EGR 224/Spring 2023/Test 2

This page is the review sheet for Test 2 for EGR 224 for Spring, 2022.

Coverage

While the test is, by nature, cumulative, there will be certain aspects of the Electrical Fundamentals of Mechatronics which form the core of this test. Specifically, topics from lectures 10-18, HW 5-8, and the accompanying labs. More specifically, topics include, but are not limited to,

1. Reactive elements (Capacitors and Inductors)
   1. Know main model equation relating voltage and current and what it means for the voltage across a capacitor or the current through an inductor
   2. Know the equation for energy stored in a capacitor or an inductor. Note that if you use superposition to find the capacitor voltage or inductor current, you must wait until the end of the superposition process, when you have the total voltage or current, to find the energy stored.
2. DC steady-state analysis of reactive circuits
   1. Be able to state the conditions for the DC Steady State and be able to identify if something is "illegal" or "weird" in this context
   2. Recall if the DCSS conditions are satisfied that capacitors act like open circuits inductors act like short circuits
3. DC Switched circuits / constant source circuits
   1. Determine initial conditions given constant forcing functions
   2. Be able to determine the inductor voltage or capacitor current just after a condition in the circuit has changed (i.e. switch changes position or constant source changes...constant...
   3. Set up and solve a first-order differential equation with initial conditions and constant forcing functions
   4. Accurately sketch solutions to switched circuit / constant source circuit
4. Complex numbers and sinusoids
   1. Be able to perform basic phasor analysis and calculations efficiently with your calculator or using Maple / Python as a calculator
   2. Seriously - do not spend 30 minutes randomly pushing buttons on a problem whose calculations should take under a minute
5. AC Steady State / Phasor Analysis
   1. Draw circuits correctly in the frequency domain - be sure there is a clear difference in your time domain and frequency domain variables
   2. Determine a system of equations using NVM, MCM, and/or BCM to solve relationships in frequency domain (you will not be required to solve more than 2 simultaneous equations)
   3. For "simple" circuits (solvable with current or voltage division, Ohm's Law, or at most two equations), be able to determine output phasors numerically and translate into the time domain
   4. Use superposition to solve based on either different sources or different frequencies or both. Note that you can solve ACSS problems with sources of different frequencies, but you can only solve for one frequency at a time - do not mix phasors that represent signals at different frequencies! Solve for each frequency's time-domain, then add those time-domain representations at the end.
6. Transfer Functions
   1. Be able to find transfer functions between outputs and inputs in the frequency domain.
   2. Use the derivative property to get a differential equation from a transfer function or a transfer function from a differential equation.
   3. Use the transfer function to figure out the magnitude ratio and phase differences between a single-frequency source and the resulting output signal.
7. Filters
   1. Be able to determine filter type by transfer function based on magnitude information
8. Singularity functions
   1. Know what $$\delta(t)$$, $$u(t)$$, $$r(t)$$, and $$q(t)$$ and how they relate to each other
   2. Given a function consisting of scaled $$u(t)$$ and $$r(t)$$, be able to accurately sketch it and be able to accurately represent it as a piecewise function
   3. Given a graph showing a function that has value and slope changes, be able to write it as a combination of scaled, shifted step and ramps
9. Convolution
   1. Given two functions that consist of scaled, shifted impulse, step, ramp, and/or exponential functions, be able to efficiently calculate the convolution of those functions
   2. Shortcuts (* represents convolution below):

\( \begin{align*} \delta(t-a)*f(t)&=f(t-a)\\ u(t)*u(t)&=t\,u(t)=r(t)\\ u(t)*r(t)&=\frac{1}{2}t^2\,u(t)=q(t)\\ r(t)*r(t)=u(t)*q(t)&=\frac{1}{6}t^3\,u(t)=c(t)\\ e^{-at}u(t)*e^{-at}u(t)&=te^{-at}\,u(t)\\ e^{-at}u(t)*e^{-bt}u(t)&=\left(\frac{e^{-at}-e^{-bt}}{b-a}\right)\,u(t)~\mbox{assumes }b\neq a \end{align*} \)

Relevant Prior Test Questions

In all cases below, if there is a Bode Plot, Laplace Transform, or Op-Amp problem, skip it.

From the Test Bank:

• EE/ECE 61
  • Spring 2001 Test 2 (V)
  • Fall 2001 Test 2 (IV)
  • Spring 2001 Test 3 (I, IV, V)
  • Fall 2001 Test 3 (I, II, III)
• ECE 280
  • Spring 2010 Test 1 (IV(c,d), V(c,d))
• ECE 382
  • Spring 2007 Test 1 (I kind of..., V) - I will not have you do that much rote algebra
  • Spring 2008 Test 1 (IV a)
  • Spring 2009 Test 1 (Ia)
  • Spring 2010 Test 1 (I, II)
• ECE 382 / ME 344
  • Spring 2011 Test 1 (I)
  • Spring 2012 Test 1 (I)
• EGR 224
  • Spring 2008 Test 1 (I-III, V (a, b, d))
  • Spring 2008 Test 2 (I-III)
  • Spring 2009-2021 Test 2

Not on the test

• Bode Plots
• Laplace Transforms
• Operational Amplifiers

Questions

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References