Fig 1 - uploaded by Arunas Tamasevicius
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Circuit diagram of chaotic oscillator with the Schottky diode. DC bias circuit is not shown for simplicity.
Source publication
The considered chaotic oscillator consists of an amplifier, 2nd order
LC resonator, Schottky diode and an extra capacitor in parallel to the
diode. The diode plays the role of a nonlinear device. Chaotic
oscillations are demonstrated numerically and experimentally at low as
well as at high megahertz frequencies, up to 250 MHz.
Context in source publication
Context 1
... simplified diagram of the dynamical noise generator is shown in Fig. 1. A series 2nd-order LC resonator and a non-inverting amplifier are common building blocks of a classical sinusoidal oscillator. However, additional elements, namely the Schottky-barrier diode and an extra capacitor C * are inserted in the positive feedback loop. The diode plays the role of a nonlinear device, while the capacitor C * ...
Citations
... Örnek olarak çok hızlı Schottky diyotlar kullanılarak MHz mertebesindeki frekanslarda salınan kaotik osilatörler yapılabilir [25]. Şekil 3'te bu çalışmada kullanılan 1N5817 Schottky diyotunun v-i karakteristiğine yer verilmiştir [26]. ...
Van der Pol Osilatörü 1926 yılında, Philips’te çalışan
elektrik mühendisi ve fizikçi Dr. Balthasar Van der Pol
tarafından keşfedilmiştir. Bu osilatör çeşidinin oldukça zengin
dinamikleri mevcuttur. İlk yapılan Van der Pol Osilatörü’nde
bir triyot kullanılmıştır. Günümüzde Van der Pol Osilatörü,
farklı yarı iletken elemanları kullanılarak yapılabilmektedir.
Bu çalışmada, nonlineer devre elemanı olarak Schottky
diyotlar kullanılmıştır. Bir endüktör, bir kondansatör, tersparalel bağlı Schottky diyot dizisi ve paralel bağlanmış negatif
direnç devresinden oluşan bu yeni Van der Pol Osilatörü’nün
devre denklemleri türetilmiş ve benzetimi yapılarak
incelenmiştir. Benzetimlerde devrenin sınır döngüsü, devre
elemanlarının akımları ve devrenin gerilimi LTspice devre
analizi programı ve Matlab’in Simulink paket programı
kullanılarak elde edilmiştir.
The Van der Pol Oscillator was discovered in 1926 by
electrical engineer and physicist Dr. Balthasar Van der Pol.
This oscillator type has very rich dynamics. A triode is used in
the original Van der Pol Oscillator. Nowadays, a Van der Pol
Oscillator can be made using different semiconductor circuit
elements. In this study, Schottky diodes are used as the
nonlinear circuit elements. The circuit equations of the new
Van der Pol Oscillator which consists of an inductor, a
capacitor, anti-parallel connected Schottky diode strings, and
a negative resistor circuit connected in parallel are derived
and it is examined using simulations. The limit cycle of the
circuit, the currents of the circuit elements and the voltage of
the circuit were obtained using LTspice circuit analysis
program and Simulink toolbox of Matlab.
... It is worth remembering that at high-frequency, parasitic capacitance (Hayes and Horowitz, 1991;Karki, 2000;Kuendiger et al., 2001;Jung, 2005) and inductance (Karki, 1998) appear in Op-Amps, though, to the best of our knowledge, no schematic of the latter has been found in the literature. The methods of compensating these parasitic effects in electronic circuits are well known (Karki, 2000), however these are not taken into consideration in the modeling of electronic circuits for chaos, unlike Op-Amps-based chaotic circuits that are studied at high-frequency (Mykolaitis et al., 2005). If both parasitic capacitance and inductance were to be considered in an Op-Amp, how would the schematic of the equivalent circuit look, and what would be their contribution to the dynamics of the whole circuit? ...
A novel modeling of general purpose operational ampli ers (Op-Amps) is made to approximate at best the
real model at high frequency. With this new modeling, it appears that certain oscillators usually studied under
ideal considerations or under many existing real models of Op-Amps have hidden subtle and attractive chaotic
dynamics hitherto unknown, which can now be revealed. With the new considerations, a "two-component"
circuit consisting simply of a capacitor in parallel with a non modi ed and usually presented as linear negative
resistance, turns to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement
with the theoretical predictions.
