Technical Papers and Presentations

Predicting the stochastic behaviour of electromagnetic systems is important in microwave circuit in applications such as terahertz, millimetre wave circuits, resonating structures, substrate integrated waveguides etc. Computational cost in predicting the variations due to the stochastic errors in the geometry and material properties is high in such problems because the number of degrees of freedom is large for the models involved. Certain intrusive methods can be applied for material variations which are efficient in terms of computation time, but for geometric variation, these do not work well due to the re-meshing requirements for geometrical alterations. Monte Carlo methods can be applied for such problems but involve estimating a large number of samples, which is impractical in the scenario.

The stochastic collocation method is a good candidate for geometrical variation assessment, which involves evaluating a few samples to predict the system stochastic behaviour for general probability distribution of an input parameter. This work implements the stochastic collocation method to estimate the geometric tolerance in microwave circuits using the COMSOL Multiphysics^® via LiveLink™ for MATLAB^®

. The geometric distribution is assumed to be varying as Gaussian and uniform distribution. The collocation uses the Lagrange interpolation scheme to realize the distribution of the transmission coefficient and resonant frequency of the EM system. The probability distribution of these output parameters is predicted with the assumed distribution of certain geometric parameters. The estimate of the mean and standard deviation of the system behaviours provides an insight into the tendency for the system to deviate from the designed permeances. The result is validated by comparing it with a few sample realisations in the Monte Carlo method.

The application of the method is demonstrated with a metallic post inside a waveguide. The post dimensions are assumed to be varying randomly. The analysis is carried out over a frequency range to estimate the tolerances of the device over the working frequency range. This method can be extended for general EM problems.