EGR 224/Spring 2009/Final

This page is the review sheet for the Final Exam for EGR 224 for Spring, 2009. The final will be held Saturday, May 2nd, from 2-5PM in Teer 203, in accordance with the Exam Schedule for Spring 2009

HW 9 Issues

1. Part 1
   • Be sure to convert Hz to rad/s for all calculations! Also, \(\omega=2\pi f\,\!\)
   • Putting a buffer right at the source isolates the source from the circuit and thus draws no power from it.
   • While not on the test, note that for the bode command in MATLAB, a first-order numerator needs a trailing zero. That is, a numerator of R/L * s would be [R/L 0]

Coverage

This exam is cumulative. Note, however, that specific questions about digital logic, sensors, actuators/motors, or Simulink will not appear on this final. The focus will be on the material presented in lectures 1-23.

1. Circuit elements
   1. Know the voltage/current model equations for R, L, and C
   2. Know continuity condition for L and C
   3. Properly apply passive sign convention to circuits with R, L, C
   4. Determine instantaneous power for R, L, C circuits
2. Circuit analysis
   1. Label circuit and determine equations using NVM, BCM, MCM
   2. Determine Thevenin and Norton equivalent circuits; for resistive circuits, be able to draw the components - for reactive circuits, be able to calculate their equivalent impedance at a single frequency
   3. Use superposition to subdivide analysis into several simpler parts
   4. Be able to use voltage and current division in general, and in concert with supoerposition in particular
3. DC steady-state analysis of reactive circuits - all sources must be DC
   1. Capacitors act like open circuits
   2. Inductors act like short circuits
4. 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.
5. Impedance and transfer functions
6. Passive 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 or quarter-power if repeated root) frequencies
      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/cut-on frequencies, logarithmic center frequency, and linear center frequency. You will not be asked to build any passive filter that requires more than three components.
7. 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
8. DC Step response of 1st order circuit
   1. Determine initial conditions using continuity requirements
   2. Determine differential equation using time or frequency techniques
   3. Determine solution to 1st order differential equations with constant forcing functions
   4. Accurately sketch solution to 1st order differential equations with constant forcing functions including slopes at time constants
9. Higher order circuits
   1. Determine transfer functions between a source and an output
   2. Determine differential equation using time or frequency techniques
10. Operational Amplifiers
    1. Know ideal op-amp assumptions and their applications in negative-feedback circuits
    2. Design 1st and 2nd order filters based on filter parameters such as passband gain, half-power or quarter-power frequencies, natural frequency, linear center frequency, or bandwidth.
    3. Design circuits to perform addition, subtraction, scalar multiplication based on summation, difference, inverting and noninverting configurations.
11. Laplace Transforms
    1. Know the MOAT forwards and backwards and be able to use it to solve problems using Laplace transforms.
    2. Be able to use partial fraction expansion to help with inverse Laplace transforms of simple frequency space representations.