... Alternatively , Elwakil and Kennedy [2000a] have suggested a semi-systematic methodology for chaotic oscillator designs based on classical sinusoidal oscillators. This methodology has led to several developments of simple chaotic oscillators based on a current feedback opamp [Elwakil & Kennedy, 2000b] [Mykolaitis et al., 2005; Tamasevicius et al., 2005], jerk dynamics [Sprott, 2011], and a biquad filter [Banerjee et al., 2010; Banerjee et al., 2012]. It can be noticed that these chaotic oscillators utilize a noninverting amplifier as a major active building block, and therefore the circuit essentially requires more than six components since other three energy storage elements and a single nonlinear device are required for chaos. ...
This paper presents a simple autonomous chaotic oscillator. The design method is primarily based on a linear oscillator constructed by a closed loop connection of two building blocks, i.e. an inverting active integrator and a passive second-order LC integrator. A diode is inserted in parallel to the two building blocks for inducing chaos. The mathematical model reveals a set of three-dimensional ordinary differential equations, containing seven terms with four constants and an exponential nonlinearity. The dynamics properties are investigated in terms of an equilibrium point, Jacobian matrix, chaotic attractors, bifurcation, Lyapunov exponents, and chaotic waveforms in time domain. The proposed chaotic oscillator potentially exhibits complex dynamical behaviors through the utilization of only six minimal electronic components.
... Hence, a wide variety of approaches have been developed and presented in the literature [5][6][7][8][9][10][11]. However, for applications in engineering, the investigation of small and simple chaotic systems has been widely done in the last decade [12][13][14][15], but still remains actual. In this sense, there are some new chaotic systems recently proposed in the literature such as the simple jerk chaotic systems [16,17], or circuits with a maximum of four electronic components [18,19] or even three as the simplest chaotic circuit proposed by Muthuswamy and Chua [20]. ...
Firstly, the synchronization problem of the simplest two-component Hartley chaotic systems is considered. A simple and effective controller is used to achieve synchronization between the drive and response systems. The proposed controller is built around a linear and a nonlinear parts with each contributing to the achievement of the synchronization process. The stability of the drive–response systems framework is proved through the Lyapunov stability theory. Secondly, the impact of channel on the signal coming from the drive system to synchronize the response system is taken into consideration. In this second part, the conditions to obtain synchronization between both master and slave systems are investigated. For the purpose of illustration, PSpice simulations are given as complement of the numerical analysis.
... Such a category is of particular interest as most components, except the nonlinear diode, are linear building blocks commonly found in classical sinusoidal oscillators. Although 6 minimum numbers of components are desirable if each type is reduced to one component, most chaotic oscillators in this category have employed more than 6 components [3][4][5], but never been demonstrated clearly using a current-tunable technique. In this letter, four current- tunable chaotic oscillators are presented in a set of two diode-reversible pairs. ...
Four current-tunable chaotic oscillators are presented in a set of two diode-reversible pairs. The first pair employs a floating-diode technique whereas the second pair employs a virtually-grounded-diode technique. Two chaotic attractors of a pair are 180-rotated images of each other. Each oscillator consists of 6 basic electronic components which are minimal in a category of chaotic oscillators that exploit a capacitor-inductor-capacitor (CLC) network, op-amp(s), diode(s) and resistor(s). Current-tunable bifurcations are demonstrated.
... An auxiliary unit is the current source Io used to set the dc bias of the diode D. The voltage across the R (also the output voltage of the OA1), the voltage across C1, and the voltage across C2 can be taken as the output of the oscillator. High frequency implementation of the oscillator using fast Schottky diodes is discussed in [20]. ...
... As discussed in Section III the oscillator has unstable non-zero steady state. By setting L1, C1, and C2 values the oscillator has been tuned to operate in a megahertz frequency band [20]. The diode D in Fig. 9 is low junction capacitance (≈1 pF) fast recovery (≈10 ps) BAT68 Schottky device; Io = 7.5 mA. ...
Chaos controllers used for stabilizing unstable periodic orbits and/or unstable steady states are very sensitive to unavoidable latency of the controlling feedback force. When the delay value exceeds some critical value the controller fails to work. We consider a specific case of a derivative control applied to stabilize unstable steady state in a third-order autonomous chaotic oscillator. We demonstrate from equations, by PSPICE simulations, and hardware experiments that inserting in the feedback control loop the Taylor predictor essentially improves the performance of the controller.
Chaos controllers used for stabilizing unstable periodic orbits and/or unstable steady states are very sensitive to unavoidable latency of the controlling feedback force. When the delay value exceeds some critical value the controller fails to work. We consider a specific case of a derivative control applied to stabilize unstable steady state in a third-order autonomous chaotic oscillator. We demonstrate that by inserting in the feedback control loop the Taylor predictor the performance of the controller can be essentially improved.
