Analytical design of dual-band impedance transformer with additional transmission zero

This study presents a three-stage dual-band impedance transformer, capable of providing good match between two circuit modules and generating an additional and selectable transmission zero. The input impedances of the output circuit module are unequally complex at two uncorrelated frequencies. Among the three stages of the proposed transformer, the first stage transforms the complex impedance of the load to become equal resistance at the two frequencies. The second stage cancels out the susceptance produced by the first stage at the two frequencies concurrently and generates the desired transmission zero. The final stage transforms the equal and real impedance to the input circuit module. This study provides analytical formulation of each stage to obtain the required circuit parameters instead of numerical solution or optimisation. The proposed impedance transformer has up to four configurations, subsequently decreasing the possibility of using an extremely narrow or wide transmission line. Simulations and measurement demonstrate the reliability of the proposed structure and design formula. The simulation results agree measured results well, and comply with the specifications.