PROCEDURE FOR THE SYNTHESIS OF ROD DISTRIBUTED STRUCTURES IN THE PLANE OF TWO FREQUENCY VARIABLES

Abstract

The generalization of Richards' theorem to the positive real function (PRF) of two complex frequency variables is carried out. It is shown that the positive real function of two complex frequency variables can be implemented in the form of a unit element loaded on a resistance described by the PRF of the order no larger than the original PRF. It is shown that the reactance function of power n of two frequency variables is implemented by a cascade connection of n symmetrical single elements, short-circuited or open-circuited at the far end. The obtained ratios allow synthesizing circuits based on heterogeneous transmission lines. Examples of the synthesis of circuits with a given input resistance are given. When designing microwave circles, segments of long lines with the same electrical length, but with different wave impedances (Richards circles) are used. The disadvantages of such circles include the periodicity of the amplitude-frequency characteristics (AFC) and the need to implement lines with very low or very high characteristic impedance, which in some cases is difficult or impossible. One of the ways to eliminate these shortcomings is to use long lines with a characteristic impedance that varies along their length (non-uniform lines (NL)). By choosing the characteristic impedance of the NL, you can change the electrical characteristics of the transmission line: input impedance, complex transmission coefficient under real and complex loads, increase the operating frequency range of various distributed devices (resonators, filters, matching circuits, frequency tuning ranges, etc.). Current tasks in this direction are the research of various types of NL for the development of filtration circles with more advanced characteristics in contrast to existing analogues. The purpose of this work is to determine a procedure for identifying unit elements using arbitrary quadripoles for complex frequency variables.