CN203933654U - Realization has the chaos analog circuit of single nonlinear exponent item - Google Patents

Abstract

The utility model discloses a chaotic analog circuit for realizing a single nonlinear exponential item. According to the mathematical equivalence , The circuit is realized by a multiplier and a natural exponential circuit, and the voltage is realized by using the multiplier U4 operation, and keep the voltage constant positive; use the proportional operation circuit of U1 to realize operation, is the proportional coefficient of the proportional operation circuit, It is the input voltage of the proportional operation circuit; the triode combination circuit and the integrated operational amplifier U1 form a natural exponential circuit to realize operation, using the inverter of the integrated operational amplifier U1 to realize the . The circuit has precise operation and good stability, can generate more complicated chaotic signals for selection in applications, adds chaotic systems and circuit types for realizing chaotic systems, and can form an automatic switching chaotic system with existing chaotic systems.

Description

Implementing a chaotic analog circuit with a single nonlinear exponential term

technical field

The utility model belongs to the field of electronic communication, relates to a chaotic circuit capable of generating pseudo-random signals, in particular to a chaotic analog circuit realizing a single nonlinear exponential item.

Background technique

The chaotic system can be used as a random signal source to design a pseudo-random sequence generator, and the security of the sequence generated by the chaotic pseudo-random sequence generator depends on the complexity of the chaotic system. The basic requirement of the chaotic system is that the mathematical structure is simple and the chaotic signal is complex. Existing chaotic systems generally contain two or more nonlinear function items, including piecewise linear and product (xy, x ² , y ² ) type nonlinear items. In order to increase the complexity, a chaotic system composed of natural exponent ^ex (or e ^xy , e ^xx , etc.) and product nonlinear terms has also appeared. This kind of chaotic system contains two or more natural exponential nonlinear terms, or contains a natural exponent and a product term, which makes its mathematical structure more complicated, and the base e of the natural exponent is fixed, which limits the variety of exponential functions sex. For this reason, the utility model realizes that only contains a non-linear exponential function The new chaotic analog circuit makes the mathematical structure of the chaotic system very simple, and the exponential function The base d of can be changed arbitrarily within a certain range, which makes the chaotic signal more complex, has a larger parameter and key space, and further increases the complexity of the chaotic signal.

Contents of the invention

Aiming at the deficiencies of the prior art, the utility model proposes a novel chaotic circuit.

The utility model comprises an integrated operational amplifier U1, an integrated operational amplifier U2, an integrated operational amplifier U3, a multiplier U4, a diode D1, a diode D2, a triode Q1 and a triode Q2.

The 3rd pin, the 5th pin, the 10th pin, and the 12th pin of the integrated operational amplifier U1 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; The l pin is connected to the second pin of the integrated operational amplifier U1 through the resistor R2, and the seventh pin of the multiplier U4 is connected to the second pin of the integrated operational amplifier U1 through the resistor R1; the first pin of the integrated operational amplifier U1 Connected between diode D1 and diode D2, the output terminal of the circuit composed of diode D1, diode D2, transistor Q1 and transistor Q2 is connected to the sixth pin of integrated operational amplifier U1, and the seventh pin of integrated operational amplifier U1 passes through Resistor R5 is connected to the 6th pin of the integrated operational amplifier U1; the 7th pin of the integrated operational amplifier U1 is connected to the 9th pin of the integrated operational amplifier U1 through the resistor R18, and the 8th pin of the integrated operational amplifier U1 The pin is connected to the 9th pin of the integrated operational amplifier U1 through the resistor R19; the 8th pin of the integrated operational amplifier U1 is connected to the 13th pin of the integrated operational amplifier U1 through the resistor R8, and the 1st pin of the integrated operational amplifier U3 The first pin is connected to the 13th pin of the integrated operational amplifier U1 through the resistor R6, and the 14th pin of the integrated operational amplifier U1 is connected to the 13th pin of the integrated operational amplifier U1 through the resistor R7.

