Broadband permittivity measurements of low-loss materials using the Hilbert transform

A new method for calculating the broadband permittivity of non-magnetic, low-loss materials, from measured s-parameters made on a material sample placed in a transmission line, is proposed. The method assumes that the real part of permittivity can be modeled as a linear function of frequency with a negative slope. The imaginary part of permittivity is then calculated as the Hilbert transform of the real part. The problem of determining the Hilbert transform of a first order polynomial is addressed. An example that illustrates the validity of the approach is given. Measurements are made on two standard materials using the proposed technique.