High Precision LC Ladder Synthesis Part I: Lowpass Ladder Synthesis via Parametric Approach

In this paper, a novel, high precision lowpass LC ladder synthesis algorithm is presented. The new algorithm directly works on the driving point input immitance function which describes the lowpass LC ladder in resistive termination. The crux of the idea is that, at each step of the proposed method, a simple pole at infinity is removed then, the remaining immitance function is corrected using the parametric method. Parametric method warrants the exact lowpass LC ladder nature of the remaining immitance function. Thus, at the end of the synthesis process, a lowpass LC ladder is obtained with high numerical precision. Examples are presented to exhibit the implementation of the synthesis algorithm. A randomly generated driving point input immitance is synthesized with 19 elements yielding a relative error less than 10^-6. Furthermore, numerical robustness of the novel synthesis method is tested. Based on the tests, we can confidently state that, proposed synthesis algorithm can safely extract more than 40 elements from the original immitance function with a relative error less than 10^-2. Newly developed synthesis algorithm is coded on MatLab environment and it is successfully combined with the “Real Frequency-Direct Computational Technique” to construct practical impedance matching networks.