Date of Award

Fall 2011

Degree Type


Degree Name

Master of Applied Science (MASc)


Electrical and Computer Engineering


Natalia K. Nikolova


John W. Bandler



Committee Member

Mohamed H. Bakr, Ali Emadi


This thesis proposes a new analytical self-adjoint sensitivity analysis to calculate the Jacobian of the S-parameters for metallic shape parameters. This method is independent of the full-wave numerical analysis and the respective system matrix. The theory works for both volumetric and infinitesimally thin metallic shapes. It exploits the computational efficiency of the self-adjoint sensitivity analysis (SASA) approach where only one EM simulation suffices to obtain both the responses and their gradients in the designable parameter space.

There are three major advantages to this development: (1) the Jacobian computation for metallic structures is completely analytical and there is no approximation involved in the sensitivity analysis of shape parameters; (2) the implementation is straightforward and in the form of a post-processing algorithm operating on the exported field solutions on the surface or around the edge of the metallic structure; and (3) it provides the possibility for exact sensitivity analysis with all electromagnetic high-frequency simulators whose system matrices are not available to export or are not differentiable with respect to shape parameters, e.g., simulators based on the FDTD method and the MoM.

The method was verified in a number of examples using a commercial finite-element solver. The agreement between the results calculated with the proposed method and the reference self-adjoint sensitivity curves provided with the simulator are very promising.

Suggestions for future work are provided.

McMaster University Library