Improved Approximations for the Fringing and Shielded Slab-Line Capacitances

Given the dimensions w/(b - t) and t/b for the slab-line geometry or the dimensions s/b and t/b for the fringing capacitance geometry, it is shown how the capacitances associated with each geometry can be determined accurately from new explicit expressions rather than by a computerized search. The two expansions for the nome q´, in terms of the dimensions, which are essential for the calculations, are identical except for signs. Finally, comparisons are made with values of the capacitances obtained by a computerized search.