Learning Outcomes
Upon successful completion of the course, the student will be able:
1) Τo get familiar with the use of electrical measurement instruments in Non Linear Systems.
2) Τo implement electrical circuits with Non Linear Dynamics behavior and monitoring their function by taking measurements.
3) Τo get familiar on applying the theory of electrical circuits in practice.
4) To develop experience in the written presentation of experimental measurements.
Course Content (Syllabus)
Course Content
- Two-terminal resistors. v-i characteristics. From linear to nonlinear resistor. Diode. Tunnel diode. Bilateral elements. Connections of nonlinear elements i) in series ii) in parallel ii) mixed connection. Binaryity. Zener diode circuits. Exercises.
- The piecewise linear techniques. Concave and convex resistors. Characteristics. Exercises. Neon lamps. Resistors controlled by current and voltage. Operating points in DC current - DC analysis. Analytical method. Graphical and numerical method. Exercises.
- Operational Amplifier (OA) circuits. Overall operation in the linear region and in the saturation regions. Ideal (OA) model. Negative and positive feedback circuits. Exercises.
- Nonlinear feedback. Negative impedance converter. Algorithm for plotting piecewise linear characteristics. N- and S-type characteristics. Exercises.
- Memristors.
- Chaos. Dynamical systems. Phase space. Autonomous and non-autonomous nonlinear oscillators. (Van der Pol and forced, Duffing and Ueda - Van der Pol).
- Poincare section, chaotic oscillation, bifurcation diagrams.
- Spectrum analysis of time series.
- Lyapunov exponents. R-L varactor circuit.
- Intermittency and crisis in chaotic attractors. Antimonotonicity.
- Applications from linear to nonlinear oscillators. Dynamic behavior of Chua circuits. Biological oscillators Bonhoffer- Van der Pol.
- Simulation programs of the Chua oscillator (Adventures of Bifurcation and Chaos (ABC). Learning and application on the Department's computer island.
- Design and construction of negative resistors, measurement of v-i characteristics. Laboratory implementation of nonlinear resistors. Circuit simulation using computer programs.
Keywords
Nonlinear circuits, Chaos, Antimonotonicity, bifurcation diagram, phase portrait, Poincare, Memristor,