Wien Oscillator Research Articles

Understanding Injection Locking and Synchronization with Van der Pol-Like Self-sustained Oscillators

The exchange of energy between real systems can be better understood by the analysis of their associated differential equations. While numerical simulations offer limited insight of such real systems or interconnected self-sustained oscillators, representative electronic circuits can provide additional intuitive understanding. Representative electronic circuits allow the manipulation and analysis of various parameters in the system involved. Here, we present such a prototype consisting of a nonlinear Wien oscillator. It was tested by analyzing the frequency near synchronization during injection locking, the formation of a dead band and the synchronization between oscillators by using the envelope amplitude and instantaneous frequency formalism. The width of the dead band grows when either the injected current is increased or the oscillator stored energy is decreased. The sympathy between self-sustained oscillators was analyzed using the same tool to produce a general condition for energy transfer controlled by the frequency of the oscillators and the stored energy of each oscillator. Additionally, a finite network of different oscillators with adjustable coupling was explored to identify unlocked (different frequency), completely locked (same frequency and phase ratio), partially locked (same frequency but phase ratio changing with time) and mixed states. This analysis can be used to explore detailed interactions between a system and its peculiar manifestation near symmetry breaking.

Realization of fractional order circuits by a Constant Phase Element

Fractional-order calculus has been used for generalizing many modern and classical control theories including the well establish PID paradigm. The obtained controllers, of non-integer order, must be approximated with high order integer ones, in order to be realized. Successively, analog or digital implementations are used for the real world applications. This approach offers the hip to a classical criticism to fractional calculus. Why design a fractional-order system, which is usually of low order, if you need a high order system to implement it? In order to face this problem, in this paper, a fractional-order capacitor, more specifically a Constant Phase Device, is applied for implementing a first order fractional transfer function. Due to the intrinsic nature of the realized device, just one capacitor is needed for the implementation, avoiding therefore the need of high order RC approximation. Furthermore a fractional-order Wien oscillator and a chaotic Duffing circuit are presented confirming the potentiality of the proposed device in realizing fractional order circuits.

Realization of fractional-order capacitor based on passive symmetric network

In this paper, a new realization of the fractional capacitor (FC) using passive symmetric networks is proposed. A general analysis of the symmetric network that is independent of the internal impedance composition is introduced. Three different internal impedances are utilized in the network to realize the required response of the FC. These three cases are based on either a series RC circuit, integer Cole-impedance circuit, or both. The network size and the values of the passive elements are optimized using the minimax and least mth optimization techniques. The proposed realizations are compared with well-known realizations achieving a reasonable performance with a phase error of approximately 2o. Since the target of this emulator circuit is the use of off-the-shelf components, Monte Carlo simulations with 5% tolerance in the utilized elements are presented. In addition, experimental measurements of the proposed capacitors are preformed, therein showing comparable results with the simulations. The proposed realizations can be used to emulate the FC for experimental verifications of new fractional-order circuits and systems. The functionality of the proposed realizations is verified using two oscillator examples: a fractional-order Wien oscillator and a relaxation oscillator.

Synthesis of compact VDTA-based Wien oscillators with grounded capacitors

After building the nullor-mirror models of the VDTA and filtering the port admittance matrices for the Wien oscillator, the NAM expansion method for systematic synthesis of the VDTA-based Wien oscillator is presented in detail, generating a family of the Wien oscillator, namely category A and category B. Each category oscillator has four different forms. Eight Wien oscillators are received in all. Since each of the synthesized oscillators employs only two VDTAs and two grounded capacitors, it is particularly suitable for integrated circuit implementation, and then tuning bias currents of the VDTAs can orthogonally and linearly modulate the condition and frequency to oscillate. The Multisim simulation data match the paper-and-pencil analysis results, which match the synthesized circuits.

Electrical Nonlinearity Emulation Technique for Current-Controlled Memristive Devices

Emerging memristor technology is recently drawing widespread attention due to its potential for diverse applications. Due to the lack of real solid-state memristive devices, there have been many initiatives to develop memristor emulators to study their behavior and applications. One of the most widely used ideal memristor models developed by the HP Lab does not fit the anticipated nonlinear behaviors of a real memristor. In this paper, we propose the concept and the design of a practical memristor emulator, which can be used to mimic the behavior of the well-known current controlled memristor models like- Simmons tunneling barrier model and the ThrEshold adaptive memristor model . Our proposed emulator model mimics the behavior of the electrical nonlinearity of the fabricated memristor. Prior emulators can only emulate the linear electrical behavior. In addition to the mathematical modeling and analysis of the proposed emulator, we provide SPICE simulation and experimental results. Furthermore, the proposed emulator has been used to verify some applications like Wien Oscillators. Finally, a brief comparison with the previously published emulators is presented to highlight the advantages of the proposed design.

Derivation for current-mode Wien oscillators using CCCCTAs

According to NAM expansion method and adjoint network theorem, the systematic synthesis method of CCCCTA-based current-mode Wien oscillators is given and three different classes of the oscillators are derived. The class I oscillators have 16 different forms, the class II oscillators have 24 different forms, and the class III oscillators have 16 different forms. Since the circuits use fewer active elements and grounded capacitors, the circuits are easy to be integrated and provide the attractive feature of independent electronic control of the condition and frequency of oscillation. The circuit analysis and computer simulation results have been included to support the generation method.

