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
$$ P_{max} = \frac{V_{thev}^2}{4 * R_{thev}}$$

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

AC Phasors

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