Abstract
We consider a radial transverse resonance model for a circular cylindrical waveguide composed into two layers with different frequency dependent complex dielectric constants. An inverse problem with four unknowns - three physical material parameters and one dimensional dielectric layer thickness parameter - is solved by employing TE110 and TE210 modes with different radial field distribution. First the resonance frequencies and quality factors are found fitting a Lorentzian function to the ‘measured’ data, using the method of least squares. Then found resonance frequencies and quality factors are used in a second inverse Newton-Raphson algorithm which solves four transverse resonance equations in order to get four unknown parameters. The use of TE110 and TE210 models offers one-dimensional radial tomographic capability. An open ended coaxial waveguide quarter-wave resonator is added to the sensor topology, and the effect on the convergence of numerical method is investigated.
Highlights
Extraction of material parameters and/or dimensions based on distributed resonator measurements has been around for decades
We model two annular concentric cylindrical layers which are enclosed in a finite conductive metallic pipe, each with a frequency dependent dielectric constant, see Figure
The frequency range for the pair of open ended coaxial waveguide resonator was adapted in order to keep the resonance within a sufficiently wide frequency range
Summary
Extraction of material parameters and/or dimensions based on distributed resonator measurements has been around for decades. Characterization of distributed microwave resonators dielectric material from resonance frequency and quality factor measurements is found in [ ]. A comparison of inverse methods for extracting resonant frequency and quality factor is given in [ ]. We model two annular concentric cylindrical layers which are enclosed in a finite conductive metallic pipe, each with a frequency dependent dielectric constant, see Figure. We develop reliable least squares algorithms which allow determine four unknown physical parameters using a transverse resonance radial model, with additional model of the open ended coaxial waveguide quarter wave resonators. The possible applications are characterization of metallic pipes with annular flow, or characterization of optical fibers in similar geometries
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