| Popis: |
A variety of waveguide structures have been analysed for the measurement of the complex dielectric permittivity of liquids. Mode matching techniques are im- plemented to solve the forward problem of computing the scattering parameters for a sample of known permittivity filling a rectangular metal waveguide. Three different sample geometries are used. In the first, the liquid and the sample holder completely fill the waveguide cross section. As a result, only the dominant waveguide modes are matched across the discontinuity interface and an exact an- alytical relation between the S parameters and permittivity can be written. The second and third configurations are concentric cylinders and rectangles respec- tively, partially filling a metal waveguide, hence higher order modes are taken into account in the formulation. For the partially filled rectangular sample, a generalised scattering matrix method to obtain the overall scattering parameters due to the several discontinuity regions. Iterative methods are then introduced to solve the inverse problem of recover- ing the unknown permittivity from simulated or measured scattering parameters. For the partially filled waveguides, because an exact analytical relation does not exist, objective( error) functions are defined and minimized. The partially filled rectangular sample case is extended to obtain the resonant frequency and qual- ity factor of a dielectric loaded resonant cavity, and the results compared to the approximation normally used for the cavity perturbation technique. Finally, a rectangular dielectric waveguide method for liquid measurements was developed. This method has a treatment similar to the well known free space tech- niques. It has a distinct advantage of relaxing the strict requirements of sample dimension associated with metal waveguides, especially at higher frequencies. |
