KR101335720B1 - Chaos signal generator circuit using transconductance-based non-linear negative resistance - Google Patents

Abstract

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to the implementation of an electronic circuit that generates a continuous time type chaotic signal that can be used for cryptographic communications. Chaos signal control is enabled according to the control voltage of the resistor and the shape of the current-voltage curve of the nonlinear negative resistance.

Description

Chaos signal generator circuit using transconductance-based non-linear negative resistance}

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for implementing an electronic circuit that generates a continuous time type chaotic signal that can be used for encrypted communication. More specifically, a nonlinear negative resistance based on a CMOS transconductor and a CMOS transconductor based inductor The present invention relates to an electronic circuit for controlling a chaos signal through a MOS type variable resistor capable of varying a resistance value according to a control voltage.

The word chaos is often translated as 'chaos' or 'confusion' and is a word of concept relative to cosmos, which means order. Chaos originates in Greek and is the first chaotic state of the world, the chaotic state of heaven and earth.

In the field of engineering, terms such as Chaos Theory and Chaos Engineering are used. The concept of chaos phenomenon is that a small perturbation of external input generates a unique solution through a nonlinear feedback process. It is defined as representing an unpredictable random characteristic. Chaos phenomena have been continuously conducted in 1975 by mathematical biologist R. May, who studied mathematical models of variation in living organisms. In addition, studies have been conducted to apply the complex chaos phenomenon of the nonlinear dynamometer to hardware in the form of electronic circuits and apply it to crypto communication, chaos neural network, and the like. A representative example of implementing a chaotic system as an electronic circuit is a Chua circuit.

While the chaos system appears to be similar to the system of fuzzy theory in a seemingly disordered fashion, the fuzzy system does not always have a definite answer and has the characteristic of judging true or false by the combination of 0 and 1. In addition, the chaos system is a solution to nonlinear equations that are not solved in conventional analysis, but it is different from fuzzy systems because it has a key to solve since it is obtained from a deterministic dynamic system.

Chaos systems provide the key to solving the answer, and provide signal characteristics with wide frequency characteristics similar to noise. Due to the characteristics of the chaos system, chaos signals are used in encryption processes for communication security.

The chaos system is very sensitive to initial values, so the chaos attractor is represented in the state space as an infinite unstable perildic orbit. This feature is undesirable and has been considered difficult to control. The recent chaos control has emerged as a new concept and has attracted much interest in the fields of physics, engineering, chemistry, medicine and mathematics. OGY first conducted an experiment to control the chaotic orbit as the periodic orbit. However, the OGY technique requires continuous computation and control to achieve the desired control in the chaotic state. Pyragas also introduced the concept of continuous feedback control to experiment with controlling the unstable chaos to the desired periodic state.

There have been many studies on the synchronization between chaos systems, and even though the chaos system is the same chaos system, synchronization has been regarded as a difficult problem because a small change in the initial value causes a large change immediately. When pecora and Carroll decompose the chaos system into a drive system and a stable response subsystem, when all Lyapunov indices in the response subsystem have negative values, the drive system Has reported that driving a signal results in chaotic self-synchronization. Cuomo and Oppenheim pointed out useful aspects of the analysis and synthesis of chaos signals and predicted that they would be applied in many areas. Chaos signals typically have a wide spectrum frequency characteristic and are difficult to predict, such as noise. This feature can be applied to wideband frequency communication, and it is possible to construct a communication system using an information waveform masking technique.

The circuit for generating a chaos signal may be implemented in various ways according to the chaos formula. In general, the chaos signal is generated by using passive elements such as a resistor (R), an inductor (L), and a capacitor (C). When the chaos generating circuit is configured using a passive element as in the related art, the implementation is easy, but it is difficult to obtain accurate values of R, L, C, etc., and it is impossible to implement the chip. Therefore, it is preferable to configure an active element without an inductor element, that is, an operational amplifier (Op-amp) and a resistor. Yamakawa IC chips are two-dimensional chaos signals and digital signals, which require various and complex chaos signals, and are difficult to apply when analog signals are required.

