than 76.6 Ohms. With dielectric filling, according to Chipman, "Low power dielectric filled flexible coaxial lines are available in several values of Z, the most widely used having characteristic impedances near 50 Ohms or near 75 Ohms. The latter (75) are effectively optimum design for minimum attenuation factor at constant outer diameter. The former (50) are chose to optimum design for minimum center conductor heating, for constant diamter and temperature of the outer conductor..... Dielectric, whether lossy or lossless, does not affect the optimum design for minimum attenuation factor."

BTW, this is one of the better Schaums outlines I have seen, with real practical information. 



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