The 3rd pin, the 5th pin, the 10th pin, and the 12th pin of the integrated operational amplifier U2 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; The l pin is connected to the second pin of the integrated operational amplifier U2 through the capacitor C3, and the 14th pin of the integrated operational amplifier U1 is connected to the second pin of the integrated operational amplifier U2 through the resistor R9; the first pin of the integrated operational amplifier U2 The pin is connected to the 6th pin of the integrated operational amplifier U2 through the resistor R10, the 7th pin of the integrated operational amplifier is connected to the 6th pin of the integrated operational amplifier U2 through the resistor R11; the 8th pin of the integrated operational amplifier U2 is connected to the 8th pin of the integrated operational amplifier U2 through the resistor R14 The 9th pin of the integrated operational amplifier U2, the 1st pin of the integrated operational amplifier U2 is connected to the 9th pin of the integrated operational amplifier U2 through the resistor R13, and the 14th pin of the integrated operational amplifier U2 is connected to the integrated circuit through the resistor R12 The 9th pin of the operational amplifier U2; the 14th pin of the integrated operational amplifier U2 is connected to the 13th pin of the integrated operational amplifier U2 through the capacitor C4, and the 6th pin of the integrated operational amplifier U2 is connected to the integrated operational amplifier U2 through the resistor R15 13th pin.

The 3rd pin, the 5th pin, and the 10th pin of the integrated operational amplifier U3 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; the 12th pin, the The 13th pin and the 14th pin are suspended; the 1st pin of the integrated operational amplifier U3 is connected to the 2nd pin of the integrated operational amplifier U3 through the resistor R16, and the 14th pin of the integrated operational amplifier U2 is connected to the integrated operational amplifier U3 through the resistor R9 The 2nd pin of the integrated operational amplifier U3 is connected to the 6th pin of the integrated operational amplifier U3 through the resistor R22, and the 14th pin of the integrated operational amplifier U3 is connected to the 1st pin of the integrated operational amplifier U3 through the resistor R20 6 pins, the first pin of the integrated operational amplifier U2 is connected to the sixth pin of the integrated operational amplifier U3 through the resistor R21; the eighth pin of the integrated operational amplifier U3 is connected to the ninth pin of the integrated operational amplifier U3 through the capacitor C5 Pin, the 7th pin of the integrated operational amplifier U3 is connected to the 9th pin of the integrated operational amplifier U3 through the resistor R23; the 8th pin of the integrated operational amplifier U3 is connected to the 13th pin of the integrated operational amplifier U3 through the resistor R24 pin, the 14th pin of the integrated operational amplifier U3 is connected to the 14th pin of the integrated operational amplifier U3 through the resistor R25.

The 2nd pin, the 4th pin, and the 6th pin of the multiplier U4 are grounded, the 5th pin is connected to the -15V power supply VEE, and the 8th pin is connected to the +15V power supply VCC; the 1st pin and the 3rd pin The pin is connected to the 14th pin of the integrated operational amplifier U3, and the 7th pin of the multiplier U4 is connected to the 2nd pin of the integrated operational amplifier U1 through the resistor R1.

The cathode of the diode D1 is connected to the first pin of the integrated operational amplifier U1, and the transmitter of the transistor Q1 is connected to the sixth pin of the integrated operational amplifier U1.

The utility model constructs a non-linear exponential function The new chaotic analog circuit makes the mathematical structure of the chaotic system very simple, and the exponential function The base d of can be changed arbitrarily within a certain range, which makes the chaotic signal more complex, has a larger parameter and key space, and further increases the complexity of the chaotic signal. According to the mathematical equivalence The circuit is realized by a multiplier and a natural exponent circuit, the multiplier U4 is used to realize the voltage z ² operation, and the voltage is kept positive; the proportional operation circuit of U1 is used to realize the (lnd)z ² operation, and lnd is the proportional coefficient of the proportional operation circuit , z ² is the input voltage of the proportional operation circuit; the triode combined circuit and the integrated operational amplifier U1 form a natural exponential circuit, realizing operation, using the inverter of the integrated operational amplifier U1 to realize the The circuit has precise operation and good stability, can generate more complicated chaotic signals for selection in applications, adds chaotic systems and circuit types for realizing chaotic systems, and can form an automatic switching chaotic system with existing chaotic systems.

Description of drawings

Fig. 1 is a structural diagram of the utility model.

Fig. 2 is a schematic diagram of the utility model.

