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In this paper, a parallel transmission-line transformer with complex terminal loads is introduced for dual-frequency design. Through analyzing the different cases of complex terminal loads conditions, there are four different mapping patterns of designable regions on the Electrical Length-Electrical Length (EL-EL) plane. By adding an extra vertical Frequency Ratio (FR) axis, a novel 3D cube can be created on the FR-EL-EL coordinate system, then the designable ranges of frequency ratio can be easily drawn in this 3D cube. Therefore, the visible 3D mapping approach is newly reported for matching the complex terminal load of parallel transmission-line transformer at two different frequencies. For the certain pattern, a clearly boundary could be drawn to distinguish the designable and undesignable ranges. For verification, two examples are designed, fabricated and measured. Simulated and measured results are matched very well.

A Novel Analysis Approach for Dual-Frequency Parallel Transmission-Line Transformer With Complex Terminal Loads