Optimum Design of Multi-band Transformer with Multi-section for Two Arbitrary Complex Frequency-dependent Impedances

N-frequency Transmission line transformers (TLTs) with N-section for two arbitrary complex frequency-dependent impedances is optimally designed based on an ideal transmission-line model. Optimum design equations of the proposed transmission line transformer are derived and solved by using Particle swarm algorithm (PSO) and Levenberg-Marquardt algorithm( LMA). Several numerical examples are given to verify the validity of the design.