Lowpass Network Synthesis Using "Feldtkeller Correction Approach"

• Published in: IEEE access Vol. 7; pp. 27970 - 27982
• Main Authors: Dai, Zhijiang, He, Songbai, Pang, Jingzhou, Huang, Chaoyi, Peng, Jun, Yang, Zhenxin, Li, Mingyu
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplifier design; Broadband communication; Butterworth filter; Butterworth filters; Circuits; Frequency synthesizers; Impedance; impedance transformer; lowpass LC ladders; Mathematical analysis; Mathematical model; Network synthesis; Polynomials; Power amplifiers; Principal component analysis; real frequency technique; Ultrawideband; Zirconium
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2019.2894408

In this paper, a new method named "Feldtkeller correction approach" (FCA) is proposed to correct impedance function (<inline-formula> <tex-math notation="LaTeX">Z_{in} </tex-math></inline-formula>) during the circuit network synthesis process. With this method, the remaining <inline-formula> <tex-math notation="LaTeX">Z_{in} </tex-math></inline-formula> is corrected after each element is extracted from <inline-formula> <tex-math notation="LaTeX">Z_{in} </tex-math></inline-formula>, making it possible to ensure a successful synthesis. It is illustrated that a lossless low-pass network can be represented by certain polynomials constrained by Feldtkeller equation and a successful circuit synthesis can be continuous by updating the polynomial coefficients. Few examples are given to validate the proposed correction approach when it comes to the synthesis of the highest order impedance function. First, a 30th order Butterworth filter is implemented using FCA with a relative error of <inline-formula> <tex-math notation="LaTeX">1.0464 \times 10^{-7} </tex-math></inline-formula>. Then, S-parameter simulation based on the synthesis elements is performed and proved to be entirely consistent with theoretical values. To demonstrate the robustness of this method, several randomly generated impedance functions are tested and the average relative error of 100 generated 35th-order impedance functions is calculated to be <inline-formula> <tex-math notation="LaTeX">3.7567\times 10^{-5} </tex-math></inline-formula>. Third, a 1-3 GHz transformer impedance function acquired by real frequency technique is successfully synthesized via FCA. Finally, an ultra-wideband power amplifier is also designed with the aid of FCA. These results demonstrate that the proposed approach can be used to successfully synthesize the impedance function lower than 36th order.