Lowpass Network Synthesis Using “Feldtkeller Correction Approach”

Abstract

In this paper, a new method named ''Feldtkeller correction approach'' (FCA) is proposed to correct impedance function (Z in) during the circuit network synthesis process. With this method, the remaining Z in is corrected after each element is extracted from Z in , 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 1.0464 x 10 −7. 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 3.7567 × 10 −5. 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.