ELE 2011 - Electric Circuits II: Theory and Applications

• Demonstrate working knowledge of electric circuit quantities and their fundamental relationships for AC circuits, including complex number representation in exponential form
• Symbolically analyze and numerically evaluate AC circuits using phasors, including complex power, frequency response with basic AC transfer functions, and op-amp circuits
• Perform transient analysis of series and parallel first and second order electric circuits, including initial conditions, using differential equation-based time domain techniques
• Perform transient analysis of series-parallel circuits, including initial conditions, using Laplace transform domain techniques

• Complex number arithmetic and logarithmic scales
• Integration and differentiation of elementary functions
• DC and AC circuit analysis
• Mathematical software and simulation in circuit analysis
• Ideal op-amp circuits in standard configurations

• AC steady-state series-parallel circuit analysis: admittances, superposition, circuits with two sources of different frequencies
• AC sinusoid in complex exponential form; analytic interrelationships between polar, exponential, and time domain expressions for AC sinusoidal waveforms
• Voltage-current time-domain and phasor relations of passive components, analytic conversion of symbolic time domain relationships to phasor relationships in complex exponential form
• Development of complex power expressions from the exponential forms of phasor voltage and current, complex power for single-phase AC circuits using VI* (power factor correction is introduced), three-component application examples
• Ideal transformer, dot convention, the concept of a component with an electrical input and an electrical output
• Dependent source modeling, equivalent circuit concept extended to model components, circuits, and devices with an input and an output with dependent sources (analysis of circuits with randomly placed dependent sources is not the focus)
• Determination of DC and AC Thevenin and Norton equivalent circuits, including dependent sources with test source method; conversion between equivalent circuits
• Ideal transformer:  reflected input impedance; coupled (mutual) inductors with dependent source model (mutual inductor operation and analysis is covered in a subsequent electromagnetic fields course)
• Transfer function, break frequency, dB relationship to a power ratio, magnitude and phase slopes, and Bode approximations of series RL and RC AC circuits
• Analysis of single op-amp non-standard configurations using circuit principles, including simple active filters
• Three-component RLC resonant circuits:  pure series, pure parallel, and a tank circuit with a nonideal inductor; impedance and/or admittance expressions as a function of frequency, resonance concept, resonant frequency development, quality factor (Q), half-power bandwidth, resonant frequency response plots
• Graphical application of time domain inductor and capacitor i-v relations to simple waveforms
• Step response transient analysis of series and parallel RL and RC circuits with initial conditions using differential-equation based time domain techniques:  differential equation setup and solution, identification of the time constant
• Step response transient analysis of series and parallel RLC circuits with initial conditions using differential-equation based time domain techniques:  differential equation setup and solution, identification of damping type and parameters
• Step (switching) function u(t), ramp, and impulse function
• Signal delay property, utilization with switching functions in expressing simple composite waveforms
• Laplace transform circuit analysis concept; Laplace transforms of basic signals using transform pairs table
• First-order circuit transform analysis
• Partial fractions expansion (PFE), cover-up method with real poles, PFE with MATLAB (or equivalent)
• Step and impulse initial condition models for inductors and capacitors including the impulse concept
• Second-order circuit analysis with Laplace transforms with initial condition models
• Inverse Laplace transform with complex conjugate poles
• Transfer functions in the complex frequency (s) domain for simple RL, RC, and RLC series-parallel circuits [H(s)]
• Pole concept and significance; zeros, initial value, and final value from a transfer function (introduction for awareness in subsequent courses)

• No formal lab but a few experimental assignments will be made as homework