Characteristic Impedances of Rectangular and Circular Waveguides for Fundamental Modes

Abstract

In this paper we analyze possible approaches for the calculation of characteristic impedances of rectangular and circular waveguides operating at their fundamental modes. Theoretical estimation and comparison of characteristic impedances is necessary for designing of modern microwave devices based of guides with different types of cross-sections. For waveguides the characteristic impedance is not a unique value. The paper presents three possible approaches to determine the characteristic impedances of waveguides. The definitions of the maximum voltage and current in the waveguide are proposed. Obtained formulas for characteristic impedances can be used in the development of various microwave devices based on rectangular and circular waveguides. The maximal voltage, current and average power have been defined for the fundamental TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</inf> mode of a rectangular waveguide. Based on these values the characteristic impedances for a rectangular waveguide have been obtained. The characteristic impedance for a rectangular waveguide is a product of a coefficient, ratio of narrow and broad wall sizes of a waveguide and its wave impedance. Besides, the maximal voltage, current and average power have been defined for the fundamental TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> mode of a circular waveguide. Using these values, the characteristic impedances for a circular waveguide were obtained. The characteristic impedance for a circular waveguide equals to a product of a coefficient and its wave impedance.