Efficient analysis of parameter uncertainty in FDTD models of microwave circuits using polynomial chaos

An FDTD-based model is developed to analyze three dimensional microwave circuits with uncertain parameters, such as variability and tolerances in the physical dimensions introduced by manufacturing processes. The proposed method uses generalized polynomial chaos to expand the time-domain electric and magnetic fields in terms of orthogonal polynomial basis functions of the uncertain variables. The technique is validated by modelling a low pass microstrip filter with uncertain stub lengths. The computed S-parameters are compared against Monte Carlo simulations, and good agreement is found for the statistics over 0-20 GHz. A considerable computational advantage over the Monte Carlo method is also achieved.