具阻抗轉換暨任意功率分配之全對稱與半對稱鼠競環耦合器之精確合成

Abstract

本論文提出一種全對稱及半對稱的鼠競環混成器及耦合器，且此架構可以實現阻抗轉換及任意功率分配等特性。其中阻抗轉換特性是指輸入輸出埠的阻抗值可以不同，而任意功率分配特性則是指兩個輸出埠的功率比值可以為任意值。由於其半對稱的特性，傳統的奇偶模電路拆分法以及其相關的分析方法並不再適用。本論文提出兩種訊號激發的方法用來轉換原本的四埠混成器或耦合器變成為相關的兩埠網路。緊接著，本篇論文會詳細地演示S域濾波器合成方法，此方法可以用來合成這些兩埠網路。由於使用Ｓ域合成技術，所有關於濾波響應的規格皆為使用者可自定義，例如中心頻、頻寬、反射損耗的水平高度以及切比雪夫濾波響應的階數。此外，本論文也推導了一組簡單的設計方程式用來實現不等功率分配的特性。使用這些方程式，等功率分配的全對稱及半對稱鼠競環混成器可以被轉換成具有任意功率分配的鼠競環耦合器，其耦合器所有其它的規格皆跟原本的混成器相同。四個鼠競環電路被實作用來驗證本論文所提出的分析以及合成方法。其中兩個被製造的電路分別為六階全對稱鼠競環混成器以及五階半對稱鼠競環混成器。另外兩個則分別為二比一以及十比一功率分配五階半對稱鼠競環耦合器，且兩者同時具有輸入輸出埠分別為五十及七十歐姆的阻抗轉換特性。

This thesis proposes the full- and half-symmetric rat-race ring hybrids/couplers, in which the impedance transformation and arbitrary power division characteristics can be implemented. The impedance transformation property implies that the input and output port impedances can be different. The arbitrary power division property implies that the power ratio at two output ports can be arbitrary values. Because of the half-symmetry, the conventional even- and odd-mode partition and corresponding analysis method cannot be applied. Two signal-excitation methods are proposed to reduce the original four-port rat-race ring hybrids or couplers into corresponding two-port networks. Next, the S-domain filter synthesis method is demonstrated in this thesis in detail, and this method can be adopted to synthesize these two-port networks. Duo to the S-domain synthesis technique, all the specifications of filtering responses are user-defined such as a center frequency, a bandwidth, a return loss level, and an order of the Chebyshev response. In addition, the simplified design equations for realizing the unequal power division characteristics are derived in this thesis. By using these equations, the equal power division full- and half-symmetric rat-race ring hybrids can be transformed into the arbitrary power division rat-race ring couplers which other specifications are the same as original hybrids. Four rat-race ring circuits are implements to verify proposed analysis and synthesis methods. Two of these fabricated circuits are a sixth-order full-symmetric rat-race ring hybrid and a fifth-order half-symmetric rat-race ring hybrid, respectively. The other two circuits are the 3-dB and 10-dB power division fifth-order half-symmetric rat-race ring couplers with input/output impedance transformation of 50/70 ohm.