ECE 110/Concept List/S25

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Lecture 1 - 1/8 - Course Introduction, Nomenclature

  • Circuit terms (Element, Circuit, Path, Branch and Essential Branch, Node and Essential Node, Loop and Mesh).
  • Accounting:
    • # of Elements * 2 = total number of voltages and currents that need to be found using brute force method
    • # of Essential Branches = number of possibly-different currents that can be measured
    • # of Meshes = number of independent currents in the circuit (or generally Elements - Nodes + 1 for planar and non-planar circuits)
    • # of Nodes - 1 = number of independent voltage drops in the circuit

Lecture 2 - 1/13 - Electrical Quantities

  • Electrical quantities (charge, current, voltage, power)
  • Passive Sign Convention and Active Sign Convention and relation to calculating power absorbed and/or power delivered.
  • Power conservation
  • Kirchhoff's Laws
    • Number of independent KCL equations = nodes-1
    • Number of independent KVL equations = meshes
  • Example of how to find $$i$$, $$v$$, and $$p_{\mathrm{abs}}$$ using conservation equations and how to check using extra conservation equations

Lecture 3 - 1/15 - Sources and Resistors

  • $$i$$-$$v$$ relationships of various elements (ideal independent voltage source, ideal independent current source, short circuit, open circuit, switch)
  • Resistor symbol (and spring symbol)
  • Resistance as $$R=\frac{\rho L}{A}$$
  • $$i$$-$$v$$ relationship for resistors; resistance [$$\Omega$$] and conductance $$G=1/R$$ $$[S]$$
  • $$i$$-$$v$$ for dependent (controlled) sources (VCVS, VCCS, CCVS, CCCS)

Lecture 4 - 1/22 - Equivalent Circuits

  • Combining voltage sources in series; ability to move series items and put together
  • Combining current sources in parallel; ability to move parallel items and put together
  • Equivalent resistances
    • series and parallel
    • Examples/Req
    • Delta-Wye equivalencies (mainly refer to book)

Lecture 5 - 1/27 - Division

  • Voltage Division and Re-division
  • Current Division and Re-Division

Lecture 6 - 1/29 - Node Voltage Method

  • Basics of NVM
  • NVM
    • Labels:
      • Really Lazy: label ground, then make every other node a new unknown. Voltage sources, voltage measurements, and current measurements will provide additional equations.
      • Lazy: label ground, then label any node connected to ground if it has a voltage source or voltage measurement. Make every other node a new unknown. Voltage sources not connected to ground, voltage measurements not connected to ground, and current measurements will provide additional equations.
      • Smart: label ground; once a node gets labeled, if there is a voltage source or a voltage measurement anchored at that node, use the source or measurement to label the other node it is attached to. Current measurements will provide additional equations.
      • Really Smart: same as smart, only also use voltage drops across resistors with current measurements to relate node voltages.
    • #KCL = #nodes - 1 - #v. sources
    • Write KCL at nodes not touching a voltage source; if there are voltage sources, look at nodes on either side or source to make a supernode

Lecture 7 - 2/3 - Current Methods

  • Examples on Canvas
  • BCM
    • Labels:
      • Label each (essential) branch current, using as few unknowns as possible by incorporating current source and current measurement labels
  • MCM
    • Labels:
      • Label each mesh current, understanding that current sources, current measurements, and voltage measurements will require additional equations.

Lecture 8 - 2/5 - Computational Methods

  • Using Maple to set up and solve simultaneous equations

Lecture 9 - 2/10 - Linearity and Superposition

  • Definition of a linear system
  • Examples of nonlinear systems and linear systems
    • 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
    • Use combinations of Phm's Law, Voltaeg Division, and Current Division, rather than setting up and solving multiple equations
    • If there are dependent sources, you must keep them activated and solve for measurements each time - this likely means that superposition may not actually make solving things easier.

Lecture 10 - 2/12 - Thévenin and Norton Equivalent Circuits

  • 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 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.
  • Side note: MCM by inspection

Lecture 11 - 2/17 - Operational Amplifiers

  • Model using two resistors and a VCVS
  • Without feedback, only really good as a comparator
  • Feedback from output to inverting input makes circuit more useful
  • Ideal op-amp assumptions are about the op-amp, not the circuit: $$A\rightarrow\infty$$, $$r_i\rightarrow\infty$$, $$r_o\rightarrow 0$$
  • Using ideal op-amp with a circuit with feedback from output to inverting input leads to a very useful circuit with implications of:
    • No voltage drop between the input terminals
    • No current entering the input terminals
    • Still possible to have current at the output terminal!

Lecture 12 - 2/19 - More Op-Amp Circuits

  • Various configurations that are directly or nearly-directly from the circuit developed in Lecture 11:
    • Inverting
    • Non-inverting
      • Buffer / Voltage follower as a specific instance
    • Inverting summation
      • Mixing board
    • Difference
  • Creating a circuit to produce a proscribed linear combination of input voltages
  • Analyzing op-amp circuits that are not directly based on circuit developed in Lecture 11

Lecture 13 - 2/24 - Test 1

Lecture 14 - 2/26 - Capacitors and Inductors

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

Lecture 15 - 3/3 - Initial Conditions and Finding Equations

  • DCSS equivalents
  • Finding values just before and just after circuit changes
    • For $$t=0^+$$, can model inductor as independent current source and capacitor as independent voltage source
  • First-order switched circuits with constant forcing functions
  • Sketching basic exponential decays

Lecture 16 - 3/5 - First-Order Circuits

  • Using methods (NVM, MCM, BCM) to get model equations
  • Setting up and solving with Maple

Lecture 17 - 3/17 - Sinusoids and Complex Numbers

  • Solving even a simple differential equation with a sinusoidal input is somewhat complicated
  • At the heart of complex analysis is an understanding of Complex Numbers