THE USE OF TWO FREQUENCY VARIABLES IN THE SYNTHESIS OF DISTRIBUTED CIRCUITS

Abstract

It is shown that in the synthesis of distributed circuits based on transmission lines, in general, complex functions of two frequency variables should be used, which allow constructing arbitrary circuit functions and fully cover the classes of physically realized transfer functions. The properties of an antimetric quadrupole in a complex two-dimensional space were investigated and the properties of converging (convergent) and divergent (divergent) lines were compared. A description of the elements "inductance" and "capacitance" in the class of functions of two complex frequency variables was obtained, which allows synthesizing circuits using the ideas and methods of Richards circuit theory. One of the main tasks facing developers of frequency-selective devices is to simplify designs and create calculation methods that will ensure filters with precision characteristics in their mass production. This is especially true for nodes on strip lines, since their design eliminates the possibility of any adjustments. The complexity and labor intensity of calculating and designing filters increases as the requirements for their characteristics increase. This leads to the need to create synthesis methods that require minimal labor and allow a unified approach to the design of various devices. When solving this problem, a significant role is played by transformations of the frequency variable. As for microwave devices, the analytical apparatus of frequency transformations is currently represented by Richards substitutions and can only be used for the synthesis of circuits consisting of proportional segments of homogeneous lines. In this regard, another type of frequency transformation is needed, which makes it possible to compare an NL of any class with a concentrated element or circle.