EGR 224/Spring 2014/Final

Exam Spring 2014 Coverage

1. Basic electrical entities - be able to fill in the following chart: \(\begin{align} \begin{array}{cccc} \mbox{Name} & \mbox{Variable} & \mbox{Units} & \mbox{Equation} \\ \hline \hline \mbox{charge} & q & \mbox{coulombs (C)} & q(t) = q(t_0) + \int_{t_0}^t i(\tau)~d\tau \\ \hline \mbox{current} & i & \mbox{amperes (A)} & i = \frac{dq}{dt} \\ \hline \mbox{work} & w & \mbox{joules (J)} & \\ \hline \mbox{voltage} & v & \mbox{volts (V)} & v = \frac{dw}{dq} \\ \hline \mbox{power} & p & \mbox{watts (W)} & p = \frac{dw}{dt} = vi \\ \hline \mbox{resistance} & R & \mbox{ohms}~(\Omega) & R = \frac{v}{i} \\ \hline \mbox{conductance} & G & \mbox{mhos}~(\mho) & \\ \hline \end{array} \end{align}\)
2. Power - know the general equation for instantaneous power absorbed or delivered by an element, and know three equations that can be used to calculate power in a resistive element. Know the difference between absorbed power and delivered power. Be able to solve circuit variables using the idea that net power in a circuit is zero.
3. Sources - know the four kinds of dependent source and the properties of sources (i.e. current sources can have any voltage across them and voltage sources can have any amount of current through them).
4. Ohm’s Law - know Ohm’s Law and the requirement of the passive sign convention for resistors.
5. Kirchhoff’s Laws - know what Kirchhoff’s Laws are, be able to state them clearly in words, and be able to apply them to circuit elements to solve for unknown currents and voltages.
6. Equivalent resistances - be able to simplify a resistive network with series and parallel resistances.
7. Node voltage method - be able to solve for voltages, currents, and power absorbed or delivered by clearly using the node voltage method to determine node voltages, possibly followed by functions of those node voltages to get currents or powers.
8. Current methods - be able to solve for voltages, currents, and powers absorbed or delivered by clearly using the mesh or branch current method to determine mesh or branch currents, possibly followed by functions of those currents to get element currents, voltages, or powers.
9. Current and Voltage division - be able to efficiently solve circuit problems by using current and voltage division.
10. Superposition - be able to efficiently solve circuit problems by using superposition.
    • Remember that dependent sources must be included in the different subdivisions of a superposition problem regardless of the independent source or sources you leave on.
11. Thévenin and Norton Equivalent Circuits - be able to solve for the source and resistance of a Thévenin or Norton Equivalent Circuit for a circuit comprised of independent and dependent sources and resistors. Be able to draw both Thévenin and Norton Equivalent Circuits. Be able to use Thévenin and Norton Equivalent Circuits to determine the maximum power delivered to a load and the required resistance of that load to receive the maximum power.
12. Reactive elements (capacitors and inductors)
    1. Know the basic voltage/current relationships
    2. Know the continuity conditions
13. DC steady-state analysis of reactive circuits
    1. Capacitors act like open circuits
    2. Inductors act like short circuits
14. AC steady-state analysis of reactive circuits
    1. Phasor analysis for single-frequency sources
    2. Phasor analysis coupled with superposition for circuits with sources at different frequencies - you can either do each individual component of all the sources independently or group components by frequency.
15. Impedance and transfer functions
16. Filters
    1. Be able to determine filter type by transfer function
    2. 1st order filters
       1. Determine cutoff frequency (half-power or -3dB frequency) and filter type
       2. Be able to determine filter type given a circuit or design a circuit given a filter type. This type of question would be limited to voltage-to-voltage filters
    3. 2nd order filters
       1. Be able to determine filter type given a circuit
       2. For high-pass or low-pass filters, be able to determine cutoff (half-power) frequencies (no tricky cases)
       3. For band-pass filters, be able to determine bandwidth, quality, damping ratio, cutoff frequencies, logarithmic center frequency, and linear center frequency
       4. For band-reject filters, be able to determine quality, damping ratio, cut-on frequencies, logarithmic center frequency, and linear center frequency
       5. Be able to design a band-pass or band-reject filter given sufficient information (some combination of bandwidth, quality, damping ratio, cutoff/cuton frequencies, logarithmic center frequency, and linear center frequency.
17. Bode plots
    1. Be able to sketch Bode magnitude plot approximation for multiple zero/pole system assuming poles and zeros are at least a decade away from each other (i.e. no tricky cases)
    2. Be able to interpret Bode magnitude plot with respect to bandwidth, quality, damping ratio, cutoff/cut-on frequencies, logarithmic center frequency, and linear center frequency
18. Frequency and Time Domain Relations
    1. Determine transfer functions between a source and an output
    2. Determine differential equation using time or frequency techniques
19. Laplace Transforms
    1. Understand the concepts of impulse response and step response for LTI systems and their relationship to the transfer function
    2. Be able to set up and solve circuit equations using Bilateral Laplace Transform versions of impedance equations
    3. Be able to set up and solve circuit equations using Unilateral Laplace Transform equivalents of inductors and capacitors with initial conditions other than 0.
       • Specifically, know how to replace a capacitor or inductor with a version storing no initial energy in series with an appropriate voltage source or in parallel with an appropriate current source.
    4. Know the MOAT forwards and backwards and be able to use it to solve problems using Laplace transforms.
    5. Be able to use partial fraction expansion to help with inverse Laplace transforms of relatively simple frequency space representations. Note: no repeated roots will be given.
20. Operational Amplifiers
    1. Know the requirements for the Ideal Op-Amp Assumptions (feedback between the output and the inverting input), the Ideal Op-Amp assumptions (infinite internal input impedance, zero internal output impedance, and infinite internal voltage gain), and the results of the Ideal Op-Amp Assumptions given feedback to the negative input (no voltage drop across the input terminals and no current into/out of the input terminals).
    2. Know how to analyze and build buffers, noninverting and inverting amplifiers, summing and difference amplifiers.
    3. Know how to analyze non-standard configurations (i.e. every other kind of circuit with an OpAmp, including those with reactive elements).
21. Digital Logic
    1. Understand the basic symbols involved in digital logic and the meaning of terms like \(AB\), \(A+B\), and \(\bar{A}\), and the difference between \(\overline{AB}\) and \(\bar{A}\,\bar{B}\)
    2. Understand the relationship between logical expressions and minterms
    3. Be able to construct a Karnaugh map from a logical function or a logical function from a Karnaugh map
    4. Be able to use Karnaugh maps to determine the Minimum Sum of Products (MSOP) or Minimum Product of Sums (MSOP) form for a logical expression.