Implementation Of Fractional Passive Elements Based On FPGA

Fractional calculus has been widely used in electrical engineering,signal processing,electrochemistry and other fields.In the field of fractional order circuits,people have proposed a series of methods for the construction of fractional elements,but the implementation of these methods is complicated,the number of components is large,and the order cannot be adjusted flexibly.FPGA is a kind of digital hardware with high precision,high calculation speed and flexible debugging.These features of FPGA can be used to achieve high-precision numerical approximation of fractional order operators,and the order of fractional order operators can be flexibly adjusted by modifying the program.Therefore,FPGA-based fractional passive elements have order adjustability and higher accuracy.The thesis presents a method of constructing fractional passive elements based on FPGA.Firstly,the discrete methods of fractional order operators are compared,and the method with the best approximation effect and stability is selected.Using the method,z-domain approximation of the fractional order operator in the form of an IIR filter is derived.According to its z-domain approximation,the quantization method of its filter coefficients and its FPGA implementation structure are designed.In a certain frequency band,the fractional order operator is implemented based on FPGA.According to the port characteristics of the current feedback operational amplifier AD844 AN,the circuit structure of fractional passive elements based on FPGA is designed.Firstly,an operational amplifier circuit that can realize fractional order operator with any order is designed.Using the circuit to replace the ADC,DAC and FPGA in the realazation circuit of fractional passive elements in the simulation.The simulation results verify that the input impedance characteristics of the simulated circuit meet the input impedance characteristics of fractional passive capacitance(inductance)within a certain frequency band,that is,implementation of fractional passive elements based on FPGA is completed within a certain frequency band.