3 the partial self-inductance of a thin parallelogram can be evaluated as a four-fold integral from the definition of the partial mutual inductance between two parallel thin parallelograms p and q each with a constant current density
The partial self-inductance of a thin parallelogram can be found from (2) by performing the integration over the same area.
It can be verified that (6) reduces to the expression of the self-inductance of a thin rectangle [8,11-13] for t = 0.
The total inductance of a planar zig-zag spiral inductor is then calculated with (1) using (6) for the partial self-inductance of the individual parts of the inductor and (8), (10) for the partial mutual inductance between any two parts of the inductor.
Table 2 shows the comparison between the partial self-inductance values of each part of the considered planar zig-zag spiral inductors obtained with the exact expression (6), [L.