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Evaluation of Complex Permittivities of Multilayer Dielectric Substrates at Microwave Frequencies Using Waveguide Measurements

The techniques that are presently available for the measurement of complex permittivities of dielectric substrates are only applicable to single layer substrates. This paper presents a new technique which uses the Finite Element Method (FEM) to estimate the complex permittivities of individual layers from the measurement of the S-parameters of a rectangular waveguide holding a multilayer dielectric substrate sample. In this method, a network analyzer is used to measure reflection and transmission coefficients of a rectangular waveguide loaded with a layered sample. Using FEM, the reflection and transmission coefficients are determined as a function of the complex permittivities of the multilayer substrate. Measured and calculated values of the reflection and transmission coefficients are then matched using the Newton-Raphson Method to estimate the complex permittivities of the layers of the sample.