ELE 2011 - Electric Circuits II: Theory and Applications

• Demonstrate knowledge of electric circuit quantities in a steady-state AC context:  voltage, current, resistance, reactance, impedance, admittance, conductance, and susceptance, including SI units and prefixes
• Relate symbols and circuit schematics to physical components and circuit boards
• Analyze AC steady-state series-parallel circuit using impedances and admittances
• Utilize superposition for circuits with two sources of the same frequency and of different frequencies
• Symbolically analyze and numerically evaluate AC circuits for electric circuit quantities, complex power, frequency response with AC transfer functions, and op-amp circuits
• Analytically interrelate the polar, exponential, and time domain expressions for AC sinusoidal waveforms, both symbolically and numerically
• Develop the AC complex impedance relations of passive components from the voltage-current time-domain relationships
• Develop complex power expressions from the exponential forms of phasor voltage and current
• Determine complex power for single-phase AC circuits from the phasor voltage and current, including multisource circuits where a source absorbs AC real power (note: power factor correction is introduced but is not an outcome)
• Analyze AC circuits containing an ideal transformer, using the dot convention and reflected impedance where appropriate (note: mutual inductor analysis is not an outcome in this course)
• Analyze circuits with dependent sources that model components, circuits, and devices (note: analysis of circuits with randomly placed dependent sources is not a learning outcome)
• Determine DC and AC Thévenin and Norton equivalent circuits with the test source method, including when the original circuits contain dependent sources and transformers
• Determine the transfer function, the break frequency, and the magnitude and phase Bode approximations (plots) of series RL and RC AC circuits
• Distinguish power ratios in dB (10 log) from voltage, current, and other non-power ratios (20 log)
• Explain qualitatively why the phase response of a filter matters
• Analyze single op-amp circuits in non-standard configurations, including simple active filters, using circuit principles and ideal op‑amp properties
• Derive the resonant frequency of unloaded and loaded series, parallel, and series-parallel RLC resonant circuits that have a single resonant frequency
• Compute the resonant frequency and resonant impedance or admittance
• Determine the quality factor (Q) and the half-power bandwidth from resonant frequency response plots
• Determine the step response of series and parallel (not series-parallel) RL and RC circuits with initial conditions using differential-equation based time domain analysis techniques
• Identify the time constant of series and parallel RL and RC circuits
• Reduce first-order circuits using Thévenin equivalent circuit analysis to determine the transient response and time constant
• Determine the step response of series and parallel (not series-parallel) RLC circuits with initial conditions using differential-equation based time domain analysis techniques
• Identify the damping type and parameters of series and parallel RLC circuits
• Express the step (switching), ramp, and impulse functions mathematically and graphically
• Formulate composite waveform expressions using the time delay property and combinations of step, ramp, and impulse functions
• Graphically determine the voltage (current) waveform when a current (voltage) waveform is applied to a capacitor or an inductor,
• Determine Laplace and inverse Laplace transforms of basic signals by using a transform pairs table and by using software for real poles and non-repeated complex conjugate poles
• Analyze first-order and second-order circuits in the Laplace transform domain, including initial condition models where needed,
• Use software to perform partial fraction expansion for identification of poles (note: use of software as opposed to manual methods is intentional)
• Determine transfer functions in the complex frequency (s) domain for simple RL, RC, and RLC series-parallel circuits
• Explain the significance of poles as they relate to time domain and frequency domain behaviors

• 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