Abstract-A reliable methodology for accurate modeling of microwave devices is presented. Our approach exploits cokriging which utilizes low-and high-fidelity EM simulation data and combines them into a single surrogate model. Densely sampled low-fidelity data determines a trend function which is further corrected by sparsely sampled high-fidelity simulations. Low-fidelity EM data is also enhanced by using a frequency scaling. With our method, accurate models can be obtained at a fraction of cost required by conventional approximation models that are exclusively based on high-fidelity simulations. Two cases of microstrip bandpass filters are considered. Comparisons with conventional approximation models as well as application examples are also given.Index Terms-Microwave modeling, response-surface modeling, co-kriging, electromagnetic simulation.
I. INTRODUCTIONAccurate and fast models (surrogates) are indispensable in the design of microwave structures and components. Many design tasks, such as parametric optimization, statistical analysis or yield-driven optimization, require numerous evaluations of a structure of interest and the use of highfidelity electromagnetic (EM) simulations may be prohibitive because of unacceptably high computational cost.Cheap models can be obtained using response surface approximation techniques such as polynomial regression [1], radial basis functions [2], kriging [2], support vector regression [3], or artificial neural networks [4]. However, for good accuracy, these techniques require a large number of training points, which exponentially grows with the dimensionality of the design space. This high initial setup cost may be justifiable for multiple-use library models but not quite for one-time design and analysis of a specific structure.Low-cost microwave modeling can be realized using space mapping (SM) [5]. Reasonably accurate SM surrogate model can be created using a limited number of high-fidelity EM simulations by applying suitable correction to the underlying lowfidelity (or coarse) model, e.g., equivalent circuit. A drawback of SM models is that increasing the number of training points may have little effect of the model's quality [6]. Also, SM requires that the coarse model is very fast, as each evaluation of the SM surrogate requires evaluation of the underlying coarse model.In this paper, we consider models constructed using both highand low-fidelity EM simulations. Simulation of coarselydiscretized structure is less accurate but it is much faster than the