Sensitivity based statistical analysis of circuit parameters obtained from a quasi-TEM analysis of multiconductor transmission lines

The line parameters (such as propagation constants, C and L) of a multiconductor transmission line in a multilayered medium show statistical. variations, due to variations on the design parameters of the line. This statistical behaviour is analysed in the quasi-TEM approximation using a sensitivity based technique, requiring the computation of the derivatives of the line parameters with respect to the design parameters. Since we also need this information for most efficient optimisation techniques, we can perform optimisation and statistical analysis in one run. We compute the derivatives using adjoint style sensitivity evaluation. From the original quasi-TEM integral equation we derive a new integral equation with same kernel but with different right-hand side and with new unknowns equal to the derivatives of the original ones. All derivatives can be obtained with only one inversion of the integral equation.