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.

中文翻译：

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具有复杂终端负载的双频并联传输线变压器的新分析方法

本文介绍了一种具有复杂终端负载的并联传输线变压器，用于双频设计。通过分析复杂终端负载条件的不同情况，在电气长度-电气长度（EL-EL）平面上有四种不同的可设计区域映射模式。通过添加额外的垂直频率比 (FR) 轴，可以在 FR-EL-EL 坐标系上创建一个新颖的 3D 立方体，然后可以在这个 3D 立方体中轻松绘制可设计的频率比范围。因此，新报告了可视化 3D 映射方法，用于在两个不同频率下匹配并行传输线变压器的复杂终端负载。对于某种图案，可以划出明确的界限，以区分可设计和不可设计的范围。为了验证，设计了两个例子，制造和测量。模拟和测量结果非常匹配。