Left-Handed Small Impedance Transformers and Their Application to Arbitrary Phase Differentiated Lumped Baluns for Impedance Transforming

Based on the concept that a left-handed transmission line section has a negative electrical length, two pi -type lumped-element circuits are presented as equivalent circuits, and it is newly suggested that a low-pass filter type can be its lumped-equivalent circuit under a certain condition. Applying the negative electrical length concept to Smith chart, LHCCTs (left-handed constant conductance impedance transformers) are derived and two are validated by measurements, adding 180deg right-handed transmission lines to LHCCTs. The LHCCTs can be used for building lumped-element baluns, which can be used for both impedance transforming and arbitrary phase difference between two outputs. To verify the balun performances, a balun for a 40 Omega-50 Omega impedance transforming and 120deg difference between two ouputs is designed and simulated. The simulation results show perfect input matching, perfect power division and perfect phase difference 120deg, which are quite different from the conventional baluns having only 180deg phase difference between two outputs.