Finite-element analysis of the effect of geometric tolerances on performance over a frequency band

Uncertainties in the geometry of a microwave device introduced by the manufacturing process lead to a variation in the device performance. To predict this variation by repeated computational field analysis of large numbers of randomly perturbed geometries is excessively costly. An alternative is to make use of the derivatives of the performance with respect to each geometric variable, cheaply available over the whole frequency band when the appropriate finite-element method is used for the analysis. Results are presented for an E-plane waveguide bend with six geometric variables; the standard deviation of the return loss computed with the proposed method agrees well with the value obtained by direct analysis of 128 randomly perturbed geometries. A half-height capacitive metallic post in a waveguide is also analyzed, and the standard deviation of the equivalent-circuit reactances is obtained.