Design of Triple-Band Impedance Transformers Using Z-Transform Techniques

Abstract

A new formulation of one section transmission-line and load impedance circuit in the $\boldsymbol{Z}$ - plane is employed to study transformers. The design procedures employ prototypes of transfer function, parametric modeling techniques, and optimization methods; a model describing transformer of multi-section transmission-line with load impedances is proposed. Triple-band of transfer function at the microwave frequencies is studied. This transformer was designed on a PCB FR4 substrate featuring a permittivity $\varepsilon\text{r} = 4.4$ , a loss tangent $\tan\delta = 0.0245$ , and a thickness of $\text{h} = 1.6 \text{mm}$ . The results of simulation and measurement show that a complex impedance can be matched at three frequency bands. The values of characteristic impedances of transmission lines synthesizing the transformers are adjusted according to the AR process by optimization algorithms. The experimental results are in good agreement with theoretical values.