ECE 110/Spring 2014/Final

Exam Spring 2014 Coverage

1. Digital Logic
   1. Be able to represent and interpret digital logic functions through the use of a digital logic function (of course), expansion by minors, truth tables, or Karnaugh maps
   2. Be able to simplify digital logic functions into minimum sum of products and minimum product of sums forms
   3. Be able to accurate draw a gated representation of a digital logic function using NOT gates and two-input AND and OR gates
   4. Be able to determine the complexity of a representation so drawn
2. Basic electrical entities - be able to fill in the following chart: \(\begin{align} \begin{array}{cccc} \mbox{Name} & \mbox{Variable} & \mbox{Units} & \mbox{Equation} \\ \hline \hline \mbox{charge} & q & \mbox{coulombs (C)} & q(t) = q(t_0) + \int_{t_0}^t i(\tau)~d\tau \\ \hline \mbox{current} & i & \mbox{amperes (A)} & i = \frac{dq}{dt} \\ \hline \mbox{work} & w & \mbox{joules (J)} & \\ \hline \mbox{voltage} & v & \mbox{volts (V)} & v = \frac{dw}{dq} \\ \hline \mbox{power} & p & \mbox{watts (W)} & p = \frac{dw}{dt} = vi \\ \hline \mbox{resistance} & R & \mbox{ohms}~(\Omega) & R = \frac{v}{i} \\ \hline \mbox{conductance} & G & \mbox{mhos}~(\mho) & \\ \hline \end{array} \end{align}\)
3. 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.
4. 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).
5. Ohm’s Law - know Ohm’s Law and the requirement of the passive sign convention for resistors.
6. 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.
7. Equivalent resistances - be able to simplify a resistive network with series and parallel resistances.
8. 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.
9. 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.
10. Current and Voltage division - be able to efficiently solve circuit problems by using current and voltage division.
11. 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.
12. Reactive elements
    1. Be able to represent a circuit with reactive elements in the DC Steady State
    2. Switched circuits / constant source circuits
       1. Determine initial conditions given constant forcing functions
       2. Set up and solve first-order differential equation with initial conditions and constant forcing functions
    3. Be able to find the closed form solution for a circuit that can be modeled as a first-order linear differential equation with a constant forcing function and some means for determining a value for the unknown variable at some time
       1. Accurately sketch solution to switched circuit / constant source circuit
    4. Be able to determine a model equation for circuits comprised of R, C, and sources or R, L, and sources
    5. Know the equation for energy stored in a capacitor or an. 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.
13. Complex numbers and sinusoids
14. Impedance \(\Bbb{Z}=R+jX\), Admittance \(\Bbb{Y}=G+jB\), Resistance \(R\), Reactance \(X\), Conductance \(G\), Susceptance \(B\)
15. AC Steady State / Phasor Analysis
    1. Draw circuit in frequency domain
    2. Determine series of equations using NVM, MCM, and/or BCM to solve relationships in frequency domain
    3. For "simple" circuits, be able to determine output phasors numerically and translate into time domain
16. Frequency response, transfer functions
17. Linearity and superposition
    1. 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!
18. Fourier series
    1. Analysis of periodic signals comprised of sinusoids with frequencies at integer multiples of the fundamental frequency of the signal
    2. Analysis of periodic signals using analysis equation (will either be simple signal or can be left as integral)
    3. Determination of Fourier series coefficients for an output given a signal (or its Fourier series coefficients) and a circuit or a transfer function (real or ideal)
    4. Synthesis of periodic signals at output of a circuit given Fourier series coefficients
19. Filters
    1. First order (RC and RL) and second order (LRC)
    2. Determination of filter type via Bode or magnitude analysis
    3. Building a circuit to implement a particular first-order filter (will not require op-amps)
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).