EGR 224/Concept List/S23

The notes below are not meant to be comprehensive but rather to capture the general topics of covered during lectures in EGR 224 for Spring 2023. These notes are in no way a replacement for actively attending class.

Lecture 1 - 1/11 - Course Introduction, Nomenclature

• Main web page at http://classes.pratt.duke.edu/EGR224S23/
• 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 and Active Sign Convention

Lecture 3 - 1/20 - Voltage and Current; Power and Energy

• Power redux
• Passive Sign Convention and Active Sign Convention and relation to calculating power absorbed and/or power delivered.
• Kirchhoff's Laws
• Example of how to find $$i$$, $$v$$, and $$p_{\mathrm{abs}}$$ using conservation equations
• $$i$$-$$v$$ relationships of various elements (ideal independent voltage source, ideal independent current source, short circuit, open circuit, switch)

Lecture 4 - 1/23 - Equivalents

• $$i$$-$$v$$ relationship for resistors; resistance and conductance
• $$i$$-$$v$$ for dependent (controlled) sources (VCVS, VCCS, CCVS, CCCS)
• Combining voltage sources in series; ability to move series items
• Combining current sources in parallel; ability to move parallel items
• Equivalent resistances
  • series and parallel
  • Examples/Req

Lecture 5 - 1/27 - Voltage Division and Current Division

• Delta-Wye equivalencies (mainly refer to book)
• Voltage Division
• Current Division

Lecture 6 - 1/30 - Node Voltage Method

• NVM
  • Examples in Resources / HW Support / HW 03 folder on Sakai

Lecture 7 - 2/3 - Mesh and Branch Current Method

• BCM and MCM
  • Examples in Resources / HW Support / HW 03 folder on Sakai

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
  • If there are dependent sources, you must keep them activated and solve for measurements each time

Lecture 9 - 2/10 - 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.