Course Outline (updated on January 2019)

Preamble
This course is the second part of an introduction to linear circuit analysis.  This is not a course on physics but on a mathematical abstraction (a model) used to represent a variety of engineering problems (one of which, of course, is the solution of physical electric and electronics circuits).  This course assumes that the student has a working knowledge of ordinary linear differential equations, basic integral-differential calculus, a thorough knowledge of complex numbers arithmetic and representations, the Laplace Transform and the physics background that describes the basic electromagnetic entities and relationships.  The student must be completely comfortable with nodal analysis of RLC netwoks with both dependent and independent sources, as well as with Thevenin/Helmholtz equivalent circuits. The approach of the course is very dynamic, and relies heavily on the mandatory calculator device, the HP-Prime graphic calculator. 

Part I (3 weeks)
  1. Second order circuits in the time domain, the p-operator.
  2. Some functions of time: unit step, unit pulse, ramp, impulse.
  3. The Laplace Transform: why and how.
  4. Differentiation and integration in the s-domain. Initial conditions and the Laplace Transform
  5. Inverse Laplace Transform: tables. Partial Fractions expansion.
  6. Impedance in the s-domain and initial conditions in circuit representation.
Part II (4 weeks)
  1. Transfer functions in the complex frequency domain: poles and zeros. Analytic extension of the Laplace Transform.
  2. Bode Plots: amplitude and phase plots. dB plots of the amplitude and half-frequency points: bandwith.
  3. Asymptotic Bode plots: single pole/zero contribution to amplitude and phase.
  4. Asymptotic Bode plots: double pole/zero contribution to amplitude and phase.
  5. Asymptotic Bode plots: complex conjugate pair of poles/zeros contribution to amplitude and phase.
  6. System identification: impulse response. Matlab prony routine. (?)
  7. Introduction to passive filters.
  8. Two port networks. Basic sets of parameters.
Part III (4 to 5 weeks)
  1. Sinusoidal time functions represented as complex numbers.  RMS value, and phase shift of a sine wave.
  2. Multiplication with a complex number as: scaling and "rotation" of a sine wave.
  3. Circuit elements represented as complex impedances.  Current to voltage lagging, leading relationships in each element.
  4. Power in AC steady state: Apparent power, active power, reactive power, units. Power triangle vs. impedance triangle.
  5. Thevenin/Helmholtz equivalent in AC steady state.  Maximum power transfer in AC steady state..
  6. Phasor diagrams in distribution circuits.
  7. Three phase systems.  Delta to wye conversion of a symmetrical system.
  8. Single phase solution of symmetrical  three-phase problems.
  9. Clarke Transformation from asymmetrical to symmetrical problems.
  10. The ideal transformer. Mutual inductance. Three phase connections of transformers.