Design sensitivity of frequency response in 3-D finite-element analysis of microwave devices

The finite-element method is an established computational tool for analyzing three-dimensional microwave devices. It can also provide, at little additional cost, the sensitivities of the device's scattering parameters to changes in design variables. This paper describes a method for computing these sensitivities over a whole range of frequencies in an efficient way, by solving at just one frequency and employing a Pade expansion in the complex frequency. The sensitivity of the reflection coefficient of a piece of empty waveguide to change in its length is computed with the new approach, and there is excellent agreement with the exact values available in this case. The insertion loss of a partial-height metallic post in a waveguide is also computed. The sensitivity to change in the post height found with the new method closely matches values obtained by direct analysis of the perturbed post at a number of discrete frequencies.