ECE 110/Concept List/F22

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$$\newcommand{E}[2]{#1_{\mathrm{#2}}}$$List of concepts from each lecture in ECE_110 -- this is the Fall 2022 version.

Lecture 1 - 8/29

  • Main web page: http://classes.pratt.duke.edu/ECE110F22/
  • Circuit terms (Element, Circuit, Path, Branch and Essential Branch, Node and Essential Node, Loop and Mesh).
  • Electrical quantities (charge, current, voltage, power)

Lecture 2 - 9/2

  • Passive ($$+\rightarrow -$$) Sign Convention and Active ($$-\rightarrow +$$) Sign Convention
  • Circuit topology (parallel, series)
  • Passive Sign Convention and Active Sign Convention and relation to calculating power absorbed and/or power delivered
  • Conservation Laws (conservation of power, Kirchhoff's Voltage Law, Kirchhoff's Current Law):
    $$ \begin{align*} \sum_{\mbox{all elements}}\E{p}{abs}&=0 & \sum_{\mbox{closed path}}\E{v}{drop}&=0 & \sum_{\mbox{closed shape}}\E{i}{leaving}&=0 \end{align*} $$
  • Accounting:
    • The number of independent KVL equations is equal to the number of meshes
    • The number of independent KCL equations is equal to the number of nodes minus one
  • Example of how to find $$i$$, $$v$$, and $$p_{\mathrm{abs}}$$
  • $$i$$-$$v$$ characteristics of various elements (short circuit, open circuit, switch, ideal independent voltage source, ideal independent current source, resistor)
  • Resistance $$R$$ in $$\Omega$$, Conductance $$G$$ in $$\mho$$ or S.
    • For a resistor, $$v=Ri$$
    • For purely resistive elements, $$R=\frac{1}{G}$$, so $$i=Gv$$ as well!


Lecture 3 - 9/5

  • Dependent sources (VCVS, VCCS, CCVS, CCCS)
  • Brute Force Method and labels
  • Equivalents for voltage sources in series, current sources in parallel
  • Ability to rearrange items in series or parallel (no impact on element values; may impact node / mesh values)

Lecture 4 - 9/9

  • How resistance is calculated $$R=\frac{\rho L}{A}$$
  • Equivalent resistances; Examples/Req
  • Voltage division (and redivision)

Lecture 5 - 9/12

  • Current division (and redivision)
  • Simple Node Voltage Method (resistors and voltage sources)

Lecture 6 - 9/16

  • More Node Voltage Method
    • Examples in Resources/Examples/Methods page on Sakai

Lecture 7 - 9/19

  • Mesh Current Method
    • Examples in Resources/Examples/Methods page on Sakai
  • Symbolic calculations in SymPy

Lecture 8 - 9/22

  • Branch Current Method
    • Examples in Resources/Examples/Methods page on Sakai
  • Linearity
    • Nonlinear system examples (additive constants, powers other than 1, trig):
$$\begin{align*} y(t)&=x(t)+1\\ y(t)&=(x(t))^n, n\neq 1\\ y(t)&=\cos(x(t)) \end{align*} $$
    • Linear system examples (multiplicative constants, derivatives, integrals):
$$\begin{align*} y(t)&=ax(t)\\ y(t)&=\frac{d^nx(t)}{dt^n}\\ y(t)&=\int x(\tau)~d\tau \end{align*} $$
  • Superposition
    • Redraw the circuit as many times as needed to focus on each independent source individually
    • If there are dependent sources, you must keep them activated and solve for measurements each time, and you must calculate any controlling variables each time
    • You cannot calculate power until you have the total, final currents or voltages for elements - power is nonlinear!


Lecture 9 - 9/26

  • Joseph Haydn - Piano Concerto No. 11 in D major (I mean, it had to be on the board for some reason, right?
  • Thévenin and Norton Equivalents
  • Circuits with independent sources, dependent sources, and resistances can be reduced to a single source and resistance from the perspective of any two nodes
  • Equivalents are electrically indistinguishable from one another
  • Several ways to solve:
    • If there are neither independent nor dependent sources, find $$R_{eq}$$.
    • If there are only independent sources, turn independent sources off and find $$R_{eq}$$ between terminals of interest to get $$R_{T}$$. Then find $$v_{oc}=v_{T}$$ and recall that $$v_T=R_Ti_N$$
    • If there are both independent sources and dependent sources, solve for $$v_{oc}=v_T$$ first, then put a short circuit between the terminals and solve for $$i_{sc}=i_N$$. Recall that $$v_T=R_Ti_N$$
    • If there are only dependent sources, you have to activate the circuit with an external source and find the ratio of $$v_{TEST}$$ to $$i_{TEST}$$.

