OpAmps

Norton Equivalence

• Short load resistor (set resistance to 0)
• Norton Current, $I_n$ is the current through the shorted load resistor

Thevenin Equivalence

• To find Thevenin resistance $R_{thev}$
  • Short voltage sources, open current sources
• To find Thevenin voltage
  • Open circuit voltage

Max Power for DC
$$P_{max}=\frac{V_{thev}^2}{4\ast R_{thev}}$$

Max Average Power for AC
$$\overline{P_{max}}=\frac{1}{2}\frac{|V_{thev}{|}^2}{4\ast \mathrm{Re}\left\{Z_{thev}\right\}}$$

AC Phasors

$j=\sqrt{-1}$ is used instead of $i$ since $i$ is used for current in electrical engineering
$$Z_R=R$$
$$Z_C=-\frac{j}{(\omega C)}=\frac{1}{j\omega C}$$
$$Z_L=j\omega L$$