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We present Space Mapping (SM) optimization.Space mapping is a technique which uses simple surrogate models to reduce the computing time in optimization procedures where time-consuming computer-models are needed to obtain sufficiently accurate results.Thus, space mapping makes use of both accurate models and less accurate (but cheaper) alternatives using the accurate and time-intensive electromagnetic simulators.Such simulators represent "fine" models of the circuit under consideration.SM exploits the existence of a less accurate but fast "coarse" model, e.g., an empirical model.A mapping is established between the parameter spaces of the coarse and fine models.The fine model design is the inverse mapping of the optimal coarse model design.In order to ensure that the space mapping algorithm includes two models, the first model is accurate, but is not effective, and referred to as fine model while the second model is accurate enough and very effective, and referred to as the coarse model.In this thesis we work on mapping the variables in the two models using mathematical approaches as well as the HFSS software tool for analysis and design.Using the two models, the results demonstrate that the use of the coarse model provides better results and improves the effectiveness of the implemented system.The main idea of the space mapping technique is to use the coarse model to gain information about the fine model, and to apply this in the search for an optimal solution of the latter.Thus the technique iteratively establishes a mapping between the parameters of the two models which possess similar model responses.Having this mapping, most of the model evaluations can be directed to the fast coarse model.