Multiple reflection method in dielectric characterization by pade approximants

Single-port time-domain measurements to determine the dielectric under test (DUT) properties in a broad-band frequencies range are carried out. The transitory response to a step voltage of a dielectric sample in a coaxial line leads to the determination of the total reflection coefficient and consequently to the determination of the complex permittivity. The incident and reflected signals in the DUT are analyzed by single or multiple reflection methods. The dielectric magnitudes determination in the multiple reflection method involves the solution of a transcendental equation. This paper presents a procedure to solve the equation transforming it to an analytical one by using Pade approximations. The described technique improves the convergence radius with respect to Taylor series and reduces the drawbacks associated with iterative algorithms. The proposed technique allows obtaining the reflection coefficient and the complex dielectric permittivity improving the precision and spreading the frequency range with respect to Taylor's approximation techniques used in the multiple reflection method. In this work the theoretic basis of the method is presented and its merit has been verified with simulated and experimental data in the microwave range.