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In this work, a new design method has been developed for the low-pass lter LPF circuits by using the Nth Bernstein polynomials to meet the requirements on the atness of pass-band and slope at the cut-off frequency. Almost all the methods utilized in the lter design are uni ed under a framework to obtain good results in both amplitude and phase respects. A simple but general synthesis method which is based on a new basic cell is given to simulate the circuits for controlling the realization of the designed lter on the basis of the requirements. Different type of lters which were not obtained since today are developed by this new method.