Carlos Sánchez-López

Frequency limitations in generating multi-scroll chaotic attractors using CFOAs

The current-feedback operational amplifier (CFOA) allows us to implement any kind of circuit useful in analogue signal processing applications. However, it has limited performance in implementing nonlinear circuits. That way, this investigation highlights the experimental results of implementing a multi-scroll chaotic oscillator by using the commercially available CFOA AD844. The chaotic oscillator is based on saturated nonlinear function (SNLF) series, and we show and discuss its frequency limitations to generate 3- to 10-scrolls from 1 kHz to 100 kHz. Finally, we conclude that the frequency limitations are due to the nonideal characteristics of the CFOA-based SNLF block, imposed by the AD844.

Experimental verification of the Chua's circuit designed with UGCs

In this letter, experimental results of the Chuas circuit designed with unity-gain cells (UGCs) are reported. The UGCs have been implemented with the commercially available integrated circuit (IC) AD844AN from Analog Devices. Parasitic elements of the UGCs are taken in account to design suitable the grounded inductor and the nonlinear resistor (NR) into Chuas circuit. Experimental results are given, showing close agreement with theoretical conclusions.

Designing SRCOs by combining SPICE and Verilog-A

The design of single-resistance-controlled oscillators (SRCOs) is presented by using current followers (CF) and voltage followers (VF). First, the design of the followers is described by using SPICE and standard CMOS technology of 0.35 µm. Second, a SRCO is simulated in SPICE by using the designed CF and VF. Third, the SRCO is simulated in Verilog-A by using ideal and real behavioural models for the followers. Finally, the good agreement on the simulation results leads us to conclude on the usefulness to combine SPICE and Verilog-A to enhance analogue integrated circuit design.

On the Relation between the Number of Scrolls and the Lyapunov Exponents in PWL-functions-based η-Scroll Chaotic Oscillators

A challenge in the physical design of η-scroll attractors is to generate a large number of scrolls. However, an open question is: Does the large number of scrolls determine a better chaotic behavior? We present a partial answer to this question by computing the Lyapunov exponents for piecewise-linear (PWL) functions based on η-scroll third order chaotic oscillators, namely: Zhong modified Chuas circuit, Yu modified Chuas circuit, saturated function series based chaotic oscillator, and generalized Chuas circuit with saw-tooth function. Three different integration methods (forward Euler, fourth order Runge Kutta and Matlab ODE 45) are used in order to show that the positive Lyapunov exponent is not significantly incremented in relation with the number of scrolls.

Designing VFs by applying genetic algorithms from nullator-based descriptions

An automatic method is proposed to design CMOS compatible voltage followers (VFs) by applying genetic algorithms. It is described how an automatic system can deals with huge search spaces to design practical VFs by performing evolutionary operations from nullator-based descriptions. The proposed method consists of three main steps: generation of the small-signal circuitry, addition of biases, and sizing by using standard CMOS technology of 0.35 mum. Furthermore, it is described how to synthesize VFs by codifying the three main steps into three kinds of genes, and how to select small-signal, biased, and sized topologies to generate potential solutions. Finally, several applications are discussed along with the evolution of VFs to design current conveyors.

Simulation of Chua’s chaotic oscillator using unity-gain cells

A novel topology to design a chaotic oscillator which is based on Chuas circuit, is proposed. The chaotic oscillator is realized with unity-gain cells, that is, the use of voltage followers (VF) and current followers (CF) to emulate the behavior of the two most important elements of the Chuas circuit: the active three-segment voltage controlled nonlinear resistor and the grounded inductor. Furthermore, it is shown that a negative current follower (CF-) can be implemented by using the IC AD844AN type current feedback operational amplifier (CFOA). The approach shows that the proposed topology can generate chaotic oscillations, where the HSPICE simulations have been obtained by using the macromodel of the IC AD844AN in configuration of unity-gain cell. Therefore, chaotic behavior in the time domain and the state space are presented.

Behavioral modeling for synthesizing n-scroll attractors

In this letter, the nonlinear behavioral model of a thirdorder chaotic system based on CFOAs is introduced. The proposed model is more realistic than PWL approaches widely used in the literature, since herein real physical active device performance parameters along with its parasitic elements are taken into account in the modeling process. As a consequence, chaotic attractors at 1-D can not only be better forecasted, but since chaotic waveforms numerically and experimentally generated have a random behavior, statistical tests are used to measure the similitude between them. Experimental results of the chaotic system designed with the AD844AN integrated circuit are gathered, showing good agreement with theoretical simulations.

Accuracy vs simulation speed trade-off enhancements in the generation of chaotic attractors

In this paper, the trade-off between accuracy and simulation speed in the generation of muti-scroll chaotic attractors at 1-D is analyzed and improved. In a first step, a macromodel based on bipolar transistors and passive elements is used to model the behavior of Opamps, and later on they are used to approach the behavior of all nonlinear system. Hspice simulations are executed to generate chaotic attractors in the phase plane and time-series. CPU-time used during the solution of the chaotic system is computed. In a second stage, a simple and accurate nonlinear model, which includes the most influential performance parameters for Opamps, is coded in C++ and it is used to generate a nonlinear system of equations, which models the behavior of all chaotic system. CPU-time is also computed. Because chaotic waveforms generated have a random behavior, statistical tests are used to measure the similitude/accuracy between two random variables during a long time. Our results indicate that chaotic waveforms can swiftly be generated by using the simple but accurate model for Opamps without the accuracy worsens, independently of the initial conditions of the chaotic system.

Symbolic behavioral model generation of current-mode analog circuits

A novel extended method to approximate the behavioral model of current-mode analog circuits (CMACs) is presented. The nullor is employed to model the behavior of a MOS Transistor (MOST) together with its parasitic elements. In a first part, the signal-path (SP) into a CMAC is approached by using the nullor properties. In the second part, the behavioral model associated to each MOST is generated and it is more simple in comparison with the original model. As a consequence, in the third part, an admittance matrix of reduced size is built and used to compute small-signal characteristics of CMACs, where the order is given by the number of SP-nodes minus the number of nullors. The proposed technique is illustrated by computing the fully-symbolic transfer function of a Positive Second Generation Current Conveyor (CCII+) and compared with Hspice simulation.

Behavioral Modeling of SNFS for Synthesizing Multi-Scroll Chaotic Attractors

Abstract Existing models of continuous nonlinear functions used for generating multi-scroll chaotic attractors are based on a piece-wise linear (PWL) approach. These models, although relatively easy to build, do not include any information related to the performance parameters of active devices, in the context of a possible physical implementation. This is a serious drawback, since the use of a PWL model introduces a level of inaccuracy into a numerical analysis which is more evident when numerical and experimental results are compared. This paper proposes a methodology to generate the behavioral model of continuous nonlinear functions, but unlike PWL approaches, real physical active device parameters are herein taken into account. In particular, we generate the behavioral model of a nonlinear function called saturated nonlinear function series (SNFS), but in general, the proposed approach can be used to generate the behavioral model of other continuous nonlinear functions. Our results indicate that the proposed approach yields a more realistic and accurate behavioral model than PWL models. As a consequence, not only the generation of chaotic attractors is more precise, but the metrics used to measure the complexity of a chaotic system can also be better predicted. Numerical and electrical simulation results at both domains, phase and time, illustrate the benefits of the new proposed model.