On the systematic synthesis of OTA-based Wien oscillators

A NAM expansion method for systematic synthesis of OTA-based Wien oscillators is given. Moreover, the NAM expansion method for four different classes of the oscillators is considered. The class I oscillators employ three OTAs, the class II oscillators employ four OTAs, the class III oscillators employ five OTAs, and the class IV oscillators employ six OTAs. Each class has 32 different forms, resulting in 128 Wien oscillators using OTAs. Having used grounded capacitors, the circuits are easy to be integrated and their parameters can be tuned electronically through tuning bias currents of the OTAs. The MULTISIM simulation results have been included to support the generation method.

Generalized model for Memristor-based Wien family oscillators

In this paper, we report the unconventional characteristics of Memristor in Wien oscillators. Generalized mathematical models are developed to analyze four members of the Wien family using Memristors. Sustained oscillation is reported for all types though oscillating resistance and time dependent poles are present. We have also proposed an analytical model to estimate the desired amplitude of oscillation before the oscillation starts. These Memristor-based oscillation results, presented for the first time, are in good agreement with simulation results.

Generation of CCII and ICCII based Wien oscillators using nodal admittance matrix expansion

This paper introduces a new generation method of the grounded capacitor Wien oscillator circuits using current conveyors (CCII) or inverting current conveyors (ICCII) or combination of both of them. The nodal admittance matrix (NAM) of the single Op Amp Wien oscillator is taken as the starting point in the new approach of systematic synthesis of equivalent oscillators. The synthesis procedure is based on the generalized systematic synthesis framework using NAM expansion. The resulting derived 32 oscillators include many novel oscillators, using current conveyors or inverting current conveyors or both. Comparison between the generated oscillators based on the effect of parasitic elements on the oscillator performance is discussed.

Fractional-order sinusoidal oscillators: Design procedure and practical examples

Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher. Here we derive the Barhkausen condition for a linear noninteger-order (fractional-order) dynamical system to oscillate. We show that the oscillation condition and oscillation frequency of some famous integer-order sinusoidal oscillators can be obtained as special cases from general equations governing their fractional-order counterparts. Examples including fractional-order Wien oscillators, Colpitts oscillator, phase-shift oscillator and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> tank resonator are given supported by numerical and PSpice simulations.

Wien-Type Oscillators: Evaluation and Optimization of Harmonic Distortion

Theoretical study and design strategy for Wien oscillator circuits are presented. The analysis takes into account nonlinearities and allows to define an optimum design procedure minimizing distortion. The accuracy and viability of both the proposed analysis and design approach are confirmed experimentally.

Explaining and eliminating latchup in a classical Wien oscillator via nonlinear design

A classical Wien-type sinusoidal oscillator is analyzed to explain the origin of its latchup behavior. Only when a correct nonlinear model of the oscillator is derived and the stability of all equilibrium points associated with each region of operation of the fundamentally nonlinear amplifier characteristics is studied can this phenomena be predicted. It is further shown how latchup can be eliminated.

Fractional-order Wien-bridge oscillator

The classical Wien-bridge sinusoidal oscillator is studied, when both of the capacitors of the oscillator acquire a fractional order. Accordingly, the Wien oscillator is described by a set of fractional-order nonlinear differential equations. It is shown that sinusoidal oscillations are preserved but the phase-shift between the waveforms of the two state variables and the frequency of oscillation both depend on the fractional-order, leading to a significant advantage over the integer-type Wien oscillator. Findings are validated via numerical simulations.

Novel generation method of current mode Wien-type oscillators using current conveyors

A new approach to the generation of current mode Wien-type oscillators using the current conveyor is introduced. The proposed method is based on replacing the generalized current negative impedance converter in the conventional Wien oscillator by a well-known equivalent circuit realized using the current conveyor. A family of four new current mode oscillators employing grounded capacitors derived from the corresponding classical op amp Wien oscillator family is given. The proposed oscillators have the attractive advantage that the condition of oscillation and the frequency of oscillation can be independently controlled without affecting each other. PSpice simulation results supporting the theoretical analysis are given.

Current-mode oscillators using single output current conveyors

It is shown that the voltage-mode oscillators employing noninverting or inverting voltage controlled voltage sources can be transformed directly to current-mode oscillators by element replacement technique and using composite current conveyors. Examples of the Wien oscillator and the phase shift oscillator together with PSpice simulation results are included.

Design optimisation of transfer oscillators

An algorithm for the optimisation of self-excited transistor oscillators is presented and applied to the design of a Wien oscillator. A comparison between the actual oscillator&apos;s response and the computerpredicted response demonstrates the effectiveness of the algorithm.

A digital electronic instrument for production testing of condensers

The analysis of the inaccuracies involved, given above, and experimentation on a breadboard model of the instrument justify the conclusion that, when high-stability condensers are used in the arms of the Wien bridge, rejection of condensers deviating from their nominal value can be carried out by means of this instrument with an accuracy of the order of 0.1%, and rejection relative to a standard of comparison with an accuracy of the order of 0.05% is possible. It should be noted that lack of constancy of the other components of the two Wien oscillator bridges is of no importance, because their change will not produce the Δ1 inaccuracy, but only inaccuracies Δ4 and Δ5, which are very small. When ordinary condensers are used as standard capacities Cs, the instrument will guarantee a relative accuracy of at least 0.1% in routine acceptance tests, and even better accuracy in spot tests.