The transmission-line properties of a round wire between parallel planes

A transmission line is useful as a primary standard of impedance if there is a formula relating its wave resistance to its cross sectional shape. For this purposes the round wire between parallel planes is computed to a very close approximation. The method is based on dividing the usual single pole into a pair of spaced half-poles, between parallel lines on the plane of cross section. The resulting fomula covers all shape ratios to a high degree of approximation. Simple explicit formulas are given for the shape ratio and the wave resistance, each in terms of the others sufficiently close for practical purposes. For examples a line made of perfect conductors (assumed) and air dielectric (laboratory conditions), has a wave resistance of
50.000\pm.003
ohms if the ratio of radii is 0.54850 =1/1.82315.