This research presents a method using modal analysis by which electromagnetic characterization of materials in a partially filled rectangular waveguide, having a single top air gap, can be accurately performed. Thermal expansion of waveguides commonly occurs during high-temperature measurements, resulting in air gaps between the sample and waveguide walls. Higher order modes are excited by the discontinuous geometry, which are not accounted for in most closed form extraction algorithms. A correction must be applied that considers the complex power transmitted and stored by higher-order modes, not merely the dominant mode. Characterization independent of sample distance from the calibration plane is also presented.Expanding upon previous analysis of partially filled rectangular waveguides, a modal solution for a single air gap between the top of the material sample and the waveguide wall is developed. The analysis is performed on samples of dielectric to verify the method, and further tests are performed on magnetic shielding material.Boundary conditions between the empty and partially filled regions are formulated so it is only necessary to explicitly satisfy two of the existing three field components, the third being linearly dependent.Calculation of the complex permittivity and permeability of magnetic shielding material, within 10% of the true value, was achieved by using less than 20 modes.
AcknowledgementsTremendous thanks go out to several people: My wonderful wife who always loved me and tried her best to keep me on track through these 18 months -you'll have many more chances in the future. To my son -you're so wonderful! How hard it was for me to leave the house for work when I wanted to spend time with you! Thank you for being so well behaved.To Dr. Havrilla, my advisor and best professor, who put up with a lot of my procrastination, but was (and is) always patient with me, and made me realize the importance of thinking physically and caring about details. Thanks for the neverending encouragement. The support of Dr. Crittenden was invaluable, and I owe a large part of this work to his guidance.