Derivatives of partial inductances for the sensitivity analysis in PEEC systems

When applying the adjoint sensitivity analysis to an electromagnetic (EM) field solver, the derivatives of the system matrix elements with respect to the design parameters have to be computed. In this paper the partial element equivalent circuit (PEEC) method is utilized in the magneto-quasi-static regime where the system matrix elements represent partial resistances and inductances. Closed-form solutions for the derivatives of these elements with respect to the shape parameters under consideration are found for arbitrary positioned parallel conductors with rectangular cross sections. Results are presented for the AC impedance of a sole conductor and are compared with finite-difference approximations.