Lecture 10 - 9/30

  • Intro to capacitors and inductors
  • Basic physical models
  • Basic electrical models
  • Energy storage
  • Continuity requirements
  • DCSS equivalents

Lecture 11 - 10/3

  • First-order switched circuits with constant forcing functions
  • Sketching basic exponential decays


Lecture 12 - 10/7

  • Sinusoids and characteristics of sin waves
  • Complex numbers and representations (Cartesian, Polar, Euler) Complex Numbers
  • Basic mathematical operations with complex numbers

Lecture 13 - 10/14

  • Test Review

Lecture 14 - 10/17

  • Test 1

Lecture 15 - 10/21

  • ACSS and phasors
  • Solving ACSS using just trig gets complex very quickly - we will use complex analysis to simplify the process.
  • Represent signal $$x(t)=X\,\cos(\omega t+\phi_x)$$ as the real part of $$Xe^{j\phi_x}e^{j\omega t}$$.
  • For ACSS with a single frequency, all terms have $$e^{j\omega t}$$ part, so unique information can be stored in a complex number called a phasor that tracks magnitude and phase; $$\mathbb{X}=Xe^{j\phi_x}=X\angle \phi_x$$
  • A derivative of an ACSS variable in the time domain is equal to $$j\omega$$ times the phasor in the frequency domain.
  • A ratio of phasors is a transfer function
    • The magnitude of a transfer function represents the ratio of the output phasor magnitude to the input phasor magnitude
    • The phase of the transfer function represents the difference between the output phasor phase and the input phasor phase.
    • If $$\mathbb{H}(j\omega)=\frac{\mathbb{X}_{out}}{\mathbb{X}_{in}}$$, then:
      • $$X_{out}=X_{in}*|\mathbb{H}(j\omega)|$$
      • $$\phi_{out}=\phi_{in}+\angle \mathbb{H}(j\omega)$$

Lecture 16 - 10/24

  • Impedance and AC Circuit Response
  • Reminder: a phasor is a complex number whose magnitude represents the amplitude of a single frequency sinusoid and whose angle represents the phase of a single frequency sinusoid
  • Impedance: a ratio of phasors (though not a phasor itself)
    • $$\mathbb{Z}_R=R$$
    • $$\mathbb{Z}_L=j\omega L$$
    • $$\mathbb{Z}_R=\frac{1}{j\omega C}$$
    • $$\mathbb{Z}=R+jX$$ where $$\mathbb{Z}$$ is impedance, $$R$$ is resistance, and $$X$$ is reactance
    • $$\mathbb{Y}=\frac{1}{\mathbb{Z}}=G+jB$$ where $$\mathbb{Y}$$ is admittance, $$G$$ is conductance, and $$B$$ is susceptance
      • $$\frac{1}{\mathbb{Z}}=\frac{R-jX}{R^2+X^2}$$ so
        • $$G=\frac{R}{R^2+X^2}$$
        • $$B=\frac{-X}{R^2+X^2}$$
      • $$\frac{1}{\mathbb{Y}}=\frac{G-jB}{G^2+B^2}$$ so
        • $$R=\frac{G}{G^2+B^2}$$
        • $$X=\frac{-B}{G^2+B^2}$$
  • Impedances add in series and admittances add in parallel
  • Conservation laws (KCL, KVL), methods derived from conservation laws (NVM, MCM, BCM), and methods derived from Ohm's Law (voltage division, current division) apply in the phasor domain!

Lecture 17 - 10/28

  • Mechanical Systems

Lecture 18 - 10/31

  • Resonant circuits
    • In the ACSS, resonant circuits have inductors and capacitors that balance each other
    • Generally found by finding where the denominator of a transfer function is purely real or where the effective impedance is purely real.
  • Ideal and practical first-order filters
    • Practical filters characterized by maximum gain (largest magnitude of transfer function) and half power frequency ($$\omega$$ where the magnitude is $$\frac{1}{\sqrt{2}}\approx 0.7071$$ of the maximum value.)
    • For a series RC circuit,
      • Voltage across the capacitor relative to total represents a low-pass filter with $$\mathbb{H}=\frac{1}{j\omega RC+1}$$, maximum gain of 1, cutoff frequency of $$\frac{1}{RC}$$; phase at cutoff is -45$$^{\circ}$$
      • Voltage across the resistor relative to total represents a high-pass filter with $$\mathbb{H}=\frac{j\omega RC}{j\omega RC+1}$$, maximum gain of 1, cutoff frequency of $$\frac{1}{RC}$$; phase at cutoff is 45$$^{\circ}$$
  • Ideal filters are either wholly on or wholly off. Ideal filters have no phase shift.

Lecture 19 - 11/4

  • Second-order filters
  • Can be very dangerous near resonant frequency - ACSS voltage drop across inductor or capacitor can be larger than source!

Lecture 20

  • Fourier Series review

Lecture 21

  • Introduction to Operational Amplifiers
  • Large signal model
  • Comparators
  • Ideal operational amplifier assumptions
  • Assertions for circuits with ideal op amps and negative feedback
  • Buffer / Voltage follower circuit
  • Non-inverting amplifier
  • Inverting amplifier

Lecture 22

  • Summation amp
  • Difference amp
  • General solution techniques

Lecture 23

  • Test 2

Lecture 24

  • More op-amp examples

Lecture 25

  • Binary and conversion to/from decimal
  • Boolean algebra
  • NOT, AND, OR
  • DeMorgan's Theorem
  • Truth tables
  • Minterms and maxterms
  • Logic gates (NOT, AND, OR, NAND, NOR, XOR)
  • Complexity
  • Schematics

Lecture 26

  • Minterm and maxterm representation
  • Gray code
  • Karnaugh maps
  • Minimum sum of products
  • Minimum product of sums

Lecture 27

  • More MSOP and MPOS

Lecture 28

  • Review





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