Synthesis of a Complex R<sup>i</sup>CR Filter with Flat Passband Characteristics

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  • Fujii Tatsuya
    Graduate School of Systems and Information Engineering, University of Tsukuba
  • Shouno Kazuhiro
    Graduate School of Systems and Information Engineering, University of Tsukuba

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Other Title
  • 平坦な通過域特性を持つ複素R<sup>i</sup>CRフィルタの一構成
  • 平坦な通過域特性を持つ複素R[i]CRフィルタの一構成
  • ヘイタン ナ ツウカイキ トクセイ オ モツ フクソ R[i]CR フィルタ ノ イチ コウセイ

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Abstract

<p>In this paper, a synthesis of a RiCR filter with flat passband characteristics is proposed. Because the RiCR filter include no inductors, we can reduce the required elements when we realize the filter using OTA's and C's. The transfer function Tc of the proposed circuit is obtained through the frequency transformation based on the special case of BLLT. Its prototype transfer function Tb is also a complex transfer function and has multiple transmission zeros placed at ω=-1 and 1. The kernel function of Tb is obtained by an analytical method not by numerical calculations depending on computers as used in many of the conventional methods. The proposed filter can be designed through a graphical method based on the relationship among ωc/bw (selectivity), ωc (center frequency) and Amin (minimum attenuation). The proposed circuit can be composed of 2n+4 OTAs and 2n capacitors. As an example, a 5th-order RiCR filter is designed. The proposed filter is compared with the complex Butterworth filter from the view point of the frequency characteristics and the number of the required elements. It is shown that the proposed RiCR filter has maximally flat response in the passband.</p>

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