quarterwavetransformator

Quarter-wave transformer, also known as a quarter-wave transformer, is a short section of transmission line with electrical length equal to one-quarter of the wavelength at the design frequency. It is used to match a source impedance Zs to a load impedance ZL in RF and microwave circuits by transforming the load impedance through the line’s characteristic impedance Z1.

For a lossless line, the input impedance looking into a quarter-wavelength section terminated by ZL is Z_in = Z1^2 / ZL. To achieve a perfect match at the design frequency, the characteristic impedance of the section is chosen as Z1 = sqrt(Zs ZL). Then Z_in equals Zs, and the source sees the load as its own impedance.

In practice the transformer is realized as a short piece of transmission line—coax, microstrip, or stripline—designed to have the required Z1 and to be electrically lambda/4 long at the target frequency. Because the transformation depends on frequency, the match is narrowband and sensitive to manufacturing tolerances, temperature, and dispersion. Losses in the line also affect performance, especially at higher frequencies.

For broader or more complex impedance environments, engineers use multi-section quarter-wave transformers, tapered transmission lines, or other matching networks (such as L or Pi configurations) to extend bandwidth or accommodate varying source and load impedances.

The concept is a standard tool in RF design, illustrating the impedance inversion property of quarter-wavelength lines and underpinning many classic RF adapters and matching networks.