ECE 110/Concept List/S24

Lecture 1 - 1/11 - 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
• Electrical quantities (charge, current, voltage, power)

Lecture 2 - 1/16 - Electrical Quantities

• 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
• $$i$$-$$v$$ relationships of various elements (ideal independent voltage source, ideal independent current source, short circuit, open circuit, switch)
• Resistor symbol (and spring symbol)

Lecture 3 - 1/18 - Equivalents

• 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)
• 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

Lecture 4 - 1/23 - Brute Force Method; Delta-Wye; Voltage Division Part 1

• Brute Force method
• Delta-Wye equivalencies (mainly refer to book)
• Voltage Division

Lecture 5 - 1/25 - Voltage Division Part 2, Current Division, and Node Voltage Division Part 1

• Voltage Re-Division
• Current Division and Re-Division
• Basics of NVM

Lecture 6 - 1/30 - Node Voltage Method

• Examples on Canvas
• NVM
  • Labels:
    • Very 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.

Lecture 7 - 2/1 - 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 - 2/6 - 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 9 - 2/8 - 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.

Lecture 10 - 2/13 - 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 11 - 2/15 - 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
• Using Node Voltage Method to get model equations

Lecture 12 - 2/20 - Test 1

Test

Lecture 13 - 2/22 - First-Order Circuits (constant forcing functions)

• First-order switched circuits with constant forcing functions
• Sketching basic exponential decays
• Using the Node Voltage Method to get model equation

Lecture 14 - 2/27 - ACSS and Phasors

• Overview of Calculator Tips
• At the heart of complex analysis is an understanding of Complex Numbers
• 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
• 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

Lecture 15 - 2/29 - More ACSS and Phasors

• 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
• 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 16 - 3/5 - More Phasors; Filters

• 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 somin - this will allow us to use frequency techniques to back out differential equations
• An $$RC$$ 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"