The non-uniform fields that occur due to the slot in the cavity through which the sample is inserted and those due to the sample geometry itself decrease the accuracy of dielectric characterization by cavity perturbation at microwave frequencies. To address this problem, we measure the natural frequency and damping ratio of a resonant cavity as a function volume as a sample is inserted into the waveguide cavity. We found that for a range of cavity fillings, a linear regression on the natural frequency and damping ratio versus the effective volume fraction of the sample in the cavity could be used to extract the complex permittivity of the sample. We verify our technique by measuring a known quartz substrate and comparing the results to finite-element simulations. When compared to the conventional technique, we show about an order of magnitude improvement in the accuracy for our samples. We also investigate two samples: a neat stoichiometric mixture bisphenol A epoxy resin and one containing a mass fraction of 3.5% multi-walled carbon nanotubes. At the TE103 mode (7.31 GHz), the permittivity and loss tangent of the epoxy were measured to be εr = 2.93±0.11 and tanδ = 0.029±0.002, respectively. The epoxy with a mass fraction of 3.5% multi-walled carbon nanotubes had a permittivity of εr = 8.01±0.48 and loss tangent of tanδ =0.144±0.011.
IEEE Transactions on Microwave Theory and Techniques
microwave, metrology, noncontact, nondestructive, resonator, x-band, electrodeless, nanocomposites, bisphenol A expoxy, multi-walled carbon nanotubes, gigahertz