Detailed ways

Below in conjunction with accompanying drawing and preferred example the utility model is described in further detail.

Mathematical model of the present utility model is:

$\frac{\mathrm{<span\; class="notranslate">\; dx</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; ay</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{cy}+x$ a=9; b=3; c=0.65; d=4.7

$\frac{\mathrm{<span\; class="notranslate">\; dz</span>}}{\mathrm{<span\; class="notranslate">\; dt</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; bz</span>}$

As shown in Figure 1, the triode combination circuit and the integrated operational amplifier U1 realize the exponential voltage Operation, characterized in that: according to the equivalent relationship in mathematics The circuit is realized by a multiplier and a natural exponent circuit, the multiplier U4 is used to realize the voltage z ² operation, and the voltage is kept positive; the proportional operation circuit of U1 is used to realize the (lnd)z ² operation, and lnd is the proportional coefficient of the proportional operation circuit , z ² is the input voltage of the proportional operation circuit; the triode combined circuit and the integrated operational amplifier U1 form a natural exponential circuit, realizing operation, convert (lnd)z ² to The triode combination circuit includes diodes D1, D2, triodes Q1, Q2, and capacitors C6, C7, which form an exponential operation circuit with the integrated operational amplifier of U1, which can eliminate crossover distortion and have complementary output functions, because the voltage emitter current of the triode There is an exponential relationship between i _E and its U _T :

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}}$

The triode current that changes exponentially is converted into a voltage that changes exponentially through the conversion circuit in the integrated operational amplifier U1, thereby realizing the exponential operation of the voltage:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\frac{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; I</span>}}}{{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}}}\mathrm{<span\; class="notranslate">\; R</span>}$

Among them (lnd)z ² is used as the input u _I , and the voltage output is obtained through the conversion circuit Then utilize the integrated operational amplifier U1 inverter to realize get:

${\mathrm{<span\; class="notranslate">\; e</span>}}^{{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; ln</span>}\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

As shown in Figure 2, the one containing a single nonlinear exponential term The chaotic analog circuit is composed of integrated operational amplifier U1, integrated operational amplifier U2, integrated operational amplifier U3, multiplier U4, diode D1, diode D2, transistor Q1, transistor Q2, capacitor C6 and capacitor C7. The integrated operational amplifier U1 , integrated operational amplifier U2, integrated operational amplifier U3 realize signal addition, inversion, integral function, multiplier U4, diode D1, diode D2, transistor Q1, transistor Q2, capacitor C6 and capacitor C7 and integrated operational amplifier U1 realize exponential operation Function: the multiplier U4, the associated ratio, addition and inversion circuit in the integrated operational amplifier U1, and the associated integral and inverting circuit in the integrated operational amplifier U2 realize the operation of the first equation of the exponential chaotic system, and the integrated operational amplifier U2 The integral, addition and reverse in U3 realize the operation of the second equation of the exponential chaotic system, and the associated addition, integral and reverse in the integrated operational amplifier U3 realize the operation of the third equation;

The 3rd pin, the 5th pin, the 10th pin, and the 12th pin of the integrated operational amplifier U1 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; The l pin is connected to the second pin of the integrated operational amplifier U1 through the resistor R2, the seventh pin of the multiplier U4 is connected to the second pin of the integrated operational amplifier U1 through R1; the first pin of the integrated operational amplifier U1 is connected to Between the diode D1 and the diode D2, the output terminal of the circuit composed of the diode D1, the diode D2, the transistor Q1 and the transistor Q2 is connected to the sixth pin of the integrated operational amplifier U1, and the seventh pin of the integrated operational amplifier U1 passes through R5 Connected to the 6th pin of the integrated operational amplifier U1; the 7th pin of the integrated operational amplifier U1 is connected to the 9th pin of the integrated operational amplifier U1 through R18, and the 8th pin of the integrated operational amplifier U1 is passed through R19 Connected to the 9th pin of the integrated operational amplifier U1; the 8th pin of the integrated operational amplifier U1 is connected to the 13th pin of the integrated operational amplifier U1 through R8, and the first pin of the integrated operational amplifier U3 is passed through R6 Connect to the 13th pin of the integrated operational amplifier U1, and the 14th pin of the integrated operational amplifier U1 is connected to the 13th pin of the integrated operational amplifier U1 through R7.

