Parametric and Structural-Parametric Synthesis of Nonuniform Transmission Line Resonators
A. V. Zakharov
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0i</sub> . We will call optimal resonators if they have a minimum ratio m = Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0max</sub> /Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0min</sub> 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: ZN(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 ZN(S) should be the minimum possible (N = N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> ) to implement the required ratio between certain critical frequencies; the characteristic impedances of the composite sections Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0i</sub> take only two values Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0min</sub> or Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0max</sub> . 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.