A transformer of one-third wavelength in two sections - For a frequency and its first harmonic

The quarter-wave transformer transforms in one frequency f(0), but not its first harmonic 2 f(0). The transform in 2 f(0) is needed in a dual-hand operation of GSM and PCS. This requirement can be fulfilled in a two line-sections of 1 / 6 wavelengths each, adding to 1 / 3 wavelengths for the total transformer length in the lower band centering at f(0) (fundamental), or 2/3 wavelengths in the upper band centering at 2f(0) (1st harmonic). The 1/3-wave transformer is analytically inexact but effectively exact for engineering applications. For example, for impedance transforms of K = 4, the inexactness gives a reflection of \Gamma\ = 0.013.