Analysis of transmission line resonators using minimax polynomials

Input impedances of low-loss transmission line resonators are generally expressed in terms of transcendental functions. Poles and zeros of the resonators are not explicitly shown in these expressions. Minimax polynomials have been reported to accurately approximate some transcendental functions. In this paper, a minimax polynomial is used to approximate the input impedance expression of transmission line resonators. The approximate formula is used to find poles and zeros in the frequency range of interest. A numerical example shows that the input impedance calculated by the approximate formula agrees very well with that of the exact one.