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In this paper, we present a method of microwave circuits design combining frequency space-mapped neuromodeling (FSMN) approach with S-B adaptive frequency sampling technique. In neuromodeling, frequency space-mapping technique decreases the cost of training, improve generalization and reduce the complexity of NN topology. A Stoer-Bulirsch adaptive frequency sampling (S-B AFS) technique is used to decrease the cost for frequency sweeps in sampling. We use S-B AFS technique for FSMN implementation. The example of designing a microstrip parallel-coupled bandpass filter by means of electromagnetic bandgap (EBG) structure confirms the validity of this approach in both reducing the sampling time and increasing the accuracy of the neuromodeling.