75 to 50 ohm

[Bob Bruhns]

Hi Alex,

I found information on air-dielectric coaxial line in The ARRL Antenna Book.

Impedance of air-dielectric line (ohms) = 138 log(D/d)
 where D = inside diameter of outer conductor
   and d = outside diameter of inner conductor (in same units as D)

Working that backwards:
 For air dielectric, d = D / (10^(Z/138))
 where d = outside diameter of inner conductor,
       D = inside diameter of outer conductor (in same units as d),
   and Z = impedance in ohms.

So if your 3/4" line outer conductor is a pipe 3/4" OD and 0.550" ID, with air dielectric, then the center conductor should be 0.239" for 50 ohms, and 0.157" for 75 ohms.  If you taper a center conductor from between these diameters over a length of about 1 wavelength (about 5" at 2400 MHz) or longer, you should have it.  If the line uses foam dielectric, which it probably does, I think the center conductor will be thinner for a given impedance.  But I think the tapering ratio of the center conductor should be the same (1.522:1) if there is no gap between the center conductor and the foam, and the length should be the same (5" or longer for 2400 MHz).

  Bob, WA3WDR