Generalized short step transformers for multi-band impedance matching

The use and synthesis of stepped impedance transformers for multi-band applications is revisited from a new point of view. A short step commensurate transformer can be used for impedance matching simultaneously at several frequencies/bands, even for the important first harmonic frequency 2 f₀. An automated synthesis procedure borrowed from the lowpass filter theory is fully described. This procedure can provide reflection zeros at arbitrary frequency locations, thus leading to general responses in terms of return losses and matching frequencies. Finally, to validate the theory a microstrip prototype has been manufactured and measured.