具精確頻寬之平行耦合微帶線帶通濾波器合成方法

Abstract

在本論文，作者提出平行耦合微帶線帶通濾波器之新合成方法，可獲取精確頻寬。傳統上，一段平行線耦合級係以兩段1/4波長傳輸線及中間夾一個導納轉換器來等效，由於導納轉換器並不具隨頻率改變之特性，因此此種等效模式僅在設計小頻寬時較為準確，當設計較大頻寬時，實際頻寬會明顯大幅縮減。為改善此問題，論文第一部份提出以頻帶邊緣等效取代中心頻率等效之觀念來修正傳統公式，以獲取較為精確之頻寬。更進一步地，論文第二部份提出以介入損耗函數來合成具有精確頻寬之平行耦合線帶通濾波器之方法。介入損耗函數可直接由耦合級串接之ABCD 矩陣推導得出，而不需使用含導納轉換器之等效電路，藉由與最大平坦函數及柴比雪夫函數比對係數，得出所需之合成公式。由於在某些嚴苛設計規格下，耦合線線寬及線距可能過窄難以實現，此時可運用合成公式提供之自由度適當選擇解答，放寬中間耦合級之尺寸，將困難移至兩端(輸入及輸出端)耦合級，並採用擇定饋入法(Tapped input)方式來實現端級。作者並實際合成數組大頻寬濾波器作為範例，以模擬及量測數據來與本文之理論計算結果做比較，證實此方法可行且頻寬相當精確。

In the thesis, authors propose the new synthesis methods of parallel-coupled microstrip bandpass filters (PCBPFs) with accurate bandwidth. In a conventional design, the equivalence of a coupled stage is established by using two quarter-wave transmission line sections with a J-inverter in between. Since the J-inverter is independent of frequency, the conventional equations are accurate only for filters with relatively narrow bandwidths. When a large bandwidth is designed, filters synthesized based on the conventional method will have a fractional bandwidth less than specification. In the first part of the dissertation, for recovering the bandwidth decrement, the correction □ = (□/2)(1 ± □/2) is incorporated into the synthesis formulas to modify the conventional method. Furthermore, the insertion loss (IL) functions are derived for synthesis of PCBPFs with accurate bandwidth. The synthesis is based on the composite ABCD matrix of all coupled stages instead of modeling each stage with the J-inverter equivalent circuit. Synthesis equations are established by matching the coefficients of IL function with the maximally-flat and Chebyshev functions. The under-determined conditions leave several degrees of freedom in choosing the circuit dimensions. By properly utilizing these degrees of freedom, the problem resulted from the tight coupled-line dimensions can be resolved by gathering all difficulties to the end stages and employing tapped input/output to replace the end stages. Several filters are simulated, fabricated and measured to demonstrate the formulation and circuit synthesis. The measured results manifest very accurate bandwidths.