IMPEDANCE AND POWER TRANSFORMATIONS BY THE ISOMETRIC CIRCLE METHOD AND NON-EUCLIDEAN HYPERBOLIC GEOMETRY

摘要

An introductory investigation on the means by which modern (higher) geometry can be used for solving microwave problems is presented. It is based on the use of an elementary inversion method for the linear fractional transformation, called the "iso¬metric circle method," and on the use of models of non-Euclidean hyperbolic geometry.nAfter a description of the isometric circle method, the method is applied to numerous examples of impedance and reflection-coefficient transformations through bilateral two-port networks. The method is then transferred to, and generalized in, the Clayey-Klein model of two-dimensional hyperbolic space, the "Clayey-Klein diagram," for impedance transformations through lossless two-port networks. A similar transfer and general¬ization is performed in the Clayey-Klein model of three-dimensional hyperbolic space for impedance transformations through lossv two-port networks.