2.3. Nonlinear Electrical Phenomena

Slides:

Advertisements

Similar presentations

Electromagnetic Oscillations and Alternating Current

Advertisements

Alternating Current Circuits

2. Nonlinear Systems. Part I 1.Nonlinear Mechanics 2.Competition Phenomena 3.Nonlinear Electrical Phenomena 4.Chemical and Other Oscillators.

Dr. Jie ZouPHY Chapter 32 Inductance. Dr. Jie ZouPHY Outline Self-inductance (32.1) Mutual induction (32.4) RL circuits (32.2) Energy in a.

EEE340Lecture 191 Example 5-1: Vacuum-tube diode Electron cloud where  (y) is negative. The velocity is Newton’s law Hence where (5.9) (5.11) (5.8) y.

Lecture 20-1 Alternating Current (AC) = Electric current that changes direction periodically ac generator is a device which creates an ac emf/current.

Poincare Map. Oscillator Motion  Harmonic motion has both a mathematical and geometric description. Equations of motionEquations of motion Phase portraitPhase.

G L Pollack and D R Stump Electromagnetism Electromagnetic Induction Faraday’s law If a magnetic field changes in time there is an induced electric.

van der Pol Oscillator Appendix J

Magnetically Coupled Circuits

Mechanical Vibrations Jeff Rhoads and Terry Ballinger MSU 2006.

Van der Pol. Convergence  The damped driven oscillator has both transient and steady-state behavior. Transient dies outTransient dies out Converges to.

Self-inductance and inductors(sec. 30.2) Magnetic field energy(sec. 30.3) RL circuit(sec. 30.4) LC circuit (sec. 30.5) RLC series circuit (sec. 30.6) Inductance.

Physics for Scientists and Engineers II, Summer Semester Lecture 17: July 1 st 2009 Physics for Scientists and Engineers II.

Capacitance in a quasi-steady current circuit Section 62.

Series RLC Network. Objective of Lecture Derive the equations that relate the voltages across a resistor, an inductor, and a capacitor in series as: the.

Inductance Self-Inductance A

28. Alternating Current Circuits

Oscillations and Waves Forced Oscillations and Resonance.

RC, RLC circuit and Magnetic field RC Charge relaxation RLC Oscillation Helmholtz coils.

Alternating Current Circuits

Harmonic Oscillation 1. If a force F acts on a spring, the length x changes. The change is proportional to the restoring force (Hooke’s Law). A spring.

Alternating Current Circuits

First-Order Circuits. Now that we have considered the three passive elements (resistors, capacitors, and inductors), we are prepared to consider circuits.

Advanced Higher Physics Inductors & Inductance. Magnetic Flux Magnetic flux, , is a measure of the magnetism in an area, given by –  = B A where - 

Lecture 18-1 Ways to Change Magnetic Flux Changing the magnitude of the field within a conducting loop (or coil). Changing the area of the loop (or coil)

Exam review Inductors, EM oscillations

Chapter 23 Alternating Current Circuits Capacitors and Capacitive Reactance The resistance in a purely resistive circuit has the same value at all.

Oscillators fall CM lecture, week 4, 24.Oct.2002, Zita, TESC Review simple harmonic oscillators Examples and energy Damped harmonic motion Phase space.

Chapter 30 Inductance. Inductor and Inductance Capacitor: store electric energy Inductor: store magnetic energy Measure how effective it is at trapping.

Short Version : 13. Oscillatory Motion

Brief Survey of Nonlinear Oscillations Li-Qun Chen Department of Mechanics, Shanghai University, Shanghai , China Shanghai Institute of Applied.

ECE 4991 Electrical and Electronic Circuits Chapter 2

Chapter 14 - Oscillations

Ahmed El Moutaouakil EE 484: Properties and synthesis of L-C networks Instructor: Iickho Song October 18 th 2007.

My Chapter 20 Lecture Outline.

Resonant Circuits The resonance phenomenon and its characterization Filter Networks Networks with frequency selective characteristics: low-pass, high-pass,

Chapter 30 Inductance, Electromagnetic Oscillations, and AC Circuits.

Ryan Dickmann RLC Circuits. RLC Basics An RLC Circuit is comprised of at least one resistor, one inductor, and one capacitor. They act similarly to LC.

Lecture 19-1 Potential Difference Across Inductor VV ++ - I internal resistance Analogous to a battery An ideal inductor has r=0 All dissipative effects.

Chapter 31 Lecture 33: Alternating Current Circuits: II HW 11 (problems): 30.58, 30.65, 30.76, 31.12, 31.26, 31.46, 31.56, Due Friday, Dec 11. Final.

Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures.

Magnetic Induction electricity and magnetism meet!

Electric Energy Notes.

Basic Components used in Electronics. Used in electronic circuits to charge up to a given potenti al.

The RLC Circuit AP Physics C Montwood High School R. Casao.

Chapter 36 Inductance Capacitance Electric energy Magnetic energy Inductance.

Source-Free Series RLC Circuits.

EM OSCILLATION & AC. LC oscillation.

1 ECE 3301 General Electrical Engineering Section 30 Natural Response of a Parallel RLC Circuit.

Lecture 19-1 RL Circuits – Starting Current 2. Loop Rule: 3. Solve this differential equation τ=L/R is the inductive time constant 1.Switch to e at t=0.

PHY238Y Lecture 3 Damped oscillations Forced oscillations. Resonance References: Halliday, Resnick, Walker: Fundamentals of Physics, 6 th edition, John.

Chapter 21 Magnetic Induction and Chapter 22.9: Transformers.

For vacuum and material with constant susceptibility M 21 is a constant and given by Inductance We know already: changing magnetic flux creates an emf.

electricity and magnetism meet!

Induction and Inductance

Levitation above a Superconductor

Alternating Current Kirchoff’s rules for loops and junctions may be used to analyze complicated circuits such as the one below, powered by an alternating.

Vibrations & Waves Part 1: Periodic Motion.

AC circuits Physics /27/2018 Lecture IX.

Physics 111 Practice Problem Solutions 14 Oscillations SJ 8th Ed

Waves & Sound Waves.

Alternating Current Circuits

Chapter 30 Inductance.

Dr. Unnikrishnan P.C. Professor, EEE

Alternating Current Circuits

Alternating Current Circuits

人間の二足歩行モデルにおけるシミュレーション

Chapter 30 Induction and Inductance

Presentation transcript:

2.3. Nonlinear Electrical Phenomena Nonlinear Inductance An Electronic Oscillator (the Van der Pol Equation)

2.3.1. Nonlinear Inductance Iron core inductor Kirchhoff's law

2.3.2. An Electronic Oscillator (the Van der Pol Equation) Limit cycle: A periodic motion to which the system approaches irregardless of the initial conditions. All electronic oscillator circuits display limit cycles. van der Pol equation :

X > 1: damping is purely dissipative. X < 1: "damping" term amplifies. Oscillator can be self-excited. X = const ( 1) : limit cycle. Tunnel Diode Oscillator: Example 2-3.nb 02-3.nb

Self-sustained oscillations occur whenever a periodic motion is coupled to an energy source. Tacoma Narrows Bridge (1940)