Research Of Fractional-order Filter

The fractional calculus theory has been widely used nowadays.It has played an important role in many fields.The fractional calculus theory has been introduced into the design of filter and the capacitor has been replaced with fractional order capacitance.The fractional filter be accurately designed,which allows for stepping the stop-band attenuation very precisely.This kind of filter can be used in biomedical and other areas with special requirements.However,there is no commercial fractional capacitance at present.Instead of fractional components,RC circuit network has been widely used in the study of fractional order filter.In a certain range of frequency,the impedance characteristic of the designed RC circuit network is very close to the impedance characteristic of the fractional capacitor.This thesis uses RC circuit network to replace the fractional order capacitor and studies three kinds of filters: the first order RC filter,the Butterworth filter and the Chebyshev filter.The order of these filters is extended to fractional which are called fractional order filters.The fractional order filters are designed based on the typical model of circuits.Further more,the thesis discusses the realization of the high order of fractional order Butterworth filter and fractional order Chebyshev filter.Finally,the 0.7 order active filter,the 1.4 order Butterworth filter and the 1.8 order Chebyshev filter are selected for the actual circuit test.The amplitude frequency response corresponding to each frequency in the actual circuit is compared with the ideal amplitude frequency response.And the cause of the error is analyzed.According to the actual effect of the circuit,the three kinds of filters designed in this thesis are successfully realized,and the filtering effect meets the requirement of the index.