Equivalent characteristic impedance formula of waveguide and its applications

Abstract

AbstractThe equation widely known as the characteristic impedance of the waveguide is defined from the voltage in the cross section, wall current along the axial direction and Poynting vector. For the rectangular waveguide, the impedance has a form proportional to (b/a)λ. However, it is not possible to derive a correct reflection coefficient with this form of characteristic impedance. It has been predicted empirically by the present authors and others that the characteristic impedance connected directly to the reflection coefficient has a form proportional to bλg. However, investigation of the theoretical foundation has not been carried out clearly.In this paper, based on the fundamental differential equation describing the characteristics of the nonuniform waveguide, a transmission line equivalent to the waveguide is derived. By means of this transmission line, the forementioned characteristic impedance is proven to be theoretically correct. Here, this quantity is called the equivalent characteristic impedance.Based on this result, it is proved that there are several different procedures for the analysis of the characteristics of the tapered waveguide and that they all arrive at the same results. The theoretical results are verified by three different experiments. In addition, the applications of this equivalent characteristic impedance are described for the design of the connecting tapered waveguide and the quarterwave transformer.