CN107124260A - A kind of Second-order Non-autonomous Chaotic Circuit based on active diode bridge memristor - Google Patents

Abstract

The invention discloses a second-order non-autonomous chaotic circuit based on active diode bridge memristor. The circuit is composed of an AC voltage signal source AC, an operational amplifier U, a resistor R, a capacitor _C1 and a first-order active generalized memristor G _M. A simple, reliable chaotic signal generator with simple circuit topology is realized. The chaotic signal generated by the signal generator can be used as a random signal in chaotic secure communication, chaotic signal synchronization and artificial noise.

Description

A second-order non-autonomous chaotic circuit based on active diode bridge memristor

technical field

The invention relates to a chaotic signal generator, which realizes a simple and reliable second-order non-autonomous chaotic signal source.

Background technique

Memristor is a new concept proposed by Chinese scientist Cai Shaotang in the 1970s. It is the fourth basic component besides inductors, capacitors and resistors. The salient features of memristors are memory and nonlinearity, which can simulate neuron-like behavior, and are the most ideal physical devices for simulating the human brain. In 2008, Hewlett-Packard's laboratory made nano-scale TiO ₂ devices for the first time, which shocked the international electrotechnical and electronic technology circles. In the following years, reports on memristor and its related applications showed a blowout growth. Memristor chaotic circuit is one of the application branches. After the introduction of memristor, the chaotic circuit has more complex dynamic behavior than the conventional nonlinear circuit. Finding a chaotic circuit with a simpler topology and fewer components to form a reliable and practical electronic circuit with significant features and advantages can enrich the application of chaotic signal generators in engineering.

Contents of the invention

The technical problem to be solved by the present invention is to realize an active second-order memristive chaotic signal generator.

In order to solve the above technical problems, the invention provides a second-order non-autonomous chaotic circuit based on active diode bridge memristor, its structure is as follows:

The main circuit is shown in Figure 2, including: a standard sinusoidal voltage signal source AC, an operational amplifier U, a resistor R, a capacitor C ₁ , and a first-order active generalized memristor G _M ; the positive terminal of the signal source AC is connected to the operational amplifier The non-inverting input terminal of U, the negative terminal of AC is connected to "ground"; the inverting input terminal of U is connected to the output terminal, at this time U forms a voltage follower (also called a buffer); the left end of the resistor R is connected to the output of U terminal, the right end of R is connected to the positive terminal of capacitor _C1 , and the negative terminal of _C1 is connected to "ground"; the positive terminal of generalized memristor G _M is connected to the positive terminal of capacitor _C1 , and the negative terminal of G _M is connected to "ground";

The realization circuit of the first-order generalized memristor G _M is shown in Figure 1, including: resistors R _a , R _b , R _M , R ₀ , diodes D ₁ , D ₂ , D ₃ , D ₄ , inductor L, and operational amplifier U _M . Note that the input end of the generalized memristor G _M is "1", and the output end is "2". The "1" terminal is connected to the non-inverting input terminal of the operational amplifier U _M , the resistor R _a is connected between the non-inverting input terminal and the output terminal of U _M , the resistor R _b is connected between the inverting input terminal and the output terminal of U _M , and the resistor The upper end of R _M is connected to the inverting input end of U _M , and the lower end of R _M is connected to the "2" end. _The anode of diode D1 is connected to the cathode of D4, which is referred to as terminal a, and terminal a is connected to the generalized memristor input terminal " ₁ "_; the cathode of diode D1 is connected to the cathode of D2, which is referred to as terminal b _; the anode of diode _D2 is connected to The negative pole of D ₃ is connected to terminal c, and terminal c is connected to the generalized memristor output terminal "2"; the positive pole of diode D ₃ is connected to the positive pole of D ₄ , which is denoted as terminal d; terminal d is connected in series with inductor L and resistor R ₀ and then connected to b end.

The beneficial effects of the present invention are as follows:

The second-order non-autonomous chaotic circuit based on the active diode bridge memristor of the present invention has an extremely simple structure and can generate complex nonlinear phenomena, and can be used as a new chaotic signal source.

Description of drawings

In order to make the content of the present invention easier to understand clearly, the present invention will be further described in detail below according to specific embodiments in conjunction with the accompanying drawings, wherein

Fig. 1 Memristor symbol and first-order active generalized memristor equivalent circuit;

Figure 2 A second-order non-autonomous chaotic circuit based on active diode bridge memristor;

Fig. 3 state variable x-y plane numerical simulation phase track diagram;

Fig. 4 state variable v ₁ (t)-i _L (t) plane experiment phase orbit diagram;

detailed description

Mathematical modeling: the present invention adopts a first-order active generalized memristor, and its equivalent realization circuit is shown in Fig. 1 . Let the input terminal voltage and current of the first-order active generalized memristor G _M be v and i respectively, and the current flowing through the inductance L of the internal dynamic element of the memristor be i _L , the mathematical model of the memristor can be described as

Among them, ρ=1/(2nV _T ), I _S , n and V _T represent the reverse saturation current, emission coefficient and cut-off voltage of the diode respectively, I _S =5.84nA, n=1.94, V _T =25mV.

The first-order generalized memristor described by formula (1) is used to construct the second-order non-autonomous chaotic circuit, as shown in Figure 2. _Its dynamic _model can be _expressed as

Wherein, v _s =Asin(2πft) is a sinusoidal voltage signal, A=2V, f=6kHz.

Do the following scale transformation for formula (2):

The dimensionless equation of formula (2) can be written as

Numerical simulation: According to a second-order non-autonomous chaotic circuit based on active diode bridge memristor shown in Figure 2, using the MATLAB simulation software platform, the numerical simulation analysis of the system described by formula (4) can be carried out. The Runge-Kutta (ODE) algorithm was chosen to solve the system of equations. Select typical circuit parameters C ₁ =20nF, R=2kΩ, R _a =R _b =2kΩ, R _M =1kΩ, R ₀ =50Ω, L=100mH, A=2V, f=6kHz. Substituting the scale-transformed parameters into formula (3), the MATLAB numerical simulation phase trajectory diagram of the chaotic circuit state variable x(t)-y(t) plane can be obtained, as shown in Figure 3.

Experimental verification: select the AD711KN operational amplifier and provide ±15V DC operating voltage, the diode model is 1N4148, the capacitor is a monolithic capacitor, the resistor is a precision adjustable resistor, and the inductor is hand-wound. Make an experimental circuit, use the digital signal source of the model Tektronix AFG 3102C to provide a standard sinusoidal voltage signal, and use the digital oscilloscope of the model Tektronix TDS 3034C to verify the circuit state variables in the v ₁ (t)-i _L (t) plane under typical parameters The phase track diagram is shown in Figure 4. By comparison, it can be found that Figure 3 and Figure 4 are basically consistent, and this result further confirms the correctness of the analysis of the chaotic phenomenon that can be generated by a second-order non-autonomous chaotic circuit based on active diode bridge memristor.

A second-order non-autonomous chaotic circuit based on the active diode bridge memristor realized by the invention has a simple structure and can be used as a simple and feasible new chaotic signal generating circuit. It is believed that this invention will greatly promote the development of chaotic systems.

The above-mentioned embodiments are only examples for clearly illustrating the present invention, rather than limiting the implementation of the present invention. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here.

Claims (4)

1. A second-order non-autonomous chaotic circuit based on an active diode bridge memristor, characterized in that it includes a sinusoidal signal source AC, an operational amplifier U, a resistor R, a capacitor C ₁ , and a first-order active generalized memristor G _M . 2. A kind of second-order non-autonomous chaotic circuit based on active diode bridge memristor according to claim 1, characterized in that: the positive terminal of signal source AC is connected to the non-inverting input terminal of operational amplifier U, and the negative terminal of AC is connected "Ground"; the inverting input terminal of U is connected to the output terminal, at this time U forms a voltage follower (also called a buffer); the left end of the resistor R is connected to the output end of U, and the right end of R is connected to the positive terminal of the capacitor _C1 The negative terminal of C ₁ is connected to "ground"; the positive terminal of generalized memristor G _M is connected to the positive terminal of capacitor C ₁ , and the negative terminal of G _M is connected to "ground". 3. A kind of second-order non-autonomous chaotic circuit based on active diode bridge memristor according to claim 1, characterized in that: the realization circuit of first-order generalized memristor G _M comprises: resistors R _a , R _b , R _M , R ₀ , diodes D ₁ , D ₂ , D ₃ , D ₄ , inductor L, and operational amplifier U _M . Note that the input end of the generalized memristor G _M is "1", and the output end is "2". The "1" terminal is connected to the non-inverting input terminal of the operational amplifier U _M , the resistor R _a is connected between the non-inverting input terminal and the output terminal of U _M , the resistor R _b is connected between the inverting input terminal and the output terminal of U _M , and the resistor The upper end of R _M is connected to the inverting input end of U _M , and the lower end of R _M is connected to the "2" end. _The anode of diode D1 is connected to the cathode of D4, which is referred to as terminal a, and terminal a is connected to the generalized memristor input terminal " ₁ "_; the cathode of diode D1 is connected to the cathode of D2, which is referred to as terminal b _; the anode of diode _D2 is connected to The negative pole of D ₃ is connected to terminal c, and terminal c is connected to the generalized memristor output terminal "2"; the positive pole of diode D ₃ is connected to the positive pole of D ₄ , which is denoted as terminal d; terminal d is connected in series with inductor L and resistor R ₀ and then connected to b end. 4. A kind of second-order non-autonomous chaotic circuit based on active diode bridge memristor according to claim 1, 2 or 3, characterized in that: contain 2 dynamic element capacitors C ₁ and first-order active generalized memristor G _M , the circuit differential equation can be expressed by two state variables v ₁ and i _L , and the normalized dimensionless differential equation can be expressed by two state variables x, y.