Fourier Series and Fourier Transform. Intro, Basic Derivation


20161122112648EE44

1. Circuits Fundamentals: Definitions, graph properties, current & voltage, power & energy
2. Circuits Fundamental: Passivity and Activity, KCL and KVL, Ideal Sources
3. Circuits Fundamentals: Resistance, Ohm's law, linearity, time-variance, diode circuits.
4. Nodal Analysis: ground, Y-Matrix, node voltage & stimulus vectors, Linear algebra, determinant
5. Nodal Analysis: Examples, dependent sources, existence of a solution
6. Nodal Analysis Continued: Nodal analysis, dependent sources, with voltage sources, super nodes
7. Mesh Analysis & Diode Circuits: Mesh analysis, 3D networks, super mesh, diode circuit design
8. Circuit Theorems: Superposition, Thévenin, Norton, Source Transformation, Network Equivalence
9. Circuit Theorems: Source Transportation, Substitution Theorem, Maximum Power Transfer, Y-Delta
10. Active circuits: Op-Amp, Feedback, Asymptotic Equality, Inverting and non-inverting amplifiers
11. Singularity Functions: Introduction, Unit Step, Pulse, and Dirac Delta (Impulse) Functions
12. Linear Systems: Dirac Delta, Sifting Property, Impulse Response, LTI, Convolution
13. Linear Systems: Convolution, Examples of System Response, Convolution Examples
14. Time-Domain Response: Capacitors and Inductors, RC Response, General 1st-Order System
15. Time Domain Response: RC Step and Impulse Response
16. Heaviside Operator: Introduction, basic examples
17. Heaviside Operator: Low-Pass Operator, High-Pass Operator, Solving Differential Equations
18. Heaviside Operator: Circuit Examples
19. Heaviside Operator: Nodal Analysis Examples, Order of System, Oscilloscope Probe
20. Impulse Response of 2nd Order System: Complex Numbers, Real Poles, Underdamped and Over-damped
21. Heaviside Operator: Partial Fraction Expansion (PFE), Example
22. Heaviside Operator: PFE with Multiple Roots, Example
23. Heaviside Operator: Operator Catalog, Solving differential equation directly, Examples.
24. Heaviside Operator: Time Delay, Convolution, Example
25. Heaviside Operator: Operator Catalog Review, Convolution Example
26. Heaviside Operator: Initial Conditions
27. System Function: Forced and Natural Response, Poles and Zeros, Time Domain View, Laplace Xform
28. Stability: Definition, Criterion, Poles Location, South-Hurwitz Method
29. Laplace Transform Summary: Definition, Properties
30. Intro to Network Synthesis, Complex Impedance,
31. Sinusoidal Drive, Phasor Notations, Cascaded Systems, Intro to Bode Plot
32. Bode Plot: Properties, Poles and Zeros, Resonance (2nd Order Peaking)
33. Fourier Series and Fourier Transform. Intro, Basic Derivation
34. Fourier Transform: Spectrum, Time and Frequency Duality, Impulse, Sinc, Box
35. Fourier Transform: Modulation
36. Fourier Transform: Sampling
37. Time and Transfer Constants: Brief Introduction
38. Course Brief Final Summary

Topics include: fundamentals of circuits and network theory, circuit elements, linear circuits, terminals and port presentation, time-domain response, nodal and mesh analysis, sinusoidal response, introductory frequency domain analysis, transfer functions, poles and zeros, time and transfer constants, network theorems, introduction to state-space.