The principle of decomposition in the analysis of microwave devices

The most universal method for calculating the electrical characteristics of multi-pole microwave devices is the decomposition (decomposition) of a complex device into a number of simpler devices that allow independent analysis and are characterized by one or another matrix of parameters. These simple devices are called basic elements. If the characteristics of the basic elements are subjected to preliminary study and nominal values ​​are established that determine the matrix of parameters for each basic element, then the analysis of the electrical characteristics of a complex microwave system is reduced to the calculation of parameter matrices for combining two or more basic elements using special algorithms.

In low-frequency passive electrical circuits, described in terms of voltages and currents, the choice of a limited number of basic elements is sufficient. The simplest basic elements are: 1) resistors (power absorbers); 2) capacitors (electric field energy storage devices); 3) inductive coils (magnetic field energy storage devices). When switching to ultrahigh frequencies, the properties of accumulation and absorption of electromagnetic energy are inherent in the entire internal volume of the device being analyzed and the selection of the basic elements becomes not so unambiguous.

The traditional approach to the decomposition of microwave devices involves the replacement of each selected basic microwave element by a certain equivalent circuit consisting of lumped elements L, C and R, as well as regular segments of the transmission line. Electrodynamic calculations of a number of basic elements are performed in advance, and the results are presented in the form of approximate formulas and reference tables determining the relationship of the nominal values ​​of the equivalent circuit elements with the geometric dimensions of the basic element, wavelength and parameters of magnetodielectrics. The advantages of this approach are universality, similarity with the theory of low-frequency circuits, as well as clarity of ideas about the operation of complex microwave devices, achieved through a reasonable idealization of equivalent circuits. The disadvantages of the traditional approach are the loss of accuracy when using simplified equivalent schemes and the difficulty in quantifying calculation errors.

The noted deficiencies are successfully overcome in a later formal electrodynamic approach, focused on the direct use of powerful computers. With the direct electrodynamic approach, microwave devices are decomposed into a number of basic elements in the form of geometric configurations that allow analytical or numerical determination of the matrix of parameters by solving Maxwell's equations under given boundary conditions. The subsequent finding of the matrix of parameters of a complex microwave device is carried out using exactly the same algorithms for combining multipoles as in the traditional approach based on equivalent circuits. The electrodynamic approach in principle allows one to perform calculations with any desired accuracy, however, this loses the visibility of the analysis and narrows the class of devices calculated by a specific computational program.

There are no deep fundamental differences between the traditional and electrodynamic approaches, and therefore the subsequent presentation of the methods for analyzing microwave multipoles using the principle of decomposition is based on the traditional approach based on the equivalent circuitry of the basic elements. In this case, two levels of decomposition should be distinguished: 1) representation of enlarged basic microwave elements in the form of equivalent circuits from segments of transmission lines and elements L, C and R, 2) division of the microwave path into enlarged basic elements and the use of multiplexing algorithms.