為了同時提供具寬頻特性與波束可調性的訊號給個人行動裝置，相位陣列天線需要對頻寬和輻射場型覆蓋範圍進行進一步的調整。近年來學術界、工業界和政府實驗室為了實現波束成型網路，在研究上付出了大量的努力。本文提出了一款基於4×4巴特勒矩陣的寬頻波束成形網絡（BFN），目的在實現波束控制的效果，並對該設計進行模擬與實作驗證。為實現連續性的波束控制，本文應用一種有效的激發方法，該方法同時激發了巴特勒矩陣的兩個波束端口，與傳統的 BFN（如：Butler、Nolen和Blass矩陣版本的設計方式）相比，本文提出的設計可以透過減少輸入端口數量，以實現連續性的波束掃描。所提出之設計具有寬頻特性，同時滿足低成本、低損耗、覆蓋空間廣的應用情境。
實現該設計的主要結構為寬頻可調式功率分配器 (TPD)，其功率分配比(PDR)理論上可達–∞到+∞。為了實現所需的TPD設計，論文中提出了一款基於嵌入式變容器結構的相位可重製合成傳輸線 (PRSTL)的設計，以提供TDP所需的相位移動特性。該傳輸線結構包含一組共用均勻線之間串接的左/右手結構。集總網絡的電容器由變容二極管取代，以達到調整相位響應的目的，而均勻線則會產生所需的額外相位延遲。與市面上常見的相移器相比，本文所提出的相移器設計具有結構簡單、低成本、低功耗的優點，同時保持具競爭性的效能。透過使用PRSTL作為調整元件，所提出之TPD在2.16 GHz至2.64 GHz間具有低反射係數和良好的隔離度表現，且該結構的傳輸損耗結果為3.5 dB，同時在2.16 GHz到2.64 GHz的頻率範圍間，其輸出端口的漸進相移平均偏差小於20°，與理論分析結果一致。

In order to supply individual mobile devices simultaneously and selectively with high bandwidth, phased array antenna design requires improvement in bandwidth and spatial coverage. Recently, there have been extensive efforts in academia, industry, and government laboratories expended to bring beamforming networks that can fulfill this requirement to reality. In this thesis, a broadband beamforming network (BFN) based on a 4-by-4 Butler matrix with the purpose of achieving full beam-steering capability is presented and experimentally verified. To enable continuous beam-steering capability, we apply an effective excitation method that simultaneously excites two beam ports of the Butler matrix. In comparison to conventional BFN, such as switch-beam version Butler, Nolen, and Blass matrices, the proposed topology can accomplish continuous beam scanning with a reduced number of input ports. The BFN can work at a broadband frequency range and is suitable for applications requiring low-cost, low-loss, and wide spatial coverage.
The main component in fulfilling the design is a broadband tunable power divider (TPD), whose power division ratio (PDR) can be theoretically tuned from –∞ to +∞. To realize the TPD design, a new combination of phase reconfigurable synthesized transmission lines (PRSTL) constructed based on embedded varactors is presented to provide phase shifting characteristics. The topology of PRSTLs comprises a cascaded left/right-handed structure in-between a pair of common uniform lines. The capacitors of the lumped network are replaced with varactor diodes in order to adjust the phase response, and the uniform lines generate the required extra phase delay. Compared with commercial phase shifters, the proposed phase shifter has the advantages of its simple structure, low-cost, and low-power consumption, while maintaining comparable performance. By utilizing PRSTLs as tuning elements, the TPD design has a low reflection coefficient and good port to port isolation from 2.16 GHz to 2.64 GHz. The transmission loss for the new BFN design is 3.5 dB, and the average deviation of the progressive phase shift at the output port is less than 20° from 2.16 GHz to 2.64 GHz, which is highly consistent with theoretical analysis.

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