Application Of Active Low-pass Filter In Chaotic Circuit

Filter,as a kind of circuit,which makes the useful frequency signal pass and restrains the useless frequency signal,its amplitude-frequency characteristic and the filtering effect have been well-known and widely used.However,from the perspective of the phase frequency group time delay,in addition to the attenuation of the useless band signal,the filter also has an important characteristic,namely,the signal has a phase shift function which can achieve the delay.The problem of realizing delay of chaotic signal using low-pass filter from the theoretical point of view is studied in this paper.The circuit structure is simple and easy to realize.Besides infinite dimensional equation can be translated to ordinary differential equation,which offers a new way to analysis of time delayed chaotic system.The filter is applied to chaotic circuits,such as delayed chaotic systems,chaotic delayed feedback control and generalized synchronization of delayed chaotic systems.And through the combination with numerical calculation and fulfillment in the circuit,the paper obtains same results with the theoretical analysis.The work done in the paper is as follows:1.Theoretical analysis of low pass filter.Firstly,this study analyzes characteristics of amplitude frequency and group delay of two order filter of Butterworth,Bessel,Chebyshev.The theoretical analysis is carried out towards the two class connection and higher order form of the Butterworth filter and Bessel filter,which lays the theoretical foundation for the realization of the chaotic signal without distortion delay.2.Implementation of delayed chaotic circuit.Taking a three order and two order delayed chaotic system as an example,the dynamic characteristics of them are analyzed,and the appropriate filter and connection method are selected to realize the non distortion delay of chaotic signal.Combined with the numerical calculation and circuit experiment,the theoretical analysis results of the filter delay effect are confirmed from the practical application.3.Chaotic delayed feedback control.The basic idea of the delayed feedback control is to make the delayed signal from a signal in the system feed back to the system to make the system remain stable in a certain periodic state.Taking a three order continuous chaotic system as an example,utilizing the filter to achieve the delay of the chaotic signal,multiple periodic orbits are obtained so as to achieve the purpose of delayed feedback control.4.Generalized synchronization of delayed chaotic systems.Taking Rossler delayed chaotic system as an example,the generalized synchronization and state switching between the drive system and the response systemare realized by applying the active and passive synchronization method.And the low-pass filter is implemented on the circuit;it is found that the theoretical analysis is consistent with results of numerical calculation.