Optimization techniques using polynomial metamodels have been proved useful in computational aerodynamics, mechanical engineering and structural design. However, to the best of author’s knowledge, these techniques nave not been applied to optimization of microwave devices. In this paper, second order polynomial metamodel framework is described, with emphasis on optimization of frequency-selective microwave devices, such as filters. Polynomials are used to approximate the dependence of S-parameters on model parameters at different frequencies. Polynomial coefficients are obtained by solving a set of linear equations. It is shown, that generalized pseudoinverse matrix algorithm, such as skeleton matrix expansion or singular value decomposition, is obligatory for this purpose. Initial sensitivity analysis, one step per model parameter, does not provide enough data to build quadratic metamodel. However, implemented formulae can be easily applied to build linear model. Compared to traditional second-order polynomial model algorithms, the number of sensitivity analysis steps is effectively minimized.
The optimization problem is formulated as a set of nonlinear equations y = y*, where y is metamodel response, y* is desired response. This set is solved with modified Levenberg-Marquardt algorithm, which can handle simple box-type constraints. Specific weight factors are used to approach equal ripple, Chebyshev-type response. Test problem is used to illustrate better convergence properties of presented technique, compared to quasi-Newton method.