Erik Lindberg | Technical University of Denmark (DTU) (original) (raw)

Papers by Erik Lindberg

A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 an... more A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance. two ideal capacitors and one non-linear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The non-linear conductor is realized with a diode. a negative impedance converter and a linear resistor. The performance of the circuit is investigated by means of numerical integration of the appropriate differential equations.

 Users may download and print one copy of any publication from the public portal for the purpose... more  Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Elektronika ir Elektrotechnika

a discussion of various concepts

Concepts like finite, infinite and zero are discussed. Numbers are the birth of mathematics. Math... more Concepts like finite, infinite and zero are discussed. Numbers are the birth of mathematics. Mathematics is a language that is used in connection with the creation of models of the physical observations of our environment, the universe. The concepts of absolute and time-varying coordinate systems are discussed. The dimension of the universe is discussed. Space and time are discussed. Einstein's coupling of space and time is questioned. Do we understand these concepts? Please contact the author ( erik.lindberg@ieee.org ) with your comments concerning this fractal note. I believe that some valuable ideas are presented despite of the chaotic nature of the note. https://www.researchgate.net/profile/Erik Lindberg

Nonlinear Analysis: Modelling and Control, 2008

We describe an extremely simple second order analogue electrical circuit for simulating the two-w... more We describe an extremely simple second order analogue electrical circuit for simulating the two-well Duffing-Holmes mathematical oscillator. Numerical results and analogue electrical simulations are illustrated with the snapshots of chaotic waveforms, with the phase portraits (the Lissajous figures) and with the stroboscopic maps (the Poincar´e sections).

Oscillators are normally designed according to the Modified Barkhausen Criterion i.e. the complex... more Oscillators are normally designed according to the Modified Barkhausen Criterion i.e. the complex pole pair is moved out in RHP so that the linear circuit becomes unstable. By means of the Mancini Phaseshift Oscillator it is demonstrated that the distortion of the oscillator may be minimized by introducing a nonlinear ”Hewlett Resistor” so that the complex pole-pair is in the RHP for small signals and in the LHP for large signals i.e. the complex pole pair of the instant linearized small signal model is moving around the imaginary axis in the complex frequency plane.

A discussion of the Barkhausen Criterion which is a necessary but NOT sufficient criterion for st... more A discussion of the Barkhausen Criterion which is a necessary but NOT sufficient criterion for steady state oscillations of an electronic circuit. An attempt to classify oscillators based on the topology of the circuit. Investigation of the steady state behavior by means of the time-varying linear approach (”frozen eigenvalues”).

AbstractA tutorial study of the Colpitts oscillator family deﬂned as all oscillators based on a n... more AbstractA tutorial study of the Colpitts oscillator family deﬂned as all oscillators based on a nonlinearampliﬂer and a three-terminal linear resonance circuit with one coil and two capacitors. The originalpatents are investigated. The eigenvalues of the linearized Jacobian for oscillators based on singletransistors or operational ampliﬂers are studied.IntroductionAn electronic oscillator is a nonlinear circuit with at least two memory components (charge,°ux or hysteresis based). When excited with a dc source an oscillator responds with a steadystate signal which may be chaotic of nature in case of more than two memory components. TheColpitts oscillator is one of the most used oscillators especially for high frequencies. The aim of thistutorial is to study Colpitts oscillators deﬂned as any oscillator made from a nonlinear ampliﬂerand a three-terminal linear resonance circuit with one coil and two capacitors called the Colpittsresonator.Electronic oscillators may be classiﬂed in fam...

World Scientific Series on Nonlinear Science Series B, 2002

ABSTRACT An introduction to the design of chaotic oscillators is presented from an electrical eng... more ABSTRACT An introduction to the design of chaotic oscillators is presented from an electrical engineering point of view. Oscillators are amplifiers with unstable bias points. The basic design principle behind chaotic oscillators is the connection of two electronic circuits which are not in harmony. A number of configurations which may serve as the physical mechanisms behind chaotic behavior are listed. The behavior of an oscillator is explained by means of eigenvalue studies of the linearized Jacobian of the differential equations for the mathematical model of the oscillator. The basic design principle is demonstrated by means of different simple examples.

2015 European Conference on Circuit Theory and Design (ECCTD), 2015

A tutorial discussion of negative resistance oscillators based on simple RLC circuits is presente... more A tutorial discussion of negative resistance oscillators based on simple RLC circuits is presented. Two cases are based on parallel RLC circuits and two cases are based on series RLC circuits. Distortion is minimized by introducing symmetry in the movement of the complex pole-pair of the small signal model.

A generalized approach to the design of oscillators using operational amplifiers as active elemen... more A generalized approach to the design of oscillators using operational amplifiers as active elements is presented. A piecewise-linear model of the amplifier is used so that it make sense to investigate the eigenvalues of the Jacobian of the differential equations. The characteristic equation of the general circuit is derived. The dynamic nonlinear transfer characteristic of the amplifier is investigated. Examples of negative resistance oscillators are discussed.

Elektronika ir Elektrotechnika

a discussion of various concepts

Nonlinear Analysis: Modelling and Control, 2008

World Scientific Series on Nonlinear Science Series B, 2002

2015 European Conference on Circuit Theory and Design (ECCTD), 2015

We are searching for the truth of the universe. We invent languages like physics and mathematics,... more We are searching for the truth of the universe. We invent languages like physics and mathematics, so we can discuss our observations. Sometimes we lose our way and we discuss our models instead of the reality. We observe an oscillating pattern on all levels from the galaxies to the superstrings. We introduce the concept of time which is built from the past and the future. We live in a dynamic world. We live in the start moment of the future. The size of this moment is zero and infinite at the same time. When we become conscious about this moment, it is in the past. We do not understand the concept of TIME. We believe in GOD because we are created by GOD. We create GOD in our picture because GOD wants us to understand. GOD is equivalent to LIFE. LIFE is eternal.

HAIKU: An electrical circuit. The circuit can't find a DC bias point. Steady state oscillations.

a discussion of various concepts

Question: Are the statements below TRUE or FALSE? 1. All human beings have the same genetics crea... more Question: Are the statements below TRUE or FALSE? 1. All human beings have the same genetics created by GOD. 2. We create religions which have a lot in common. 3. We create gods in our picture because GOD want us to understand. 4. We are curious and we want to understand the universe. 5. We observe our environment, the universe. 6. We invent languages like our mother-language, mathematics and physics so we can discuss our observations 7. We create models of our observations. Unfortunately the models are not complete. 8. Some times we fall in love with our models and forget about the real thing. 9. We observe particles and waves. 10. Seen from a galaxy our globe is a particle. 11. When we zoom on our globe we observe oscillations.