In addition, many techniques for controlling chaotic signals have been studied. The OGY method requires continuous calculations, and the Pyragas method has a technique of controlling the unstable periodic track (UPO) to a stable track by feedback control. However, such a control method controls the chaos signal by applying a signal from the outside as a periodic signal. There is a technique of chaos synchronization between pecora and Carroll as a technique for controlling chaos signals as chaos signals.

In the prior art, Korean Patent No. 0202423, "Chua Chaos Generation Circuit," discloses an invention of an improved Chua chaos circuit which is most widely used as an electronic circuit for generating such a chaos signal. In the prior art, a technique of designing a three-dimensional churn state equation by a state variable circuit implementation method using an operational amplifier and implementing it on a substrate has been disclosed.

1 shows a general follower circuit. Chua circuits consist of fixed resistors, inductors, capacitors, and nonlinear resistors called chua diodes. Chaos signals can be obtained by solving differential equations of the state variables, ie, current and voltage, under certain conditions. In order for an electronic circuit composed of a resistor, a capacitor, and an inductor to exhibit chaos, it must be a tertiary or higher system including at least one nonlinear element.

[Equation 1]

When the state variables are defined as V1, V2, and V3, the circuit is represented by three ordinary differential equations as shown in Equation 1, from which a chaotic signal can be obtained under specific conditions.

In Fig. 1, a nonlinear resistor having a negative resistance can be generally realized through an appropriate combination of an operational amplifier and a linear resistor. The circuit shown in FIG. 1 is implemented using a typical nonlinear resistor consisting of individual elements, and FIG. 2 shows a current-voltage characteristic curve of the nonlinear resistor portion of the circuit of FIG.

The key to the hardware implementation of the Chua circuit is the implementation method of nonlinear resistors with negative resistance. Many types of nonlinear resistors have been implemented, but most are based on hybrid types that utilize op amps and resistors. On the other hand, for various engineering applications such as encryption communication, not only stable controllability of chaos signals but also integration possibilities for miniaturization are required. So far, the Chua circuit has remained a hybrid form of discrete component structure, and it has been difficult to control chaos signals because it is implemented around simple passive elements.

The implementation using the op amp has been difficult to integrate because it requires a large number of active devices, and it is time for the development of the Chua Chaos circuit to solve this problem.

Korean Registered Patent No.0202423 "Chua Chaos Generation Circuit"

T. S. Parker and L. O. Chua, "Chaos: a tutorial for engineers", Proc. IEEE, vol. 75, no. 8, pp. 982-1008, 1987. L. O. Chua, et al., "A universal circuit for study and generating chaos-part I: routes to chaos", IEEE Trans. Circuits and Syst., Vol. 40, no. 10, pp 732-744, Oct. 1993. L. O. Chua "Chua's circuit 10 years later", Int. J. Circuit Theory and Application, vol. 22, no. pp. 279-305, 1994.

SUMMARY OF THE INVENTION The present invention relates to an electronic circuit implementation for generating a continuous time type chaotic signal usable for cryptographic communications, except for a conventional capacitor, using a CMOS OTA based equivalent inductor, instead of a passive inductor, for ease of integration. Also, it is composed of CMOS OTA-based nonlinear negative resistor, and according to the shape of the current-voltage curve of this nonlinear negative resistor, the state variable of Chaos equation is differently implemented and MOS active resistor with control terminal instead of passive resistor is used. The purpose is to control the signal.

In order to achieve the above object, the chua chaos signal generation circuit of the present invention includes a CMOS OTA-based inductor-first capacitor circuit connected in parallel with each other, and a node of one side of the CMOS OTA-based inductor-first capacitor. A transconductance-based nonlinear resistor connected in series between a variable resistor connected in series with a node on one side of the circuit, and a node on the other side of the variable resistor and a node on the other side of the CMOS OTA-based inductor-first capacitor circuit. And a second capacitor connected in parallel with the transconductance-based nonlinear resistor.

