Useful path-independent integrals associated with TEM-mode transmission lines and a procedure for computation of rate of variation of capacitance with a cross-sectional dimension

Some path-independent integrals are shown to exist in the potential field of transmission lines in the TEM mode. These integrals have physical significance that can be used effectively in design, optimisation and inspection. In particular, they will be useful in sensitivity analysis of capacitance or impedance with cross-sectional dimensions, and the relative importance of cross-sectional dimensions. Each represents the rate of decrease of potential energy of the system with an increase in a dimension of the conductor. In the paper, the integrals are defined, and their relationship with line parameters such as capacitance or impedance are given. Examples are included to illustrate the validity of path independence. An alternative method, the stiffness derivative procedure, for a numerical calculation of the line integrals is also presented