Quarter wave impedance transformer

A quarter-wave impedance transformer, often written as λ/4 impedance transformer, is a component used in electrical engineering consisting of a length of transmission line or waveguide exactly one-quarter of a wavelength (λ) long and terminated in some known impedance. The device presents at its input the dual of the impedance with which it is terminated.

It is a similar concept to a stub; but whereas a stub is terminated in a short (or open) circuit and the length is chosen so as to produce the required impedance, the λ/4 transformer is the other way around; it is a pre-determined length and the termination is designed to produce the required impedance.

The relationship between the characteristic impedance, Z₀, input impedance, Z_in and load impedance, Z_L is: ${\displaystyle {\frac {Z_{\mathrm {in} }}{Z_{0}}}={\frac {Z_{0}}{Z_{L}}}}$

At radio frequencies of upper VHF or higher up to microwave frequencies one quarter wavelength is conveniently short enough to incorporate the component within many products, but not so small that it cannot be manufactured using normal engineering tolerances, and it is at these frequencies where the device is most often encountered. It is especially useful for making an inductor out of a capacitor, since designers have a preference for the latter.

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