At this time, the transconductance-based inductor replaces the inductor of the passive element, and consists of two transconductors and one capacitor. The equation for equivalent inductance is given by Equation 2 below. Where gm1 and gm2 represent the transconductances of the two transconductors.

&Quot; (2) "

In addition, the transconductance-based nonlinear resistor may take the form of a positive feedback operational transconductance amplifier to exhibit nonlinear negative resistance between input and output terminals. The transconductance-based nonlinear resistor also includes a current mirror consisting of a pair of transistors and a pair of output transistors connected in series with the current mirror. The gate terminal of each of the pair of output transistors will function as two output terminals of the transconductance based nonlinear resistor.

The variable resistor may include two MOS diodes having different directions from each other, a control transistor connected in parallel to both terminals of the two MOS diodes, and a control voltage applied to a gate terminal thereof. In this case, two MOS diodes are implemented using MOS transistors.

According to the present invention, a state variable of a chua chaos state equation is implemented as an electronic circuit using a variable resistor made of MOS, an OTA based inductor made of CMOS, and an OTA nonlinear negative resistor made of CMOS. Can be. Specifically, the state variable of the chaotic equation can be represented by adjusting the variable resistance value according to the control voltage of the MOS active resistor and the resulting operational point corresponding to the current-voltage curve characteristics of the nonlinear negative resistance. This has the effect of controlling the generation of the chaos signal.

In particular, in the present invention, the conventional op-amp based chua diode is replaced with a nonlinear negative resistor based on CMOS OTA, the passive element inductor is replaced with a CMOS OTA based inductor, and the passive resistor is composed of a MOS transistor. It is produced by a variable resistor and is differentiated from the prior art.

The present invention can be implemented in a low-area to enable the chaos signal to be integrated, it is possible to control the chaos signal can be applied to the technical field, such as secret communication (chaos) memory.

1 is a schematic block diagram of a conventional chua chaotic signal generating circuit.
2 is a current-voltage characteristic curve of the circuit of FIG.
3 is a schematic block diagram of a chaotic signal generating circuit of the present invention.
4 is an example of a chaotic output waveform generated by the circuit of FIG. 3.
5 is a diagram illustrating phase characteristics of the chaotic signal of FIG. 3.
6 is a diagram illustrating a specific embodiment of a MOS-based variable resistor.
FIG. 7 is a current-voltage characteristic curve of the variable resistor of FIG. 6.
8 illustrates one specific embodiment of a transconductance based nonlinear resistor.
9 is a current-voltage characteristic curve by the circuit of FIG. 8.
10 is various examples of an output signal of a chaotic system according to a change in a control voltage of the variable resistor of FIG. 6.
FIG. 11 shows some examples of transistor conditions of the nonlinear resistor of FIG. 8, and shows signal waveforms and chaotic dynamics in the time domain for the first condition.
FIG. 12 is a diagram showing a signal waveform of a second condition and a SPICE circuit simulation result of chaos dynamics shown in FIG. 11.
FIG. 13 is a diagram illustrating a signal waveform of a third condition and a SPICE circuit simulation result of chaos dynamics shown in FIG. 11.

Other objects and features of the present invention will become apparent from the following description of embodiments with reference to the accompanying drawings.

In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. However, the present invention is not limited to or limited by the embodiments.

Preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

3 is a block diagram illustrating an example of a chua chaotic signal generating circuit of the present invention. In FIG. 3, a variable resistor using a MOS transistor is used instead of a fixed resistor, and a conventional op amp-based chur diode is replaced by a non-linear resistor based on a CMOS Operational Transconductance amplifier (OTA). In addition, instead of a passive inductor, CMOS OTA-based inductors are used to enable semiconductor integrated circuits.