The 3rd pin, the 5th pin, the 10th pin, and the 12th pin of the integrated operational amplifier U2 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; The l pin is connected to the second pin of the integrated operational amplifier U2 through the capacitor C3, and the 14th pin of the integrated operational amplifier U1 is connected to the second pin of the integrated operational amplifier U2 through the resistor R9; the first pin of the integrated operational amplifier U2 The pin is connected to the 6th pin of the integrated operational amplifier U2 through the resistor R10, the 7th pin of the integrated operational amplifier is connected to the 6th pin of the integrated operational amplifier U2 through the resistor R11; the 8th pin of the integrated operational amplifier U2 is connected to the 8th pin of the integrated operational amplifier U2 through the resistor R14 The 9th pin of the integrated operational amplifier U2, the 1st pin of the integrated operational amplifier U2 is connected to the 9th pin of the integrated operational amplifier U2 through the resistor R13, and the 14th pin of the integrated operational amplifier U2 is connected to the integrated circuit through the resistor R12 The 9th pin of the operational amplifier U2; the 14th pin of the integrated operational amplifier U2 is connected to the 13th pin of the integrated operational amplifier U2 through the capacitor C4, and the 6th pin of the integrated operational amplifier U2 is connected to the integrated operational amplifier U2 through the resistor R15 13th pin;

The 3rd pin, the 5th pin, and the 10th pin of the integrated operational amplifier U3 are grounded, the 4th pin is connected to the +15V power supply VCC, and the 11th pin is connected to the negative -15V power supply VEE; the 12th pin, the The 13th pin and the 14th pin are suspended; the 1st pin of the integrated operational amplifier U3 is connected to the 2nd pin of the integrated operational amplifier U3 through the resistor R16, and the 14th pin of the integrated operational amplifier U2 is connected to the integrated operational amplifier U3 through the resistor R9 The 2nd pin of the integrated operational amplifier U3 is connected to the 6th pin of the integrated operational amplifier U3 through the resistor R22, and the 14th pin of the integrated operational amplifier U3 is connected to the 1st pin of the integrated operational amplifier U3 through the resistor R20 6 pins, the first pin of the integrated operational amplifier U2 is connected to the sixth pin of the integrated operational amplifier U3 through the resistor R21; the eighth pin of the integrated operational amplifier U3 is connected to the ninth pin of the integrated operational amplifier U3 through the capacitor C5 Pin, the 7th pin of the integrated operational amplifier U3 is connected to the 9th pin of the integrated operational amplifier U3 through the resistor R23; the 8th pin of the integrated operational amplifier U3 is connected to the 13th pin of the integrated operational amplifier U3 through the resistor R24 Pin, the 14th pin of the integrated operational amplifier U3 is connected to the 14th pin of the integrated operational amplifier U3 through the resistor R25;

The 2nd pin, the 4th pin, and the 6th pin of the multiplier U4 are grounded, the 5th pin is connected to the -15V power supply VEE, and the 8th pin is connected to the +15V power supply VCC; the 1st pin and the 3rd pin The pin is connected to the 14th pin of the integrated operational amplifier U3, and the 7th pin of the multiplier U4 is connected to the 2nd pin of the integrated operational amplifier U1 through the resistor R1;

The cathode of the diode D1 is connected to the first pin of the integrated operational amplifier U1, and the transmitter of the transistor Q1 is connected to the sixth pin of the integrated operational amplifier U1.

Of course, the above description is not a limitation of the utility model, and the utility model is not limited to the above examples, and the changes, modifications, additions or replacements made by those skilled in the art within the essential scope of the utility model also belong to Protection scope of the present utility model.

