In all applications of transmission line, it is required that the load be matched to line, Which requires tuning out the unwanted load reactance and the transformation of resulting impedance to the required value especially at high frequencies. The impedance of the quarter line depends on load impedance and characteristics impedance as shown
When the length S is exactly quarter wavelength line then the line is lossless. If the Zo is varied, the impedance seen at the input to the λ/4 transformer will also vary accordingly, so that load may be matched to characteristic impedance of the main line. This is similar to varying turns ratio of a transformer to obtain the required value of input impedance to match the load impedance. Quarter wave transformer works as filter to prevent unwanted frequencies from reaching the load such as antenna. The name transformer is given to quarter wavelength transmission line since it behaves as a transformer depending upon the value of ZL.
If ZL = Zo then it acts as 1 : 1 transformer.
If ZL >Zo then it acts as a Step down transformer
If ZL <Zo then it acts as a Step up transformer