The Devices of Frequency Selection on Non-Regular Transmission Lines

The paper presents the results of solving the problem of parametric optimization of nine-section harmonic filter, the structure elements of which are the sections of canonical non-regular transmission lines.

Canonical non-regular transmission lines are new types of non-regular lines. Their distinctive feature is a fact that a correspondent impedance function involves four independent parameters. They are: the section length, impedances at the section ends and a constant that takes on any value on the real axis. Thus, the number of varied parameters in the parametric optimization is twice as much when compared with two parameters that characterize the regular transmission line section. This promotes the finding of the optimum solution.

The important property of the canonical impedance function is a fact, that it involves, as a particular forms, the known impedance functions for which the accurate solutions of differential equations of single-wave theory of non-regular transmission lines were found, as well as a number of new functions. Among the latest, the non-monotonous impedance functions are exceptional.

Accurate analytical relationships for the elements of classic non-normalized transfer matrix of the two-port that substitutes the canonical non-regular transmission line section were found for canonical impedance function. These formulas are compact and are expressed by the elementary functions.

The parametric optimization problem in the standard formulation was solved for the nine-section harmonic filter, the prototype of which was chosen as a stepped structure, each section of which is a regular line. The prototype parameters were taken as the initial approach. The optimization results are the numerical values of the non-regular transmission line section lengths, the impedances values at the section ends, and a real constant. A comparison of the amplitude-versus-frequency characteristics of the prototype and harmonic filter on the canonical non-regular transmission lines showed a significant (more than twice as much) broadening the stop band, the increase of the slope of the fronts together with the insignificant (about 3%) increase of the total length of the device.

The performed investigations allow us to recommend the canonical non-regular lines as structural elements of the functional units for antenna-feeder devices.