The Design Of Single Tuned LC Filter Based On The Theory Of Fractional Calculus

In recent years, the fractional calculus is used more and more widely in circuits. Many research progresses and conclusions have been made. The results show that capacitor and inductor are essentially fractional component. So to study the fractional model is more suitable and reasonable to the nature of components. Because of the addition of fractional order, a new degree of freedom is added during the process of circuit design, it makes the engineering design more flexible. Many new phenomena beyond the range of the integer order circuit is observed in the fractional order circuit. So more thoughts and research is deserved. And fractional order circuit research has guiding significance for the application of fractional component in circuit.Based on the fractional model of the capacitor and inductor, the paper focuses on the exploratory research of the design of the fractional order single tuned LC filter. The following work has been done:The research status and development direction of fractional calculus in circuits are stated. And the fractional order mathematical model of the capacitor is introduced. According to the fractional order mathematical model of capacitor, the orders of film capacitor are measured by using the relationship between the phase angle and the order. The factors influencing the order are studied. Furthermore, the relationship between the order and the series or parallel connection is analyzed.The existing realization of the fractional order circuit is studied and analyzed. According to the existing realization of 0.9 order capacitor, the realization of 0.9 order inductor is derived by using the theory of circuit. And the relationship between the voltage and current of the component is simulated.The research of single tuned LaC filter and single tuned LCa filter is carried on. The impedance and resonant frequency of the two circuits is analyzed. And the change of resonant frequency and tuning sharpness with the order is studied in detail. On this basis, filtering effect between the fractional order filter and integer order filter is compared.This paper proposes a design method of the fractional order single tuned LC filter. The filter consists of the same order fractional order capacitance and fractional order inductance. The impedance, resonance frequency and tuning sharpness of the different order circuit is shown. Three ways to calculate the capacitance are presented. The radius and maximum admittance angle of the admittance circle of detuning filter is analyzed.According to the maximum admittance angle, two calculation methods to determine the resistance are proposed. The filtering abilities of the 0.9 order single tuned LC filter group and integer order single tuned LC filter are compared.