The Corbino approach, where the sample of interest terminates a coaxial cable, is a well-established method for microwave spectroscopy. If the sample is dielectric and if the probe geometry basically forms a conductive cavity, this combination can sustain well-defined microwave resonances that are detrimental for broadband measurements. Here, we present detailed simulations and measurements to investigate the resonance frequencies as a function of sample and probe size and of sample permittivity. This allows a quantitative optimization to increase the frequency of the lowest-lying resonance.
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The lowest resonance can be compared to that of a cylindrical cavity with well-known resonance frequency for a TMmnp mode:41
$\omega _{mnp}\break = \frac{[c]}{\sqrt{\mu \epsilon }} \sqrt{\frac{x_{mn}^2}{R^2} + \frac{p^2\pi ^2}{d^2}}$
Here, R is the radius and d the height of the cylindrical cavity, and xmn is the nth root of the Bessel function of order m. [c] stands for the velocity of light and μ and ε stand for the permeability and the permittivity. For a TM0n0 mode, i.e., p = 0, this frequency does not depend on d.40.
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