Inductance computation for coplanar waveguide discontinuities with finite metallisation thickness

A variational formula in terms of the magnetic flux density is proposed in the inductance computations for coplanar waveguide (CPW) structures with finite metallisation thickness. Introducing Lagrange multipliers, the variational equation is solved by the hybrid finite-element method. Numerical results for the equivalent short-end inductance are presented and compared with published data. When the thickness is small the variational equation can be reduced to a perturbation formula involving the normal magnetic flux density which is available in the inductance computation for a CPW with zero thickness. The errors due to this approximation are investigated by comparing the results with those by the more accurate hybrid finite-element method. Numerical results for extensive discontinuities are presented by employing the perturbation formula