Impedance matching by tapered transmission lines

Expressions are found for the impedance deviations with change of wavelength at the input of a tapered section of transmission line, when the far end of the tapered section is joined to a coaxial line, which in turn is terminated by its characteristic impedance. It is found that the added resistance and reactance are least when the length of the tapered section is approximately an integral multiple of half wavelengths. If both the outer and inner conductors are tapered, there is an optimum taper which will give unity standing-wave ratio (s.w.r.) for half-wavelength sections, and a s.w.r. only slightly different from unity for other lengths. If it is desired to keep the diameter of one conductor the same on each side of the junction, the best method is to taper both conductors in opposite ways for a half-wavelength and then the same way. This produces either a bulge on the inner conductor or a constriction in the outer conductor.