The quarter-wave transformer transforms in one frequency f/sub 0/, but not its first harmonic 2f/sub 0/. The transform in 2f/sub 0/ is needed in a dual-band 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/sub 0/ (fundamental), or 2/3 wavelengths in the upper band centering at 2f/sub 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 |/spl Gamma/| = 0.013.
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Chow et al. (2002) studied this question.