Variational Principles In Electromagnetics And Their New Development

The variational theory in electromagnetics and its application in computing the characteristic impedance of conformal coaxial transmission lines are presented in this thesis. Input impedance of wire antennas is also computed with a hybrid method of variational principles and the finite-difference time-domain method. Conformal coaxial transmission lines are a kind of transmission lines with special cross-sections, and the research on their characteristic impedance is of great importance. Since the variational method is useful for determining characteristic quantities such as resonant frequency and impedance, it is mainly used in this thesis. First, with the variational method, the variational lower bounds of the characteristic impedance are respectively computed of the conformal coaxial lines with circular, regular polygonal and elliptical cross-sections. Then the optimal variational lower bound of the conformal coaxial line with a square cross-section is obtained. Thirdly, the variational upper bound of the conformal coaxial line with a square cross-section is found with the variational method. Finally, the variational principles are applied in FDTD dipole antenna input impedance simulations. The input impedance computed with this method is compared with that computed with the traditional FDTD method. The result obtained shows that the former has a better agreement with the reference values.