Therefore, since the chaotic chaos signal generating circuit shown in FIG. 3 can reduce the number of required active elements compared with the prior art, there is an advantage in integration.

The chaotic chaos signal generating circuit of FIG. 3 includes two capacitors C1 and C2 and one CMOS OTA based inductor L, and is composed of one MOS transistor variable resistor R and a CMOS OTA based nonlinear resistor.

CMOS OTA-based inductor L and capacitor C1 are connected in parallel with each other, and capacitor C2 and the nonlinear resistor are also connected in parallel. The variable resistor R is connected in series with parallel CMOS OTA-based inductor L-C1 circuits and C2-nonlinear resistor circuits.

In this case, the CMOS OTA-based inductor L is implemented as an inductor equivalent circuit having a capacitance CL connected in series to two CMOS OTAs gm1 and gm2 connected in parallel. gm1 and gm2 represent the transconductance gain of CMOS OTA, respectively.

Implementing the inductor L in such an equivalent circuit is easier to integrate on a semiconductor integrated circuit using a CMOS process.

FIG. 4 illustrates output waveforms of the chaotic signal generated by the circuit of FIG. 3, and FIG. 5 illustrates comparison of phase characteristics between V1 and V2 of the chaotic signal. At this time, the output signal is similar to the noise in the time series, and it can be seen that it has the characteristics as a chaos signal in terms of phase.

6 is a circuit of a MOS-based variable resistor, and FIG. 7 shows a current-voltage characteristic curve according to the control voltage Vc of the circuit of FIG. 6. 6 includes two diode connection transistors M1 and M2, connected in parallel in opposite directions for the flow of bidirectional current, wherein M1 and M2 are each formed using a P-type MOS transistor. M3 is composed of NMOS transistors connected in parallel between these M1 and M2, and a control voltage Vc is applied to the gate terminal of M3.

In this case, the size of each transistor in the circuit of FIG. 6 may be embodied as 100 um / 2 um for M1, 100 um / 2 um for M2, and 10 um / 2 um for M3 in one embodiment. It will be apparent to those skilled in the art that the present invention is only present, and the size does not limit the spirit of the present invention.

In FIG. 7, it can be seen that the resistance characteristic curve between both ends of the variable resistor changes according to the change of the control voltage Vc of the MOS variable resistor, which becomes a factor capable of adjusting the chaos dynamics of the chaotic system.

8 shows an improved form of a Chua diode, which is a CMOS OTA based nonlinear resistor. OTA-based chute diodes are made in the form of positive feedback to have negative resistance. M1 and M2 of FIG. 8 are composed of NMOS transistors, and each gate terminal serves as two terminals of a nonlinear resistor. M3 and M4 of FIG. 8 serve as current mirrors that supply current to M1 and M2 as current mirrors. By adjusting the W / L size of the transistors of M1 and M2 of the OTA, they can have different nonlinear resistance curves, which can be used to control the characteristics of the chaotic system.

In one embodiment shown in FIG. 8, the size W / L (channel width / channel length) of the transistors M1, M2, M3, and M4 is 60 um / 2 um, 60 um / 2 um, and 100 um / 2 um, respectively. , 100 um / 2 um and the size of the current source is 800 uA. Such numerical values are merely intended to represent one embodiment of the present invention, and it is apparent to those skilled in the art that the spirit of the present invention is not limited thereto.

The current-voltage characteristic curve of the circuit of FIG. 8 is shown in FIG. 9. In FIG. 9, the current / voltage characteristic curves of the respective cases are shown while varying the W / L conditions of M1 and M2 of FIG. 8 to 60 um / 2 um, 30 um / 2 um, and 15 um / 2 um. As shown in FIG. 9, it can be seen that the nonlinear resistance has negative resistance, and that the size of M1 and M2 of FIG. 8 can be adjusted as a means for adjusting the chaotic dynamics.

