具頻率相關耦合之步階阻抗諧振器的準橢圓函數響應濾波器之合成與實現

Abstract

本論文研究具頻率相關耦合結構的濾波器合成與實現。首先探討具頻率相關耦合特性的三元結構(Trisection)，產生一對傳輸零點的機制。具有此類型零點的濾波器一般稱為準橢圓濾波器。僅使用頻率無關耦合特性的三元結構，通常只能產生一個傳輸零點。本文所提出的新型三元結構能產生一對零點。濾波器合成的演算過程中，頻率相關耦合結構的電路模型是將複數頻率變數s乘以固定導納轉換器(J-inverter)。研究發現分接線(Tapped-line)結構的輸入輸出會產生更多零點。文中將呈現具四個零點的三階電路以及具五個零點的四階電路設計。論文的第二部分探討平行緊密並排的步階阻抗諧振濾波器。研究發現此結構的非相鄰諧振器之間亦具有頻率相關的耦合特性。因此，濾波器的通帶兩側也會各產生一個零點，使過渡帶具有較大的衰減斜率。除此之外，分接線輸入輸出結構所產生的零點也會加以探究。文中所有電路的模擬結果和測量數據都相當一致。

This dissertation aims at synthesis and realization of microstrip coupled- resonator filters with frequency-dependent cross-coupling. The first part presents the synthesis of trisection filters incorporating the frequency-dependent coupling to achieve a quasi-elliptic function response. In the admittance matrix of the lowpass prototype, the coupling is simply modeled by a constant J-inverter multiplied by the complex frequency variable s. In realization, tapped-line input/output is used and more zeros can be generated in the upper and lower rejection bands. The second part studies stepped-impedance resonators in a compact inline arrangement. It is found that certain transmission zeros can be created by nonadjacent frequency-dependent coupling. Enhanced attenuation rate in transition bands can then be obtained. Zeros created by tapped input/output structure are also investigated. For demonstrations, measured results for experimental filters are compared with simulation data.