Synthesis of lumped dual-frequency impedance transformers for complex loads using inverters

Novel lumped dual-frequency impedance transformers (DFITs) for arbitrary frequency dependent complex loads (FDCLs) are synthesized using the concepts of capacitive and inductive inverters. Such a dual-frequency impedance transformer is constructed with one Pi-shaped lumped inverter and two shunt susceptance blocks at two sides, and get simplified after susceptance merging. The shunt susceptance blocks have specified susceptance values at two frequencies and are realized with lumped circuits of certain topologies. Design formulas of the DFITs are derived and are validated by two examples. Compared with a former technique, this method uses less lumped elements and provides one design freedom, so largest matching bandwidths can be achieved by comparing a series of possible designs.