FIG. 10 is a diagram showing chaotic characteristics of the chaotic chaos generating circuit of FIG. 3 of the present invention. FIG. The chaotic characteristics of FIG. 10 are SPICE circuit simulation results for the circuit of FIG. 3. The value of the device used in the simulation is L = 7 mH, C1 = 47 nF, C2 = 4.7 nF, which also corresponds to one embodiment, it does not limit the spirit of the present invention.

According to FIG. 10, it can be seen that as the control voltage Vc applied to the gate terminal of M3 of FIG. 6 is changed, the time waveform and the characteristic characteristic curve of the circuit are different. When Vc = 1V, it shows chaotic state.When Vc = 2V, it is quasi chaotic state, when Vc = 3V, quasi periodic state, and when Vc = 4V, periodic When the state (cycle state), Vc = 5V, it can be seen that the equilibrium state has been reached.

According to the control voltage Vc of M3 of FIG. 6, the bias condition of the entire circuit of FIG. 3 is changed, and at this time, the chaotic state may appear differently according to the current-voltage characteristic of the nonlinear resistor of FIG. 8.

11 to 13 are simulation results for monitoring the characteristic change of the entire chaotic system when the current-voltage characteristics of the nonlinear resistor of FIG. 8 are changed.

11 to 13 fix M3 and M4 of FIG. 8 at 100 μm / 2 μm under the condition of Vc = 1.5 V, and change the W / L values of M1 and M2 of FIG.

The first condition is 60 um / 2 um for both M1 and M2 in FIG. 8, the second condition is 30 um / 2 um for both M1 and M2 in FIG. 8, and the third condition is 15 um / for both M1 and M2 in FIG. 8. It is a condition having a size of 2 um.

In FIG. 11, the SPICE circuit simulation result according to the first condition is shown. It shows the characteristics of V1 and V2, the dragging characteristics of V2 against V1, and shows chaotic characteristics.

In FIG. 12, the SPICE circuit simulation result according to the second condition is shown. Similarly, the characteristics of V1 and V2 and the dragging characteristics of V2 relative to V1 are shown, and it can be seen that a certain periodicity pattern appears.

In FIG. 13, the SPICE circuit simulation result according to the third condition is shown. Similarly, the characteristics of V1 and V2 and the phase characteristics of V2 relative to V1 are shown and it can be seen that the equilibrium state has been reached.

In the above, the present invention proposes a circuit that uses a variable resistor of a voltage control method instead of a conventional fixed resistor. Thus, it is possible to obtain an advantage of controlling the characteristics of the chaotic system in various ways.

Meanwhile, OTA-based nonlinear negative resistance is used to reduce the number of active devices and facilitate integration as compared with the conventional op amp. In the proposed system, the first control factor occurs in the MOS type variable resistor, and the second control factor is that the overall system characteristics can be changed by differently adjusting the component values of the OTA-based nonlinear negative resistance. .

Such various control factors of the present invention are expected to be applicable to various fields such as encryption communication, chaos memory in the future by diversifying the characteristics of the chaos system.

Claims (4)

An inductor connected in parallel with each other-a first capacitor circuit;
A node having one node connected in series with a node of one side of the inductor-first capacitor circuit;
A transconductance based nonlinear resistor connected in series between the node on the other side of the variable resistor and the node on the other side of the inductor-first capacitor circuit; And
A second capacitor connected in parallel with the transconductance based nonlinear resistor
Lt; / RTI >
The transconductance based nonlinear resistor
A chaotic chaos signal generating circuit in the form of a positive feedback arithmetic transconductance amplifier to exhibit nonlinear negative resistance characteristics between input and output terminals.
The method of claim 1,
Wherein the inductor comprises two mutually coupled transconductors and an inductance equivalent circuit in which one capacitor is connected in series.
delete The method of claim 1,
The transconductance based nonlinear resistor comprises a current mirror consisting of a pair of transistors; And
A pair of output transistors connected in series with the current mirror,
And a gate terminal of each of the pair of output transistors acts as two output terminals of the transconductance-based nonlinear resistor.

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