Compact dual-frequency impedance transformer for frequency-dependent complex source and load

This study presents a compact hybrid dual-frequency impedance transformer that is suitable for sources and loads having frequency-dependent complex impedances. The basic transformer comprises two transmission lines and two shunt stubs, and this configuration is adequate for the design of a dual-frequency impedance transformer for a few sources and loads. Compared with other studies, this work presents a distinct derivation concept to obtain the circuit parameters, thus enabling the achievement of a compact circuit. For some particular sources and loads that the basic structure is difficult to match because of line width limitations, lumped elements are added to overcome the limitation and further reduce the circuit size. The derived design formulas avoid errors caused by frequency-dependent deviations in the component values due to parasitic effects, which constitute a critical problem in Radio Frequency (RF) circuits that employ lumped elements. The simulated results are in good agreement with the measured results, and the frequency responses obtained herein validate the proposed structure and design procedure. This study presents a compact hybrid dual-frequency impedance transformer that is suitable for sources and loads having frequency-dependent complex impedances. A distinct concept to derive the analytical design formula to obtain the circuit parameters is proposed and enabling the achievement of a compact circuit. In addition, lumped elements are added to further reduce the circuit size and overcome the limitation of line width.image