Theoretical Consideration on Short- & Open-circuited Transmission Lines for Permeability & Permittivity Measurement

Abstract

  The use of short- and open-circuited transmission lines is widely known to be a simple method of measuring the permeability and permittivity of magnetic materials. Lumped element approximation is one of the methods to analyze these transmission lines. However, this approximation generally involves rather large model errors. We describe here a way to reduce these errors. The distributed element expression of short- and open-circuited transmission lines is expanded by a Taylor series, and the first and the second terms are adopted in a limited form. These analyses have clarified that this approximation could hold within ± 5% of model error if a phase shift βl is less than 90% of π/2 (1.4 radian), where β is the propagation constant and l is the sample length.