ECE 110/Concept List/S25

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 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
• Overview of Calculator Tips

Lecture 18 - 3/19 - ACSS and Phasors

• Solving ACSS using just trig gets complex very quickly - we will use complex analysis to simplify the process - this is a motivation for phasors
• 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)
  • $$\mathbb{Z}=R+jX$$ where $$R$$ is resistance and $$X$$ is reactance
  • Admittance $$\mathbb{Y}=\frac{1}{\mathbb{Z}}=G+jB$$ where $$G$$ is conductance and $$B$$ is susceptance
  • For common elements:
    • $$\mathbb{Z}_R=R$$
    • $$\mathbb{Z}_L=j\omega L$$
    • $$\mathbb{Z}_R=\frac{1}{j\omega C}$$
  • Impedances add in series and admittances add in parallel

Lecture 19 - 3/24 - More ACSS and Phasors

• To use phasors to solve ACSS,
  • Replace functions of t with their phasor representation
  • Replace $$\frac{d}{dt}$$ with $$j\omega$$
  • Solve for the output phasor as a function of the input phasor
• Find transfer function $$\mathbb{H}(i\omega)$$ as a ratio of an output phasor and an input phasor
  • Use transfer function to note that $$\mathbb{V}_{out}=\mathbb{H}(j\omega)\,\mathbb{V}_{in}$$ (input, output, or both could also be currents)
  • If given numerical values, can use those to get actual magnitudes and phases for output and convert to time

Lecture 20 - 3/26 - More Phasors

• Once in the phasor domain, use KVL, KCL, NVM, MCM, BCM, and whatever else from resistive circuits to get relationships between input phasors and output phasors
• Note that $$\frac{d}{dt}$$ in the time domain is the same as multiplying a phasor by $$j\omega$$ in the frequency domain - this will allow us to use frequency techniques to back out differential equations

Lecture 21 - 3/31 - Filters

• An $$RC$$ circuit can be both a high-pass filter (resistor voltage) or a low-pass filter (capacitor voltage)
• The "cut-off frequency" of a filter is the frequency at which the magnitude of the transfer function is $$\frac{1}{\sqrt{2}}\mathbb{H}_{max}$$ - this is also known as the "half-power frequency"

Lecture 23 - 4/7 - Digital Logic 1

• Introduction to binary
• Introduction to boolean operators
• Basic operations: not, and, or, xor
• Truth tables
• DeMorgan's Laws

Lecture 24 - 4/9 - Digital Logic 2

• Minterms and maxterms
• Digital logic gates and schematics
• Complexity
• Boolean algebra relationships and simplifications
• Manual logic function minimization
• Gray code motivation and construction
• Karnaugh maps
  • Structure
  • Use in finding minimum sum of products (MSOP) form
  • Use in finding minimum product of sums (MPOS) form

Lecture 25 - 4/14 - Digital Logic 3

• Example going from maxterm representation to minterm representation to Karnaugh map to MSOP to MPOS to schematic
• "Don't Care" conditions