The variational closed-forms of the capacitance formulae of a type of conformal coaxial lines are presented in this paper with the assumption that the equipotential lines are conformal to the contour of the coaxial line. The variational extreme formula of the functional of continuous functions is first obtained. Then the variational stable and analytical expression of the capacitance is deduced. Considering the actual applications, we give the variational stable formulae of the capacitances of the conformal coaxial transmission lines whose contours are homogeneous curves of the 1st, 2nd and n-th order. Examples are given including the conformal regular polygonal, elliptical and highorder elliptical coaxial lines.
2. Kuo, J. T. and K.-Y. Su, "Analytical evaluation of the MoM matrix elements for the capacitance of a charged plate," IEEE Trans. Microwave Theory Tech., Vol. 50, 1435-1436, 2002.
3. Collin, R. E., Field Theory of Guided Waves, McGraw-Hill, New York, 1966.
4. Cheng, D. K. and F. I. Tseng, "Gain optimization for arbitrary antenna arrays," IEEE Trans. on AP, Vol. AP-13, 973-974, 1965.