Difference between revisions of "ECE 110/Concept List/S24"

Revision as of 19:42, 7 February 2024

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)

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)

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

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.

Definition of a linear system
Examples of nonlinear systems and linear systems
- Nonlinear system examples (additive constants, powers other than 1, trig):

$$\begin{align*} y(t)&=x(t)+1\\ y(t)&=(x(t))^n, n\neq 1\\ y(t)&=\cos(x(t)) \end{align*} $$

$$\begin{align*} y(t)&=ax(t)\\ y(t)&=\frac{d^nx(t)}{dt^n}\\ y(t)&=\int x(\tau)~d\tau \end{align*} $$

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.

@@ Line 56: / Line 56: @@
 ** 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.