Parametric and Structural-Parametric Synthesis of Nonuniform Transmission Line Resonators

Abstract

This article discusses methods of parametric and structural-parametric synthesis of resonators, which contain transmission line segments of the same length. These methods allow optimizing resonators of various configurations with different segments number $N$ and characteristic impedances $Z_{0i}$ . We will call optimal resonators if they have a minimum ratio $m = Z_{\mathrm {0max}}/Z_{\mathrm {0min}}$ at given ratio between the critical frequencies (poles and zeros of the input impedance). The input impedances of the resonators under consideration at the Richards’ frequency variable $S$ are described by the reactance functions of $N$ degree: $Z^{N}(S)$ . The parametric synthesis refers to stepped impedance resonators (SIRs). The structural-parametric synthesis refers to resonators of a more general form, which contain open- and short-circuited stubs. The methods are based on two states established in this paper: the order of the reactance function $Z^{N}(S)$ should be the minimum possible ( $N = N_{\mathrm {min}}$ ) to implement the required ratio between certain critical frequencies; the characteristic impedances of the composite sections $Z_{0i}$ take only two values $Z_{\mathrm {0min}}$ or $Z_{\mathrm {0max}}$ . These methods were used to synthesize different resonators useful for practical application. With the help of the structural-parametric synthesis, the resonators of a more complex configuration are synthesized, which significantly exceed SIRs. The results of the measurements and simulation are presented.