Claims (1)

1. realize the chaos analog circuit with single nonlinear exponent item, comprise integrated operational amplifier U1, integrated operational amplifier U2, integrated operational amplifier U3, multiplier U4, diode D1, diode D2, triode Q1 and triode Q2, is characterized in that:

The 3rd pin of described integrated operational amplifier U1, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th connect+15V of pin power supply VCC, the 11st pin connects negative-15V power supply VEE; L pin connects the 2nd pin of integrated operational amplifier U1 by resistance R 2, the 7th pin of multiplier U4 received the 2nd pin of integrated operational amplifier U1 by resistance R 1; The 1st pin of integrated operational amplifier U1 received between diode D1 and diode D2, the output of diode D1, diode D2, triode Q1 and triode Q2 built-up circuit is received the 6th pin of integrated operational amplifier U1, and the 7th pin of integrated operational amplifier U1 received the 6th pin of integrated operational amplifier U1 by resistance R 5; The 7th pin of integrated operational amplifier U1 received the 9th pin of integrated operational amplifier U1 by resistance R 18, the 8th pin of integrated operational amplifier U1 received the 9th pin of integrated operational amplifier U1 by resistance R 19; The 8th pin of integrated operational amplifier U1 received the 13rd pin of integrated operational amplifier U1 by resistance R 8, the 1st pin of integrated operational amplifier U3 received the 13rd pin of integrated operational amplifier U1 by resistance R 6, the 14th pin of integrated operational amplifier U1 received the 13rd pin of integrated operational amplifier U1 by resistance R 7;

The 3rd pin of described integrated operational amplifier U2, the 5th pin, the 10th pin, the 12nd pin ground connection, the 4th connect+15V of pin power supply VCC, the 11st pin connects negative-15V power supply VEE; L pin connects the 2nd pin of integrated operational amplifier U2 by capacitor C 3, the 14th pin of integrated operational amplifier U1 connects the 2nd pin of integrated operational amplifier U2 by resistance R 9; The 1st pin of integrated operational amplifier U2 connects the 6th pin of integrated operational amplifier U2 by resistance R 10, integrated operational amplifier the 7th pin connects the 6th pin of integrated operational amplifier U2 by resistance R 11; Integrated operational amplifier U2 the 8th pin connects the 9th pin of integrated operational amplifier U2 by resistance R 14, the 1st pin of integrated operational amplifier U2 connects the 9th pin of integrated operational amplifier U2 by resistance R 13, the 14th pin of integrated operational amplifier U2 connects the 9th pin of integrated operational amplifier U2 by resistance R 12; Integrated operational amplifier U2 the 14th pin connects the 13rd pin of integrated operational amplifier U2 by capacitor C 4, the 6th pin of integrated operational amplifier U2 connects the 13rd pin of integrated operational amplifier U2 by resistance R 15;

The 3rd pin of described integrated operational amplifier U3, the 5th pin, the 10th pin ground connection, the 4th connect+15V of pin power supply VCC, the 11st pin connects negative-15V power supply VEE; The 12nd pin, the 13rd pin, the 14th pin are unsettled; Integrated operational amplifier U3 l pin connects the 2nd pin of integrated operational amplifier U3 by resistance R 16, the 14th pin of integrated operational amplifier U2 connects the 2nd pin of integrated operational amplifier U3 by resistance R 9; The 7th pin of integrated operational amplifier U3 connects the 6th pin of integrated operational amplifier U3 by resistance R 22, the 14th pin of integrated operational amplifier U3 connects the 6th pin of integrated operational amplifier U3 by resistance R 20, the 1st pin of integrated operational amplifier U2 connects the 6th pin of integrated operational amplifier U3 by resistance R 21; The 8th pin of integrated operational amplifier U3 connects the 9th pin of integrated operational amplifier U3 by capacitor C 5, the 7th pin of integrated operational amplifier U3 connects the 9th pin of integrated operational amplifier U3 by resistance R 23; The 8th pin of integrated operational amplifier U3 connects the 13rd pin of integrated operational amplifier U3 by resistance R 24, the 14th pin of integrated operational amplifier U3 connects the 14th pin of integrated operational amplifier U3 by resistance R 25;

The 2nd pin of described multiplier U4, the 4th pin, the 6th pin ground connection, the 5th connect-15V of pin power supply VEE, the 8th connect+15V of pin power supply VCC; The 1st pin and the 3rd pin connect the 14th pin of integrated operational amplifier U3, and the 7th pin of multiplier U4 connects the 2nd pin of integrated operational amplifier U1 by resistance R 1;

The negative pole of described diode D1 connects the 1st pin of integrated operational amplifier U1, and the transmitter of triode Q1 connects the 6th pin of integrated operational amplifier U1.