Low-order macromodels of planar waveguides exhibiting geometric, material, and layout uncertainty

A methodology is presented for the development of low-order macromodels of planar waveguides exhibiting uncertainty in the cross-sectional geometry of the conducting strips, the insulating material in which the waveguide is immersed, and in the waveguide layout. The proposed methodology makes use of stochastic collocation and the ideas of polynomial chaos expansion to capture the uncertainty in geometric parameters in the matrix representation of a finite-element/finite-difference model of the waveguide. Subsequently, a Laguerre-based, model order reduction process is used to generate a stochastic model of dimension significantly smaller than that of the original one. The accuracy of the proposed method is demonstrated through its application to the transient simulation of broadband signal transmission in a multi-conductor planar interconnect.