Loss minimisation in λ/4 impedance transformers using multiple lλ4 segments

Presented is an analysis of loss in quarter-wavelength impedance transformers. It is shown that the loss of an impedance transformer, S₂₁, is a function not only of the dielectric and conductor loss, but also the transformation ratio. S₂₁ is derived as a function of both loss and transformation ratio and it is shown that for high transformation ratios, using two or even three quarter-wavelength impedance transformers results in an overall lower loss.