Flexible Approximation Functions for Broadband Matching

Abstract

Introduction. Intensive use of broadband signals in RF devices for various purposes is associated with the need to develop broadband elements of RF systems. Iterative methods for designing such elements are frequently uninformative and ineffective, while analytical methods give solutions only for simple models. The problem is the small set of classical approximations, which impedes dealing with complex models of elements.Aim. Development of a wide-band matching technique based on generalized Darlington synthesis using flexible approximating functions (AF) for load models with zeros of transmission at infinity.Materials and methods. The paper is based on the generalized Darlington synthesis method. To extend the capabilities of the method, approximating functions with increased variation properties are used. In order to use the results in engineering practice, a synthesis algorithm was developed, which includes three stages: formation of the frequency response, control of analyticity of the used functions and limits of matching. The method is analytical and does not use iterative procedures. The mathematical apparatus of the method is based on the analysis of residues in the zeros of transfer function of load resistance.Results. Flexible approximating functions proved to be an effective tool for designing matching circuits with multiple transfer zeros in infinity. Variative properties of the function facilitate the realization of both smooth and wave frequency characteristics. A combination of both is also possible, ensuring the best properties of both. The proposed approximating functions allow a smooth change in the frequency response, while preserving the normalization characteristic of classical approximations. Application of such functions allowed us to virtually remove the limitations inherent in the classical AF on the minimum values of the load capacitance and more than 30 % of the limiting values of inductance in the above examples.Conclusion. The developed methodology makes the process of wideband matching physically transparent and can be applied to other classes of loads.