A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic non- linear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits.An efficient scheme to buildtheJacobian matrix with exact partial derivatives with respect to the oscillation period and with re- spect to the samples of the unknowns is described. Without any modifica- tion in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.Peer ReviewedPostprint (published version

A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits. An efficient scheme to build the Jacobian matrix with exact partial derivatives with respect to the oscillation period and with respect to the samples of the unknowns is described. Without any modification in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.Peer ReviewedPostprint (published version

Stochastic resonance in chua's circuit driven by alpha-stable noise

Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2012Includes bibliographical references (leaves: 75-80)Text in English; Abstract: Turkish and Englishx, 80 leavesThe main aim of this thesis is to investigate the stochastic resonance (SR) in Chua's circuit driven by alpha-stable noise which has better approximation to a real-world signal than Gaussian distribution. SR is a phenomenon in which the response of a nonlinear system to a sub-threshold (weak) input signal is enhanced with the addition of an optimal amount of noise. There have been an increasing amount of applications based on SR in various fields. Almost all studies related to SR in chaotic systems assume that the noise is Gaussian, which leads researchers to investigate the cases in which the noise is non-Gaussian hence has infinite variance. In this thesis, the spectral power amplification which is used to quantify the SR has been evaluated through fractional lower order Wigner Ville distribution of the response of a system and analyzed for various parameters of alpha-stable noise. The results provide a visible SR effect in Chua’s circuit driven by symmetric and skewed-symmetric alpha-stable noise distributions. Furthermore, a series of simulations reveal that the mean residence time that is the average time spent by the trajectory in an attractor can vary depending on different alpha-stable noise parameters

Chaos control of a modified 4-D memristor chaotic oscillator via passive control technique

A modified memristor chaotic oscillator is proposed for a class of four dimensional chaotic systems. This modification can serve as an alternative way of designing the memristor circuit. We used the passive control technique which requires a single controller to stabilize the system which is presented in our numerical simulations for validation. Our results show that the passive control technique is a very effective technique for controlling chaotic systems.Keywords: Chaos; passive control; memristor; controllers; chaotic oscillator; nonlinear circui

Generalized stability criteria for power amplifiers under mismatch effects

Potential instability of power amplifiers (PAs) under mismatch effects is analyzed, with emphasis on the ease and generality of application of the stability criteria. The methodology is based on the evaluation of a large-signal version of the μ factor, considering mismatch effects in the fundamental frequency and three relevant sidebands: the baseband, the lower sideband and the upper sideband. This requires an outer-tier scattering-type conversion matrix of order 3 × 3 to be obtained, with the rest of sideband equations acting as an inner tier. It is taken into account that the circuit behaves nonlinearly with respect to the termination at the fundamental frequency. The consideration of three sidebands will enable the prediction of the two major forms of large-signal instability: incommensurable oscillations and frequency divisions by two. The analysis is preceded by an evaluation of the circuit own stability properties (proviso) under open and short circuit terminations at the sidebands, for all possible values of the termination at the fundamental frequency. Three different μ factors can be defined between any two ports of the scattering matrix. The analysis of the relationships between these factors and their continuity properties will allow the derivation of a single number able to characterize the PA potential instability for each fundamental-frequency termination. Results have been exhaustively validated with independent circuit-level simulations based on pole-zero identification and with measurements, using a variable output load and loading the PA with an antenna.This work has been supported by the Spanish Government under contract TEC2014-60283-C3-1-R and the Parliament of Cantabria (12.JP02.64069

Application of dither and observer based state feedback in the control of chaotic systems

Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent University, 1996.Thesis (Master's) -- Bilkent University, 1996.Includes bibliographical references leaves 48-51.In the first part of this thesis, the application of dither for controlling chaotic systems is presented. Dither is a high frequency periodic signal that has been excunined in the literature before, for changing nonlinear systems effectively. The presented technique is based on a conjecture proposed by Genesio and Tesi and is mainly cipplicable to systems in Lur’e form. In the second part, the application of state feedback is presented. Unknown states of the system are constructed by using nonlinear full-state observers. The control strategy is mainly based on the mentioned conjecture and also on bifurcation diagriuns.Ersoy, UmutM.S

Oscillation modes in multiresonant oscillator circuits

An in-depth analysis of the oscillation modes in free-running oscillators loaded with multiresonance networks is presented. The analysis illustrates the mechanisms for the generation and stabilization of the various periodic modes and establishes the conditions for existence of a single stable periodic mode in distinct regions of the parameter plane. The mechanisms for the generation and stabilization of quasi-periodic regimes, with two concurrent oscillations, are also analyzed, considering different situations in terms of two relevant poles. The stability analysis of quasi-periodic solutions, derived in terms of admittance functions, can be applied to circuits simulated with harmonic balance, under the assumption of high quality factor resonators. The impact of the transistor biasing on the stability properties of the quasi-periodic regimes has been analyzed, demonstrating that it can be used to isolate the quasi-periodic solution from the periodic ones. The analysis procedures have been applied to a practical oscillator based on two cross-coupled transistors at the two frequencies 900 MHz and 2.5 GHz. The case of two independent oscillations operating in a synchronized regime is also analyzed, as well as its impact on the phase-noise behavior.This work has been funded by the Spanish Government under contract TEC2014-60283-C3-1-R, the European Regional Development Fund (ERDF/FEDER) and the Parliament of Cantabria (12.JP02.64069)

A preliminary investigation into the effects of nonlinear response modification within coupled oscillators

This thesis provides an account of an investigation into possible dynamic interactions between two coupled nonlinear sub-systems, each possessing opposing nonlinear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two degree-of-freedom Duffing oscillator coupled in series in which certain nonlinear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently nonlinear, and which is coupled to a bar-horn or block-horn to one, or more, material cutting blades, for example. The horn/blade configurations are also nonlinear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall nonlinear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also bfeen shown experimentally that coupling of ultrasonic components with different nonlinear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice