新型寬頻一百八十度岔路環及微帶線三角互耦濾波器

Abstract

論文包含兩大部份，分別論述一種新型的微波被動電路。論文的第一部份解析了包含相位反相器的新型一百八十度岔路環，我們使用奇偶模的分析法，對此岔路環作系統性的分析，並且利用柴比雪夫(Chebyshev)函數合成其頻率響應。理論顯示包含相位反相器的 3 dB 一百八十度岔路環，其頻率響應可以二次柴比雪夫函數描述之，對於15 dB 的折返損耗有2.6倍頻寬。另外在各輸入出端加上四分之一波長轉換器，將可增加電路頻率響應至四次柴比雪夫函數。電路對15 dB 的折返損耗有高達4倍頻寬。對等功率分配及不等功率分配的設計方程式及設計曲線均已導出，結果顯示功率分配比率差距愈大，電路的頻寬亦愈大。在電路實作方面，我們提出利用有限地寬共平面波導(finite-ground-plane coplanar waveguide)來實現電磁場相位反相的電路。並以此相位反相器製造三個 3 dB 一百八十度岔路環及一個5倍頻單平衡式混頻器來印證理論的正確性及相位反相器的特性。四個電路的量測結果都相當符合理論計算值。 論文第二部份探討的是微帶線三角互偶濾波器。我們應用串接三角網路易於實現有限頻率傳輸零點及非對稱頻率響應的特性，並利用廣義柴比雪夫函數來合成其低通原形。電路的合成是基於一個梯形等效於串接三角網路的低通原型，合成的步驟亦詳盡地論述。由於串接三角網路的非對稱頻率響應，一個不隨頻率而變的電納元件必須加入低通原形。我們套用一常用低通轉帶通的頻率轉換於此低通原型，帶通濾波器的設計參數須作修正。我們實作一包含兩個有限傳輸零點的5極點微帶線帶通濾波器，實現的方式是結合微帶線髮夾形及二分之一波長開路諧振腔，其緊密的佈局不僅縮小濾波器的大小，更實現了串接三角網路非對稱頻率響應的特性。藉由電磁模擬軟體的幫助，可以決定每個諧振腔間所須的耦合距離。電路的量測結果也相當符合理論預測值。

Two novel microwave passive circuits are investigated in this thesis. In part I of this thesis, a novel broadband Chebyshev response rat-race ring coupler is proposed and analyzed. Based on the even-odd mode analysis technique, the rat-race ring coupler containing an ideal phase inverter shows a Chebyshev response of order two and a bandwidth of 2.6:1. The bandwidth is much broader than that of a conventional one. In a further study, we find that a unit element can be added at each port to increase the frequency response order of the ring coupler to Chebyshev response of order four and to broaden the bandwidth further. Design equations based on Chebyshev equiripple functions are derived. The design curves of equal or unequal power division are also presented. Theoretical data show that the bandwidth of unequal power division with a specific return loss value increases as the power division ratio increases or decreases from unity. For a 180°hybrid with equal power division (3 dB) and 15 dB return loss, the proposed rat-race ring may have a bandwidth of 4:1. Three circuits of this novel rat-race ring and a singly balanced mixer are realized using FCPW (finite-ground-plane coplanar waveguide). The measured results match very well with that predicted by the theory. In part II of this thesis, a new configuration of odd-degree cascade trisection bandpass filter realized by combining microstrip hairpin resonators and l/2-line open-circuited resonators is proposed. The generalized asymmetric Chebyshev function is used to synthesize the cascaded trisection prototype. A equivalent ladder network of the cascaded trisection lowpass prototype is derived and the synthesis procedure is also presented in detail. Because of the asymmetric characteristics, a frequency invariant susceptance is introduced into the lowpass prototype. A usual lowpass to bandpass transformation applies to the lowpass prototype and the design parameters of bandpass filter has been modified. A 5-pole microstrip cascaded trisection bandpass filter with two asymmetrically prescribed transmission zeros located on opposite side of the passband is designed and fabricated. A full-wave EM simulator, IE3D, which is based on the method of moments, is used to determine the coupling spacing between resonators. The experimental result matches well with the theory.